handbook of conveying and handling of particulate solids

One reason is probably that the test specimen is fully confined during the consolidation step, and it may not reach the state of steady state flow in which the bulk density and shear str

The Conveying and Handling of Particulate Solids play major roles in many industries, including chemical, pharmaceutical, food, mining, and coal power plants

As an example, about 70% of DuPont's products are in the form of a powder, or involve powders during the manufacturing process However, newly designed plants

or production lines produce only about 40+40% of the planned production rate This points up clearly the lack of appropriate scientific knowledge and engineering design skills Following one's becoming aware of the problem, it should be attacked on three

f r o n t s - research, education and training

Many new products cannot be manufactured or marketed because of serious difficulties concerning conveying and handling That is because in most cases the mutual effect between handling- and conveying units is neglected during the design of

a new production line Unlike other states of materials, it is not sufficient just to know the state of a bulk material in order to determine its properties and behaviour The

"history" of a bulk material can dramatically affect its properties and behaviour We should also keep in mind the fact that an optimal manufacturing line is not necessarily made by combining individually optimized devices Therefore, "concurrent engineering" should be practised in the chemical and related industries

In order to address both of the problems presented above, an "international conference" was initiated six years ago, that relates to most processes, units, equipment and models involving the conveying and handling of particulate solids In the conference, researchers, engineers and industrialists working on bulk solids systems have the opportunity for open dialogue to exchange ideas and discuss new developments The present Handbook summarizes the main developments presented

at the last Conference, that took place at the Dead-Sea, Israel in 2000 This Handbook therefore contains research results from all round the world, and the best scientists present the state-of-the-art on a variety of topics, through invited review papers Some review papers presented at the previous Conference were added All the papers presented in this Handbook have been reviewed

The aim of the handbook is to present a comprehensive coverage of the technology for conveying and handling particulate solids, in a format that will be useful to engineers, researchers and students from various disciplines The book follows a pattern which we have found useful for tackling any problem found while handling or

fundamentals and applications Usually, each chapter, or a topic within a chapter, starts with one of the review papers Chapter 1 covers the characterization of the particulate materials Chapter 2 covers the behaviour of particulate materials during storage, and presents recent developments in storage- and feeders design and performance Chapter 3 presents fundamental studies of particulate flow, while Chapters 4 and 5 present transport solutions, and the pitfalls of pneumatic, slurry, and capsule conveying Chapters 6, 7 and 8 cover both the fundamentals and development

of processes for particulate solids, starting from fluidisation and drying, segregation and mixing, and size-reduction and -enlargement Chapter 9 presents environmental aspects and the classification of the particulate materials after they have been handled

by one of the above-mentioned processes Finally, Chapter 10 covers applications and developments of measurement techniques that are the heart of the analysis of any conveying or handling system

We hope that users will find the handbook both useful and stimulating, and will use the results of the work presented here for further development and investigations

The Editors

A Levy and H Kalman (Editors)

9 2001 Elsevier Science B.V All rights reserved

Solids flowability measurement and interpretation in industry

1 I N T R O D U C T I O N

The science of soil mechanics was integrated with the related field of powder mechanics and reduced to industrial practice by Jenike [1] in 1964 Since then, it has been possible for industry to reliably measure the flowability of powders and relate the measurements, in engineering units, to the design requirements for silo flow However, Jenike's publication was neither the first effort to quantify flowability nor the last New testing methods continue to be introduced, with varying degrees of success In many cases these alternative measurement methods are the result of an industrial necessity and reflect some shortcoming of the Jenike method In other cases, they exist because the Jenike method is not known to the people involved or is not relevant to their problem Business value can be derived from many different types of measurements

2 DESCRIBING F L O W A B I L I T Y

2.1 Applications

A surprising amount of time can be spent debating the meaning of flowability, and what does it really mean if one powder has better flowability than others From a practical standpoint, the definition of acceptable flowability is in the eyes of the beholder A person accustomed to handling pigments would be delighted if his materials had the handling properties of cement, while a cement user would wish for the properties of dry sand Industries that deal with powders in very small quantities can employ handling techniques of brute force or human intervention that are not practical in larger scale installations In many cases, the chemists developing a new process or powder are completely unaware of the difficulties in handling powders on an industrial scale, and in some cases the problems are completely different between the laboratory and the plant Finally, there are some materials, such as extremely free flowing granules that may require unconventional descriptive techniques

2.2 Clarity and simplicity

Most producers and users of bulk materials do not have the time or interest to study solids flow and powder mechanics Many are completely unfamiliar with the field since it is rarely

users Failure of the specialist to identify and address the key business issues in a way that is understandable to the intended recipients will severely limit the breadth of application of this technology

Silo design studies should show the engineering design outcome first, and the underlying technical data second Very few people are interested in yield loci from shear tests, and even the resulting flow functions often require interpretation in the context of the silo problem Flowability measurements for quality control and product development must often be reduced

to one or two numbers as discussed later in this paper Even with modem statistical techniques, it is extremely difficult to compare a series of graphs describing the properties of various bulk material samples The question then becomes which one or two numbers from large data sets to use It could be argued that the difference between a skilled technician and skilled consultant is the ability of the latter to correctly select which data to work with for a specific quality control or product development purpose While there is not a simple answer

to this question, any approach must start with a consideration of the compaction pressures that the bulk material is exposed to For free-flowing materials in small bins, the pressures might

be nearly zero For larger silos, cohesive materials, or those with high wall friction (see section 3.6, below), calculation of appropriate pressures will be required

When data is presented in the form of a few numbers, there is inevitably a risk that those requesting the data will attempt to use it for purposes for which it was not intended For example, a measure of the ratholing tendency of a material in silos may not accurately reflect the uniformity of its delivery in packaging machines Providing the users with mountains of data is not a solution, since the same person that will use a simple number inappropriately will probably also extract the wrong information from a comprehensive collection of data points This situation can best be managed by maintaining a dialog with the users on their needs and the application of the results

3 GENERAL FORMS OF FLOWABILITY MEASUREMENT

3.1 Free flowing materials - timed funnels

It can be difficult or impossible to measure cohesive strength for highly free flowing granules For such materials, the rate of flow is often more important than whether they will flow at all In these cases, the time necessary for a pre-determined volume or mass to flow through a funnel can be the most useful flowability measure This method is widely used in the fabrication of metal parts from metal powder [2, 3] The factors influencing the flow time measurements are numerous and include the particle size distribution, the friction between the particles and against the wall, the particle density, and gas permeability Many specialists in powder mechanics object to the use of such measurements because of the unknown interactions amongst the factors and the absence of any consideration of solids pressure due to the self-weight of bulk material However, in our experience this measurement can be extremely reproducible and an excellent indicator of the flow behavior in situations that resemble the test, i.e., rapid flow from small bins

3.2 Angle of repose measurements

The angle of repose formed by a heap of a bulk material is the best-known method of describing flowability Unfortunately, it is quite possibly the worst measure to use Angles of

material falls to form the heap There can be pronounced differences in angles of repose for materials that have similar real-life handling properties Cohesive materials may form multiple angles of repose in a single test, and reproducibility may be poor The measured angle cannot be directly related to any silo design parameter except the shape of the top of a stockpile heap

3.3 Hausner ratio of tapped to loose bulk density

The ratio of the tapped to the loose bulk density has been shown to relate in many cases to the gain in cohesive strength that follows the compaction of a powder or granular material Materials with relatively little gain in bulk density (Hausner ratios below about 1.25) are considered to be non-cohesive, while increasing values (ratios up to about 2.0) indicate increasing levels of cohesiveness However, we have observed that the correlation between the ratio and more sophisticated measurements is rather poor, and it is unlikely to provide precise differentiation between generally similar materials In addition, the test is actually measuring a form of compressibility, which does not always relate to cohesive strength

A serious limitation of the Hausner ratio is the elimination of any consideration of bulk density in the final calculation As discussed below, two materials with similar Hausner ratios but different densities are likely to behave much differently in practice Finally, it has been shown that tapped bulk density measurements are extremely sensitive to the apparatus being used and the number of taps Standardization of these factors is necessary to ensure consistent and comparable results

3.4 Properties based on shear testing

In many cases, the most important bulk handling behavior is whether or not the bulk material will flow reliably by gravity throughout a process This behavior relates to the material's arching (doming) and ratholing (piping) propensity, as described by the silo outlet necessary for reliable flow Jenike [ 1 ] provides a method of calculating these values that is of the general form:

A r c h i n g / r a t h o l e diameter = (factor H or G) x f c

In this equation, fc is the unconfined yield strength (also known as Cyc), a measure of cohesive strength in response to compaction pressure The bulk density is measured at the same compaction pressure as is associated with the fc measurement The appropriate value of compaction pressure depends on the situation As a first approximation, the factors H (for arching) or G (for ratholing) can be considered to be constants, so the flowability can be simply described as cohesive strength divided by bulk density Put in other words, flowability

is the ratio of the cohesive forces holding the particles together vs the gravity forces trying to pull them apart

Since fc and bulk density can both vary with compaction pressure, it is important to make the calculation of Eq (1) at the appropriate pressure This relates largely to the type of flow pattern in the silo (mass flow or funnel flow) which in turn depends on the friction of the solids against the walls of the silo Consequently, a wall friction measurement is usually necessary to help fix the range of pressures Since wall friction can also vary with pressure,

3.5 Flow functions

Flowability is often described on the basis of the flow function (Figure 1) [1 ] derived from shear testing The flow function is a graph relating a major principal stress (or1) to the unconfined yield strength (fc) that it produces in a powder specimen This graph basically describes cohesive strength as a function of compaction pressure Figure 1 shows possible flow functions for three different materials It is easy to comprehend and relate to one's own experience with moist sand or snow, etc Jenike [1] and others have often used the slope of the flow function as a flowability descriptor This can obtained by simply dividing the unconfined yield strength at a particular point by the corresponding value of major principal stress This method, while convenient, has several serious drawbacks

First, a comparison of flow function slopes for different bulk material samples based on single points presumes that the flow function graphs are linear, and that they pass through the origin Neither assumption is necessarily true (see Figure 1) Second, most shear testing methods (except Johanson's) used in industry do not directly apply a pressure of crl to the sample A different consolidation pressure is used and the final value of crl is later calculated

as part of the interpretation of the yield locus generated in the test series This means that the person conducting the test cannot pre-select which value of (3" 1 he will test at Two different samples, tested at the same consolidation pressure, may produce different values of cry, and hence relate to different points along the flow function Exact comparison of multiple samples will require that at least two flow function points for each sample be obtained so that the comparative values of fc at a particular value of ~1 can be determined by interpolation The third drawback of comparisons based on flow functions alone is the fact that such measurements completely disregard bulk density Examination of Eq 1 shows that the bulk density has equal importance to fc We have observed cases where the bulk density of a common material, such as hydrated lime, can vary by up to 50% between suppliers, while the cohesive strength (fc) varied by 30% Similarly, in one of our businesses, two products had

f

~1, Major Principal Stress

Fig 1 Typical flow functions

varied accordingly, and the business people (who had only compared the flow functions) did not understand why

3.6 Wall friction measurements

Wall friction measurements are most commonly made with a Jenike shear cell The force necessary to push (shear) a sample of bulk material, trapped in a ring, across a wall sample coupon is measured as a function of the force applied to the top of the sample (Figure 2) The resulting data is in the form of a graph of shear force versus normal force, known as a wall yield locus (WYL) For any given point on the graph, the ratio of shear force to normal force

is the coefficient of friction The arctangent of the same ratio is the wall friction angle For some materials the WYL is a straight line that passes through the origin This is the simplest case, and wall friction can be described by a single number In other cases the WYL has a curvature that causes the wall friction angle to vary inversely with normal force

The wall friction angle is the primary factor used in determining if a particular silo will empty in mass flow or funnel flow Larger values of the wall friction angle correspond to steeper angles required for the converging hopper at the base of the silo in order to achieve mass flow The procedure is described by Jenike [1] If the wall friction angle exceeds a certain value, mass flow will not occur The WYL must be closely examined for the design of new silos or the detailed evaluation of the behavior of a bulk material in existing silos If the wall friction angle exceeds the mass flow limit for a silo installation, the flow pattern in the silo will be funnel flow and consequently ratholing must be considered This means that flow function data in the appropriate silo pressure range is necessary to determine if ratholing can occur This can be a different set of testing conditions than that required if only a no-arching determination is required for a mass flow silo For quality control or product development purposes where silo design is not an issue, it is often sufficient to describe the WYL by fitting

a straight line, passing through the origin, to the data set While this method can produce errors (especially at low values of normal force) it is adequate as a descriptive tool and greatly simplifies comparisons

Fig 2 Wall friction measurement with Jenike Shear Cell (illustration adapted from Ref 3)

4.1 The Jenike Shear Tester

The Jenike shear tester (Figure 3) was developed as part of the research activities described

by Jenike [1 ] It is derived from the shear testers used in soil mechanics, which are typically square in cross section instead of the circular design used in the Jenike tester Soil mechanics tests are usually conducted at compaction (normal) stress levels that greatly exceed those of imerest in powder mechanics for silo design and gravity flow At these high normal stress levels, it is relatively easy to obtain steady state flow in which the bulk density and shear stress remain constant during shear This steady state condition is a vital prerequisite for valid test results It can also be reached at lower stress levels, but a relatively long shear stroke is required With translational shear testers (i.e., those that slide one ring or square across another) the cross sectional area of the shear zone varies unavoidably during the shear stroke The validity of the test becomes questionable if the stroke is too long

For this reason Jenike devised the round test cell, which permits preparation of the sample

by twisting A pre-consolidation normal load is applied to the cover, and the cover is twisted back and forth a number of times This preparation makes the stress distribution throughout the cell more uniform and reduces the shear stroke necessary to obtain steady state flow After the pre-shear process is completed, a specified pre-shear normal load is applied to the cover and shear movement is started Once steady state flow (constant shear force) is achieved, the initial normal load is removed and a smaller normal load (known as the shear normal load) is applied Shear travel resumes and the peak shear force corresponding to the shear normal load is noted

The preparation process requires skill and is not always successful on the first attempt Different values of the pre-consolidation load or the number of twists may be required to reach steady state flow Even with proper preparation, it is only possible to obtain one shear point from a prepared shear cell Since several shear points are typically employed to construct a yield locus, and several yield loci are necessary to construct a flow function, the cell preparation procedure must be repeated numerous times It is not uncommon to repeat the cell preparation process 9 to 25 times per flow function We typically allow 6 man-hours for 9 shear tests, so the time investment in this method can be significant

Fig 3 Jenike Shear Tester (illustration adapted from Ref 3)

granular materials, it can be nearly impossible to obtain steady state flow with elastic materials and particles with large aspect ratios, such as flakes and fibers In these cases, the allowable stroke of the shear cell may be exceeded before a steady state condition is achieved Despite these difficulties, the Jenike cell has remained the best-known and definitive shear testing method for bulk solids There are several likely reasons for this First, the method was developed first! Second, the method has been validated in industrial use and comparison

to more sophisticated testers Third, the apparatus is relatively simple and not patented, ideal for university research and users with limited budgets

4.2 Peschl Rotational Split Level Tester

Most of the difficulties with the Jenike tester are the result of its limited shear stroke Testers that rotate to shear the sample (such as the Peschl) versus the Jenike cell's translational motion can have a distinct advantage Shear travel can essentially be unlimited,

as long as there is no degradation of the particles in the shear zone This unlimited stroke makes the elaborate Jenike cell preparation process unnecessary, and also makes it possible to obtain multiple data points from a single specimen Thus an entire yield locus can be constructed from a single filling of the test cell While it is also possible to make repetitive measurements from a Jenike cell sample, the cell has to be prepared each time A second advantage of the rotational cell is that the placement location for the normal force does not move (translate) during the test Loads are placed on the centerline of rotation This makes it much easier to automatically place and remove loads from the test cell, and can lead to complete automation of the tester

Fig 4 Peschl Rotational Split Level Tester

The Peschl tester (Figure 4) rotates the bottom half of a cylindrical specimen against the top half, which is stationary The torque necessary to prevent the rotation of the top half is measured, and is converted to the shear stress acting across the shear zone The interior of the top and bottom of the cell are roughened to prevent the powder from shearing along the top or bottom ends rather than at the shear plane It should be noted that the amount of shear travel varies across the radius of the cell A particle precisely in the center of the cell sees no shear travel distance - only rotation about the center line of the tester Particles at the outside edge

of the cell have the greatest amount of shear travel, with decreasing travel distances as the radius is reduced Some researchers have voiced concern about this aspect of the tester, since the meaning of the individual shear points is somewhat confused Shear stress values become averages produced by shearing different regions of the cell different distances Although detailed studies have not been conducted, there is some evidence [4] that the Peschl tester produces slightly lower values of unconfined yield strength than the Jenike tester at comparable values of major principal stress

The Peschl tester was the first (and for a long time, the only) automated shear cell available The volume of the standard cell is relatively small, making it convenient for expensive bulk materials such as pharmaceuticals and agricultural chemicals It is widely used for quality control and product development Testing times are about 1/3 of that required with the Jenike cell

4.3 Sehulze Ring Shear Tester

The issue of non-uniform shear travel in rotational testers can be minimized if the test cell has an annular ring shape instead of a cylindrical one such as in the Peschl tester While the inner radius of the ring still has a shorter shear travel than the outer one, the difference is relatively small, particularly if the difference between the two radii is small compared to their average This concept was developed a number of years ago by Carr and Walker [5] In our experience, the early models of the device, while very robust from a mechanical standpoint, were too massive for delicate measurements It also was difficult to clean the cell, particularly the lower ring This form of ring shear tester never achieved widespread use when compared to the Jenike cell

Fig 5 Schulze Ring Shear Tester

A similar concept with a number of engineering improvements has recently been developed by Schulze (Figure 5) The mechanism is much more sensitive than that employed

by earlier ring shear testers, and the cell can be removed for cleaning and also for time consolidation testing It is commercially available Excellent correlation has been observed between the Schulze tester and the Jenike shear cell, as well as with more sophisticated research instruments An automated version is available for situations where high productivity is required As with the Peschl tester, testing times are about 1/3 of that required for comparable Jenike tests

4.4 Johanson Hang-Up Indicizer

All of the shear testers previously discussed are biaxial, which means there are forces applied or measured in two different planes (horizontal and vertical) The design of a testing machine can be simplified if all of the measurements and motions can be made in one plane, i.e in a uniaxial tester

Biaxial testers measure shear stresses related to normal stresses However, the flow- function graph and its interpretation for silo design requires the calculation of principal stresses (fc and (3"1) from the normal and shear stress data by the use of yield loci and Mohr's circles (a mathematical tool) In concept, a perfect uniaxial tester can directly apply and measure principal stresses, making the construction of yield loci and use of Mohr circles unnecessary This would expedite the completion of flow functions and reduce testing time The concept of a uniaxial tester is to compress the sample in some sort of confined fixture, then remove a portion (or all) of the fixture and measure the strength of the resulting compacted powder specimen There have been a number of efforts through the years to achieve this objective [6] While the description is simple, the execution is not The confining fixture impedes the uniform compression of the sample due to wall friction, making the state of stress in the sample inconsistent and sometimes unknown Removal of the confining fixture without damaging the compacted specimen can be difficult Painstaking work or very sophisticated apparatus is necessary to generate results comparable to Jenike tests either in accuracy or reproducibility The best attempt so far is a tester developed by Postec Research in Norway [7] However, this tester is not yet commercialized

An alternative approach is the Johanson Hang-Up Indicizer (Figure 6), a form of uniaxial tester in which a coaxial upper piston assembly is used to compress the sample, with the compressive force only being measured on the inner piston The concept is that wall friction effects are taken up by the outer piston and can be ignored The central portion of the bottom

of the fixture is then removed, and a tapered plug of the bulk solid is pushed out by the upper inner piston Several assumptions are employed to convert the force necessary to push out the plug to an estimate of unconfined yield strength Since the mass and volume of the sample during the test is known, the tester can also calculate the bulk density during the consolidation stage By combining the bulk density and unconfined yield strength data together with some further assumptions in a form of Eq 1, it is possible to make an estimate of the arching and ratholing dimensions for material tested

The Hang-Up Indicizer was found to be highly reproducible in our tests [4], but the reported values of unconfined yield strength tend to lie below those obtained with biaxial testers One reason is probably that the test specimen is fully confined during the consolidation step, and it may not reach the state of steady state flow in which the bulk density and shear stress remain constant as with the biaxial testers Despite the deviation

Fig 6 Johanson Hang-Up Indicizer| cell (dimensions in mm)

from Jenike-type results, we have found it to be a fast and convenient tool for quality control and product development purposes One notable feature of the Indicizer is its ability to "hunt" for an appropriate value of consolidation stress in response to the bulk material's changing bulk density during consolidation This makes it possible to make relevant comparisons of ratholing propensities between samples, based on single tests The concept is discussed further in [4]

5 C O M M O N DIFFICULTIES

In my experience, certain types of difficulties occur frequently in industrial measurement

of flowability Most of the problems involve obtaining samples representative of the process

in question Non-representative bulk material samples can be generated by segregation within the process or by differences between pilot plant and full-scale plant processes Lost identity

or unknown post-sampling environmental exposure history is a frequent problem, even for samples that were properly taken initially Some materials may experience irreversible chemical changes that make it impossible to duplicate process behaviors in the laboratory A detailed discussion with a chemist is always prudent before embarking on a test program The influence of varying moisture content or temperature will probably be non-linear, and threshold values may exist

Obtaining representative samples of the wall surface of process equipment (silos, hoppers, etc.) is a surprisingly difficult problem Testing conducted prior to the detailed design of silos utilizes test coupons selected from the test lab's existing library The surface

of these library samples may differ slightly from the eventual fabrication material, even if the specifications are identical After plant commissioning, the surface of process equipment that

is in service may develop coatings of corrosion, product, or by-products that are impossible to precisely reproduce in the laboratory

6 CONCLUSIONS

Many users of flowability data, especially for quality control purposes, do not have the skills, patience, or need to interpret the graphical results of shear cell testing These graphs show unconfined yield strength, bulk density, wall friction, and internal friction angles as functions of major principal stress While this data is vital for a silo designer, most quality control users would prefer a single number that would tell them in quantitative units how one sample compares to another or to a reference value

Shear testing results can be simplified, and reporting results in the form of Eq (1) has merits Since both the unconfined yield strength and the bulk density are influenced by compaction pressure, it is important to select a compaction pressure that is relevant to the situation at hand More precise comparisons between samples may require a trial and error approach in shear testing to ensure that the test results are reported at consistent major principal stress values

Even the most unusual and difficult flowability situations can be quantified in most cases There is almost always a way to make a meaningful measurement of the relevant properties, but some experimentation and judgement may be required Prudent risk taking is required whenever one deviates from the established Jenike test methods

REFERENCES

1 Jenike A.W., Storage and Flow of Solids, Bulletin 123 of the Utah Engg Experiment Station, Univ of Utah, Salt Lake City, UT, 1964 (revised 1980)

2 ASTM standard B212, Amer Society for Testing and Materials, West Conshohocken, PA

3 ASM Handbook, Vol 7, Powder Metal Technologies and Applications, ASM International, Materials Park, OH, pp 287-301, 1998

4 Bell, T.A., B.J Ennis, R.J Grygo, W.J.F Scholten, M.M Schenkel, Practical Evaluation

of the Johanson Hang-Up Indicizer, Bulk Solids Handling, Vol 14, No 1, pp 117-125,

7 Maltby, G.G Enstad, Uniaxial Tester for Quality Control and Flow Property Characterization of Powders, Bulk Solids Handling, Vol 13, No 1, pp 135-139, 1993

9 2001 Elsevier Science B.V All rights reserved 15

Flow properties of bulk solids -which properties for which application

J Schwedes

Institute of Mechanical Process Engineering, Technical University Braunschweig

Volkmaroder Str 4/5, 38104 Braunschweig, Germany

To design reliable devices for the handling of bulk solids and to characterize bulk solids the flow properties of these bulk solids have to be known For their measurement a great number of shear and other testers are available The paper gives a review of existing testers and demonstrates which tester should and can be used for which application

1 INTRODUCTION

Many ideas, methods and testers exist to measure the flowability of bulk solids People running those tests seldom are interested in exclusively characterizing the flow properties of the bulk solid in question only More often they want to use the measured data to design equipment, where bulk solids are stored, transported or otherwise handled, to decide which one out of a number of bulk solids has the best or the worst flowability, to fulfill the requirement of quality control, to model processes with the finite element method or to judge any other process in which the strength or flowability of bulk solids plays an important role Many testers are available which measure some value of flowability, only some of these shall

be mentioned here without claiming completeness: Jenike shear cell, annular shear cells, triaxial tester, true biaxial shear tester, Johanson Indicizers, torsional cell, uniaxial tester, Oedometer, Lambdameter, Jenike & Johanson Quality Control Tester, Hosokawa tester and others It is beyond the scope of this paper to describe all testers in detail and to compare them one by one Instead it will be tried first to define flow properties Secondly applications are mentioned Here the properties, which are needed for design, are described and the testers being able to measure these properties are mentioned Finally a comparison with regard to application will be tried

2 F L O W FUNCTION

The Flow Function was first introduced by Jenike and first measured with help of the Jenike shear cell [1] Therefore a short explanation of the Flow Function and the relevant procedure shall be given here The main part of the Jenike shear tester is the shear cell (Fig 1) It consists of a base A, a ring B resting on top of the base and a lid C Base and ring are filled with a sample of the bulk solid A vertical force is applied to the lid A horizontal shearing force is applied on a bracket attached to the lid Running shear tests with identically preconsolidated samples under different normal load gives maximum shearing forces S for every normal force N

Division of N and S by the cross-sectional area of the shear cell leads to the normal stress and the shear stress ~ Fig 2 shows a u,~-diagram The curve represents the maximum shear stress x the sample can support under a certain normal stress c~; it is called the yield locus Parameter of a yield locus is the bulk density 10b With higher preconsolidation loads the bulk density lob increases and the yield loci move upwards Each yield locus terminates at point E in direction of increasing normal stresses o Point E characterizes the steady state flow, which is the flow with no change in stresses and bulk density Two Mohr stress circles are shown The major principal stresses of the two Mohr stress circles are characteristic of a yield locus, c~ is the major principal stress at steady state flow, called major consolidation stress, and oc is the unconfined yield strength of the sample Each yield locus gives one pair of values of the unconfined yield strength uc and the major consolidation stress ul Plotting uc versus ol leads

to the Flow Function (see later, Fig 5) The angle q~e between G-axis and the tangent to the greatest Mohr circle - called effective yield locus - is a measure for the inner friction at steady state flow and is very important in the design of silos for flow

Very often a theoretical experiment is used to show the relationship between ~ and cy~ (Fig 3) A sample is filled into a cylinder with frictionless walls and is consolidated under a normal stress ~l leading to a bulk density lOb After removing the cylinder, the sample is loaded with

an increasing normal stress up to the point of failure The stress at failure is the unconfined yield strength ~ Contrary to results of shear tests steady state flow cannot be reached during consolidation, i.e the Mohr circle will be smaller As a result density lob and unconfined yield strength c~r will also be smaller compared to the yield locus gained with shear tests [2]

A tester in which both methods of consolidation - either steady state flow (Fig 1 and 2) or uniaxial compression (Fig 3) - can be realized, is the true biaxial shear tester [2,3,4,5] (Fig 4) The sample is constrained in lateral x - and y-direction by four steel plates Vertical deformations of the sample are restricted by rigid top and bottom plates The sample can be loaded by the four lateral plates, which are linked by guides so that the horizontal cross- section of the sample may take different rectangular shapes In deforming the sample, the stresses G• and Gy can be applied independently of each other in x- and y-direction To avoid friction between the plates and the sample the plates are covered with a thin rubber membrane Silicone grease is applied between the steel-plates and the rubber membrane Since there are no shear stresses on the boundary surfaces of the sample G• and % are principal stresses With the true biaxial shear tester the measurement of both stresses and strains is possible

Fig 1 Jenike shear tester Fig 2 Yield locus and effective yield locus

Fig 3 Unconfined yield strength Fig 4 True Biaxial Shear Tester With the true biaxial shear tester experiments were carried out to investigate the influence

of the stress history and the influence of different consolidation procedures on the unconfined yield strength [2,3,4] Only results of the second point shall be mentioned here For getting a yield locus corresponding to Fig 2 the minor principal stress o2 in y-direction (Fig 4) is kept constant during a test The major principal stress oi in x-direction is increased continuously

up to the point of steady state flow with constant values of Ol, o2 and 9b Afterwards, the state

of stress is reduced, with smaller constant o2-values and smaller maximum ol-values By setting o2 - 0 the unconfined yield strength Oc can be measured directly Additionally, comparative measurements with Jenike's tester were performed Although two different kinds

of shear testers (Jenike and biaxial shear cell) have been used, the measurements agree well

[2]

For investigation of the influence of different consolidating procedures - in analogy to the uniaxial test of Fig 3 - samples were consolidated in the true biaxial shear tester from a low bulk density to a selected higher bulk density before the shear test started The higher bulk density Pb could be obtained in different ways Fig 6 demonstrates three different possibilities (I, II, III) to consolidate the sample to get the same sample volume and, hence, the same bulk density In case of procedure I the x-axis and in case of procedure III the y-axis coincide with the direction of the major principal stress O~,c at consolidation In case of procedure II in both directions the major principal stress O~,c is acting After consolidation the samples were sheared as described above 02 in y-direction was kept constant at o2 = 0 and Ol was increased

up to the point of failure, leading to the unconfined yield strength The results are plotted in Fig 5 as Oc versus (Yl,c, being the major principal stress at consolidation The functions oc = f (Ol,c) corresponding to procedures I, II and III are below the Flow Function Oc = f (ol) The distance between the function oo = f (Ol,c) of procedure I and the Flow Function is quite small Hence, the function oc = f (Ol,c) of procedure I can be used as an estimation of the Flow Function The functions of Fig 5 are gained with a limestone sample (xs0 = 4,8 pm) The difference in the functions of Fig 5 will be different for other bulk solids, i.e a generalized estimate of the Flow Function by knowing only the function Oc = f (Ol,c) of procedure I is not possible

Fig 5 Unconfined yield strength ~c versus major

at steady state flow ~l(Flow Function) and

versus major principal stress at consolidation

~l,c (limestone: xs0 = 4,8 lxm)

Fig 6 Sample consolidation principal stress

Procedure I is identical to the procedure in Fig 3 realized in uniaxial testers, e.g the testers

of Gerritsen [6] and Maltby [7] The function •r = f (~1,r of procedure II can be compared with experiments performed by Gerritsen after nearly isotropic consolidation (triaxial test) [8] Again, a good qualitative agreement between Gerritsen's results and the results with the true biaxial shear tester could be obtained [2] More important with respect to the present paper is the function ~r = f (c~1,r of procedure III showing anisotropic behaviour of the measured limestone sample A strong influence of the stress history on the strength of the sample exists, i.e the strength is dependent on direction of the applied stresses There is one tester available

in which the procedure III of Fig 6 is realized [9] If this tester is used for bulk solids showing anisotropic behaviour it may be concluded that this tester leads to too small C~c-values It has to

be mentioned that most bulk solids behave anisotropically

The Flow Function as the dependence of the unconfined yield strength ~c on the major consolidation stress (Yl (at steady state flow) can only be determined using testers where both stress states can be realized Steady state flow can be realized in Jenike's tester, in annular shear cells, in a torsional shear cell, in the true biaxial shear tester and in a very specialized triaxial cell [2] The unconfined yield strength ~c can be determined by running tests in Jenike's tester, in an annular shear cell [10], in uniaxial testers and in the true biaxial shear tester Therefore, only Jenike's tester, annular shear cells and the true biaxial shear tester can guarantee the measurement of Flow Functions ~c = f (C~l) without further assumptions

3 APPLICATION OF MEASURED FLOW PROPERTIES

In the following, it will be shown which flow properties have to be known for special applications and which testers are suited to measure these properties

3.1 Design of silos for flow

The best known and the most applied method to design silos for flow is the method developed by Jenike [1] He distinguishes two flow patterns, mass flow and funnel flow, the border lines of which depend on the inclination of the hopper, the angle q~e of the effective

yield locus (Fig 2) and the angle q0w between the bulk solid and the hopper wall For determining the angle q~e steady state flow has to be achieved in the tester The wall friction angle q~w can easily be tested with Jenikes tester, but also with other direct shear testers The most severe problems in the design of silos for flow are doming and piping Jenikes procedure for avoiding doming starts from steady state flow in the outlet area After stopping the flow (aperture closed) and restarting it the flow criteria for doming can only be applied, if the Flow Function is known As stated before the Flow Function can only be measured without further assumptions with the help of the Jenike tester, annular shear cells or the true biaxial shear tester The latter is very complicated and cannot be proposed in its present form for application in the design of silos for flow

Some bulk solids gain strength, when stored under pressure without movement Principally this time consolidation can be tested with all testers Besides the fact that time consolidation can most easily be tested with Jenikes tester and a new version of an annular shear cell [ 10] - easily with regard to time and equipment - only these testers yield Time Flow Functions which have to be known for applying the doming and piping criteria

Piping can occur directly after filling the silo or after a longer period of satisfactory flow, e.g due to time consolidation In the latter case Flow Function and Time Flow Functions have

to be known to apply the flow-no flow criteria In the former case the pressures in the silo after filling have to be known, which are different from those during flow

The anisotropic behaviour of bulk solids mentioned in connection with Fig 5 (procedure III) is of no influence in the design of silos for flow With help of Fig 5 and 6 it was explained that steady state flow was achieved with ol (at steady state flow) acting in x- direction The unconfined yield strength was also measured with the major principal stress acting in x-direction During steady state flow in a hopper the major principal stress is in the hopper-axis horizontal In a stable dome above the aperture the unconfined yield strength also acts horizontally in the hopper axis Therefore, the Flow Function reflects reality in the hopper

a r e a

3.2 Design of silos for strength

For designing silos for strength, the stresses acting between the stored bulk solid and the silo walls have to be known Since 1895 Janssen's equation is used to calculate stresses in the bin-section His equation is still the basis for many national and international codes and recommendations [ 11] This equation contains besides geometrical terms and the acceleration due to gravity the bulk density Pb, the coefficient of wall friction kt = tan tpw and the horizontal stress ratio X For 9b the maximum possible density being a function of the largest ol-value in the silo have to be used The coefficient of wall friction kt can be gained with the help of shear testers, if the tests are carried out at the appropriate stress level and if the results are correctly interpreted [12] It shall be mentioned that the value of the angle used for the mass flow- funnel flow decision is generally not identical with the one needed in the design of silos for strength

It is a lot more difficult to get reliable values for the parameter X In Janssen's equation and all following applications X is defined as the ratio of the horizontal stress at the silo wall to the mean vertical stress Therewith a locally acting stress is related to a stress being the mean value of all stresses acting on a cross-section, i.e two stresses acting on different areas are related In research works and codes several different instructions to calculate X are suggested

From the large numbers of different recommendations it can be seen that there is still an uncertainty in calculating

A step forward to a reliable determination of X is the recommendation by the scheduled euro code [ 13] to measure k in an uniaxial compression test, using a modified Oedometer An Oedometer is a standard tester in soil mechanics to measure the settling behaviour of a soil under a vertical stress ~v Such a modified Oedometer, called Lambdameter, was proposed by Kwade et al [14] (Fig 7) The horizontal stress ~h can be meausred with the help of strain gauges, lined over the entire perimeter of the ring For further details see [ 14] A large number

of tests have been performed to investigate influences like filling procedure, influences of side wall friction, influence of friction at lid and bottom, duration of the test, minimum stress level and others 41 bulk solids having angles r of the effective yield locus between 20 ~ and 57 ~ were tested in the Lambdameter The results are summarized in Fig 8, where ~ is plotted versus q~ For comparison, the proposals by Koenen and Kezdy and the recommendation of the German code DIN 1055, part 6, are plotted in the graph It can be concluded that none of the three is in line with the measured values and that especially with high values of q~ great differences exist between the measured and the recommended k-values

The described problem in getting reliable k-values for design results from the fact that no simple, theoretical model exists which combines known bulk solid properties like q~e, q~w or others with application in a satisfactory manner As long as this relationship is not known the direct measurement in a special designed tester like the Lambdameter is the best solution

3.3 Quality control, qualitative comparison

In the chapter "Design of Silos for Flow" it was shown that the knowledge of the Flow Function, the Time Flow Functions, the angle q~e of the effective yield locus and the wall friction angle q)w is necessary to design a silo properly Having estimates of the Flow Function only (see Fig 5) uncertainties remain and assumptions are necessary to get reliable flow These assumptions are hard to check

Very often the testing of bulk solids is not done with respect to silo design Typical other questions are:

- A special bulk solid has poor flow properties and these should be improved by adding small amounts of a flow aid Which is the best kind and concentration of flow aid?

Fig 7 Lambdameter Fig 8 Horizontal stress ratio ~ versus angle of

effective yield locus (De (41 bulk solids)

- A bulk solid having a low melting point has sufficient flow properties at room temperature

Up to which temperatures is a satisfactory handling possible?

- The flow properties of a continuously produced bulk solid vary Which deviations can be accepted?

For solving these problems it is sufficient to use estimates of the Flow Function, as long as the test procedure does not change from test to test Testers, which easily can be automated, and give reproducible results are favourable [ 15] Annular shear cells, the torsional shear cell and uniaxial testers belong to this group of testers Other testers like the Johanson Hang-Up Indicizer [ 16] and the Jenike & Johanson Quality Control Tester [ 17] claim to be as good But

in these two testers and in others the states of stress are not homogeneous and therefore unknown The results are dependent on wall friction and geometrical data [18] Thus, no properties, which are independent of the special tester used, can be achieved But for characterization of flow properties it is the main requirement to get data not affected by the testing device Therefore, it is not advisable to use results from those tests as flow indices Comparative tests with different bulk solids and different testers show clearly that the Flow Functions and their estimates differ [17,19] and also that the ranking in flowability is not identical from tester to tester [ 19]

It is often mentioned as a disadvantage of the Jenike cell that it requires a high level of training and skill and much more time than other testers This is only partly true If a hopper is

to be designed, the mentioned skill and time are needed to get the necessary information If there are only needs for quality control or product development, it is also possible to use the Jenike cell or annular shear cells with a simpler procedure An estimate of a yield locus can be derived by running only one test (preshear and shear) and a repetition test, i.e with 4 to 6 tests

an estimate of the Flow Function can be determined being at least as good and reliable as results gained from the other testers Especially the use of an annular shear cell has advantages because sample preparation is significantly less expensive [10]

With results of the mentioned testers the Flow Function or estimates of the Flow Function can be derived It is also possible to measure the effect of time, humidity, temperature and other influences on the Flow Function or the estimate of the Flow Function

3.4 Calibration of constitutive models

Eibl and others have shown that the Finite Element Method can be used with success to model pressures in silos [20] To apply this method a constitutive model has to be used The models of Lade [21] and Kolymbas [22] may be mentioned as examples Each constitutive model contains parameters, which have to be identified from calibration tests The most important demand for this calibration test is that the complete state of stress and the complete state of strain can be measured in the equivalent testers From the mentioned testers this requirement can only be fulfilled by the true biaxial shear tester and by very special triaxial cells [2] Lade himself and also Eibl used results from triaxial tests for calibration Feise [5,23] could show the advantages of using the true biaxial shear tester

4 CONCLUSIONS

It can be concluded that no universal tester exists being able to measure the required properties accurately within a reasonable time Without naming the testers again the different applications shall be mentioned with emphasis to the properties needed to solve the problems:

- Design of silo for flow

The Flow Function, the Time Flow Functions, the angle toe of the effective yield locus and the angle of wall friction tOw have to be known exactly

- Quality Control

An estimate of the Flow Function, which can be measured accurately and reproducible, is sufficient

- Calibration of constitutive models

The tester must allow homogeneous stressing and straining of the sample

3 Harder, J.: Ermittlung von Fliel3eigenschaften koh~isiver Schiattgiater mit einer

Zweiaxialbox, Ph.D Dissertation, TU Braunschweig (1986)

Nowak, M.: Spannungs-/Dehnungsverhalten von Kalkstein in der Zweiaxialbox, Ph.D Dissertation, TU Braunschweig (1994)

5 Feise, H." Modellierung des mechanischen Verhaltens von Schtittgiatern, Ph D

8 Gerritsen, A.H.: The Influence of the Degree of Stress Anisotropy during Consolidation

on the Strength of Cohesive Powdered Materials, Powder Technol 43(1985),61/70

9 Peschl, I.A.S.Z.: Bulk Handling Seminar, Univ Pittsburgh, Dec 1975

10 Schulze, D.: Development and Application of a Novel Ring Shear Tester,

Aufbereitungstechnik 35(1994),524/535

11 Martens, P.: Silohandbuch, Verlag Emst& Sohn, Berlin (1988)

12 Schwedes, J.: Influence of Wall Friction on Silo Design in Process and Structural Engi- neering, Ger.Chem.Engng 8(1985), 131/138

13 ISO Working Group ISO/TC 98/SC3/WG5: Eurocode for Actions on Structures

Chapter 11" Loads in Silos and Tanks, Draft June 1990

14 Kwade, A., Schulze, D and J Schwedes : Determination of the Stress Ratio in Uniaxial Compression Tests, Part 1 and 2, powder handling & processing 6(1994),61/65 & 199/203

15 Schulze, D.: Flowability of Bulk Solids - Definition and Measuring Techniques, Part I and II Powder and Bulk Engng 10(1996)4,45/61 & 6,17/28

16 Johanson, J.R.: The Johanson Indizer System vs The Jenike Shear Tester, bulk solids handling 12(1992),237/240

17 Ploof, D.A and J.W Carson : Quality Control Tester to Measure Relative Flowability of Powders, bulk solids handling 14(1994), 127/132

18 Schwedes, J., Schulze, D and J.R Johanson: Letters to the Editor, bulk solids handling 12(1992),454/456

19 Bell, T.A., Ennis, B.J., Grygo, R.J., Scholten, W.J.F and M.M Schenkel : Practical Evaluation of the Johanson Hang-Up Indicizer, bulk solids handling 14(1994), 117/125

20 H~.uBler, U and J Eibl : Numerical Investigations on Discharging Silos, J Engng Mechanics 110(1984),957/971

21 Lade, P.V.: Elasto-Plastic Stress-Strain Theory for Cohesionless Soil with Curved Yield Surface, Int J Solids and Structure 13(1977), 1019/1035

22 Kolymbas, D.: An Outline of Hypoplasticity, Archive of Applied Mechanics

61(1991),143/151

23 Schwedes, J and H Feise : Modelling of Pressures and Flow in Silos, Chem Engng & Technol 18(1995),96/109

A Levy and H Kalman (Editors)

Investigation on the effect of filling procedures on testing of flow properties

by means of a uniaxial tester

G.G Enstad a and K.N Sjoelyst b

aTel-Tek, dept POSTEC, Kjoelnes ring, N-3914 Porsgrunn, Norway

bTelemark University College, Department of Process Technology, Kjoelnes ring,

N-3914 Porsgrunn, Norway

The uniaxial tester is an instrument where powder samples can be consolidated uniaxially

in a die at different stress levels After consolidation the die is removed and the axial compressive strength is measured By repeating the procedure at different consolidation stress levels, the compressive strength is determined as a function of the consolidation stress, indicating the flow properties of the powder Advantages of this method are that it is relatively simple to use, and it has a reproducibility that is better than most other methods In the work to further improve the reproducibility, it has been found that the procedure of filling the die is very important Three different procedures therefore have been tested, including one using vibration to pack the sample during filling of the die Although the procedure using vibrations so far has not improved the reproducibility, it may still reduce the operator dependency

1 INTRODUCTION

Testing of flow properties of powders is useful for many reasons Flow properties may be needed for the design of equipment for storage, handling and transport of powders The Jenike method for design of mass flow silos [1] is the most well known example of how flow properties measured in the Jenike tester is used In addition to the Jenike tester, there are many other types of testers [2], some more complicated and more reliable, and some less complicated and less reliable The uniaxial tester developed by POSTEC [3] is a bit more complicated apparatus than the Jenike tester, but it is simpler to use, and gives more reproducible results Although this tester is not applicable for silo design, as it does not measure a state of consolidation stress that is representative for silos, it can be useful for other purposes, such as scientific investigations of mechanical properties of powders, quality control, and for educational purposes

Reproducibility, and results independent on the operator, are requirements necessary for most applications, but these requirements are difficult to satisfy in measuring the flow properties of powders In this respect the uniaxial tester developed by POSTEC [4] is one of the most reproducible methods available Previous experience [5] indicated, however, that the procedure for filling the die was very important for the result, and one of the main reasons for the amount of scatter and operator dependency still remaining for the uniaxial tester It was therefore decided to investigate different filling procedures in order to further improve the reproducibility of the results obtained by the tester

Results of some preliminary work to develop an improved filling procedure will be reported on here

2 E X P E R I M E N T A L

The uniaxial tester has been described elsewhere [3], but for the sake of completeness a short description will be repeated here, both of the tester itself, and how it is operated

2.1 The uniaxial tester

An overall view of the tester in the consolidation stage is shown in Figure l a (partly vertical cross section) The powder sample is contained in the die, which is fixed to the lower guide, see position 10 in Figure la By moving the piston (11) downward at a constant speed, using the motor (13) and the linear drive (14) also seen in Figure la, the sample is compressed axially Monitoring the compressive force by the weigh cell (15), and the axial compression

by monitoring the position of the piston, the consolidation of the powder sample is controlled, and the process is stopped when the desired degree of consolidation has been achieved For measuring the compressive strength, the die is pulled up, leaving the consolidated sample in

an unconfined state, as shown in Figure lb In this position the piston is moved downward very slowly until the compressive axial force on the sample passes a peak value, which is the compressive strength of the sample

Fig 1 The uniaxial tester prepared for the consolidation stage a), and for the measurement of compressive strength b)

2.2 Details of the die

The die (1) is shown in detail in Figure 2, showing also the guide (10 in Figure l a) for moving the die upward along the guiding rods (16 in Figure la) offthe sample The piston (3)

is fixed to the die in the starting position shown in Figure 2, but when the die is placed in the tester, the piston is fixed to the piston rod (11 in Figure 1 a) and released from the die, and is free to be moved up and down by the piston rod

In order to avoid friction between the die (1) and the sample (2) as it is being compressed axially, a flexible membrane is fixed to the lower edges of piston and die, and a thin film of lubricating oil is added between the membrane and the die wall, reducing the friction between membrane and die wall to a minimum As the membrane is stretched, it will shrink axially with the sample as it is compressed, thereby avoiding friction from developing between the powder and the membrane The membrane is protected at the lower edge of the die by a cover (5), and the bottom cup (9) keeps the powder in place when it has been filled into the die, which is then turned back to the upright position shown in Figure 2 The bottom cup is equipped with a porous plug (8), which will allow air to escape from the powder as it is compressed, and the void volume is reduced

Fig 2 Cross section of the die with a powder sample in place, fixed to the die guide, and with other auxiliary equipment

2.3 The filling procedures

To fill the die (1), the piston (3) is fixed to the die and released from the piston rod (11), and the die is released from the guide (10), and removed from the tester It is then turned upside down and put on a special stand where air can be sucked out from the space between the membrane and the die wall This is necessary, since the axial tension of the membrane causes a radial contraction By sucking out the air from the space between the membrane and the die wall, the membrane is brought into contact with the die wall all the way, and the die is then ready to be filled as soon as the bottom cup (9) is removed

Three different filling procedures have been tested Traditionally the powder has been filled into the tester layer by layer by means of a spoon Each layer has been slightly compressed and flattened on top either by using a rod, or a brush, in order to avoid pockets of air being trapped inside the sample Only the weight of the rod or the brush is allowed to compress the powder, no extra vertical force is added This was calculated to give rise to compaction stresses of 1.42 kPa for the rod, and 0.75 kPa for the brush These traditional ways of filling were the two first filling procedures that were tested The first one is denoted rod filling, and the second one is called brush filling When the die is full, a little more powder is added on the top making a little heap, which is removed by means of a scraper, giving the powder sample a smooth bottom surface The bottom cup is put back on top of the die, which is then turned back in its upright position, before it is weighed and put back in the tester, where it is fixed to the die guide The piston is fixed to the piston rod, and released from the die Knowing the mass of the powder sample and the position of the piston makes it possible to calculate the density of the sample at any time

The third filling procedure that was tested was aimed at reducing the operator dependency, using vibrations As for the other two procedures, the die is turned upside down and placed on the suction stand, and the bottom cup is removed before filling starts A vibrating chute continuously fills the powder via a funnel into the die in a controlled manner The funnel is fixed to the top of the die, and both are fixed to the stand sucking the membrane into contact with the wall of the die, and all are fixed tightly to a vibrating unit, which for these preliminary tests was simply a sieving machine The frequency was 50 Hz, but the amplitudes

of the vibrations varied a bit at random, around 1 mm It is hard to tell what compaction stress the vibrations would give during filling

2.4 Results

The compressive strength was measured as a function of the consolidation stress for two different powders, the BCR standard powder CRM-116, and a fine ground powder named Microdol Table 1 shows the individual results of the three filling procedures for CRM-116, and also includes the averages, the standard deviations, and the coefficients of variation for each series, and Table 2 shows the corresponding results for Microdol Furthermore, by weighing the die when filled the mass of powder in the die was recorded, and the results are summarized in Table 3

Cons str Parallel 1 Parallel 2 Parallel 3 Average Std Dev Coeff of

3 DISCUSSIONS AND CONCLUSIONS

The purpose of investigating different filling procedures, was to improve the reproducibility, and to reduce the operator dependency of the tester So far the operator dependency has not been tested, but the standard deviations of the strengths of the series of tests for each filling procedure are indications of the reproducibilities that are obtained Previously it was found that the degree of filling had a strong effect on the strength that was measured Therefore this information has also been included Before discussing the results in detail, it might be worth mentioning that the standard deviations of the measurements here are less than what is usual for this type of measurement

3.1 The masses of the samples filled into the die

Using the brush in both cases gives the lowest filling, whereas vibrations gives the highest for CRM-116, and the rod gives the highest for Microdol

This indicates that vibrations may give varying compaction loads, higher than the rod for CRM-116, and lower for Microdol The filling procedure using vibrations gives the largest standard deviation of the filling mass for both powders, indicating the worst reproducibility For CRM-116 the rod gives the lowest standard deviation, whereas the brush is the best for Microdol The use of vibrations for filling does not seem to improve the reproducibility of the filling procedure On the other hand, using a sieving machine to vibrate the die may have given vibrations that varied a bit from time to time Since vibrations will reduce the operator dependency, this possibility will be investigated further with more suitable vibration equipment

3.2 Strength measurements

The results obtained with rod and brush filling are fairly close both for CRM-116 and for Microdol, whereas the strengths obtained after filling with vibrations are generally higher for CRM-116 and lower for Microdol than for the other two types of filling This can be seen in connection with the sample masses in Table 3, where vibration gave considerably higher masses than the other two types of filling for CRM-116, whereas for Microdol the average masse obtained with the rod was a bit higher than for vibration This is in agreement with the general trend seen before that a large filling mass also gives a higher strength, although this is not true when comparing brush and rod filling This indicates that other effects than the masses of the samples, which we may still not be aware of, may be of importance for the strength measurements

Looking at the standard deviation, it is seen that rod filling has the worst reproducibility for both powders Vibration filling is slightly better than brush filling for CRM-116, whereas brush filling is better than vibration filling for Microdol Hence, although these preliminary results were not completely satisfactory, they are sufficiently encouraging to carry on further investigations with better vibrating equipment, bearing in mind the potential for reducing the operator dependency that this filling method represents

R E F E R E N C E S

1 A.W Jenike, Storage and Flow of Solids, Bulletin 123, Utah University 1964

2 J Schwedes, Testers for Measuring Flow Properties of Particulate Solids, Proceedings of the International Symposium Reliable Flow of Particulate Solids III, Telemark College, Porsgrunn, August 11 - 13, pp 3 - 40, 1999

3 L P Maltby, Investigation of the Behaviour of Powders under and after Consolidation,

Thesis, Telemark College, Porsgrunn, 1993

4 F Pourcel, A Berdal, G G Enstad, A M Mosland and S R de Silva, Quality Control and Flow Property Investigations by Uniaxial Testing, Using Samples of Different Sizes,

Proceedings of the International Symposium Reliable Flow of Particulate Solids IlL

Telemark College, Porsgrunn, August 11 - 13, pp 143 - 150, 1999

5 A.M Mosland, The Uniaxial Tester- New Developments, POSTEC-Newsletter, No 16,

pp 20-26, December 1997

A C K N O W L E D G E M E N T S

The authors are indebted to the POSTEC members, AstraZeneca, Norcem, DuPont and the Norwegian Research Council for financial support during the course of the development of the uniaxial tester, and to Professor Sunil de Silva for help in the preparation of the manuscript

9 2001 Elsevier Science B.V All rights reserved 33

C h a r a c t e r i z a t i o n o f p o w d e r flow b e h a v i o r w i t h the F l e x i b l e W a l l B i a x i a l Tester

R.J.M Janssen and B Scarlett

Delft University of Technology, Faculty of Applied Sciences, Particle Technology Group Julianalaan 136, 2628 BL Delft, The Netherlands

The purpose of this paper is to use the Flexible Wall Biaxial Tester to get more insight in powder flow behavior This has been done by preparing powder samples and shearing them with constant volume and with eight different types of deformation Anisotropy is occurring

in these samples due to the structure in the powder It was seen that stresses on opposite walls differ which means that there are shear stresses It is thought that these are at least partially caused by the powder and not by the tester This would mean that the principal axes of stress are not in the same direction as the principal axes of strain

1 STRUCTURE IN POWDER

One fundamental assumption about powder flow behavior is that powder is isotropic For example the procedure that Jenike developed [1, 2] for the characterization of powder flow does only look at strain, stress and porosity or bulk density The point contact structure of the particles is not included Feise showed in an overview article [3] that the exclusion of structure can have large influences on the characterization of powders

The purpose of this work is to use the Flexible Wall Biaxial Tester for investigation of the influence of anisotropy on the flow behavior of a powder This anisotropy is thought to be a result of the structure in the powder This structure forms as a consequence of the process conditions but also as a consequence of the primary properties of the particles, the distribution

of size and shape [4]

2 THE FLEXIBLE WALL BIAXIAL TESTER

Arthur et al [5] first built a biaxial tester specifically for powder flow testing The Flexible Wall Biaxial Tester in this paper was developed by Van der Kraan [4, 6] The main idea is that the axes of the tester are the principal axes The walls of the sample holder consist of membranes (figure 1) which are in fact cubical balloons (only the X and Y direction) A balloon is configured such that one face that forms one wall of the sample holder can deform freely The balloons can be pressurized and moved by stepper motors This makes it possible

to use the tester both as a stress controlled and as a strain controlled tester The only constraint

is that the membrane faces remain flat so that the axes of the tester are the principal axes Optical sensors inside the balloons measure the deformation of the membranes No strain can be applied in the Z-direction and the Z-stress is only measured The tester is placed on a table and closed with a top lid A top membrane and a bottom membrane cover the powder,

which prevent shear stresses to occur since they deform in the same manner as the powder sample

The height of the sample holder is fixed at 80 mm, the minimum size of the sample volume

is 75*75*80 mm 3 and the maximum size is 135'135"80 mm 3 The control and the data acquisition of the system are completely automated Van der Kraan [4] gives a more detailed description of the tester All the experiments are performed with the standard BCR-limestone

[71

3 E X P E R I M E N T A L PROCEDURE

Each experiment started with the same two steps consisting of an initial consolidation, in which the volume was reduced, followed by a preshearing step with constant volume (figure 2)

After these preparing steps eight different types of experiments were performed as pictured

in figure 3 In all types the volume remained constant to the volume of the preshear step In the first type (I) the walls moved in opposite direction compared to the preshear step The second type (II) is a prolongation of the preshear step: the walls moved in the same direction

In type three wall X1 didn't move and X3 moved inwards (IIIa) or outwards (IIIb) In type four wall Y4 didn't move and Y2 moved inwards (IVa) or outwards (IVb) In the last type X1 and Y4 didn't move and X3 moved inwards (Va) or outwards (Vb) The precise values for the strains can be found in table 1

All the experiments shown here are performed in a strain-controlled manner with a strain rate of 110 s s -1

Fig 1 Schematic view of the Flexible Wall Biaxial Tester (top lid has been removed)

Fig 2 Strain path for the consolidation (1.) and the preshearing step (2.) The dotted lines represent the starting position

Fig 3 The eight different shear steps which are possible with the Flexible Wall Biaxial Tester The volume is the same for all types The dotted lines represent the starting position The filling of the tester is done by tapping the powder through a sieve Ten times during the filling the powder is gently consolidated to be sure that there are no cavities and that the bulk density is homogeneous over the height The starting volume is 110* 110* 80 mm 3 Table 1

Overview of the applied strains in the different experiments

consolidation preshear I II Ilia IIIb

The measured stresses are given in picture 4 to 11 The measured stress in the Z-direction

is not given in the figures for clarity reasons

4 E V A L U A T I N G T H E E X P E R I M E N T S

4.1 Membrane deformations

For the Flexible Wall Biaxial Tester it is assumed that the axes of the machine are the principal axes For that reason principal strains are applied on the powder sample as long as the membrane faces stay flat during the experiment From figure 12 it can be seen that the deformation of the membranes in experiment Va is most of the time less than 10 pm

4.2 P r e p a r i n g steps

The consolidation step and the preshear step are the same for all experiments The measured stresses, however, differ quite a lot In figure 13 the stresses (X and Y stresses are averaged) during the consolidation are given as a function of the bulk density

Fig 4 Type I experiment Fig 5 Type II experiment

Fig 6 Type IIIa experiment Fig 7 Type IIIb experiment

Fig 8 Type IVa experiment Fig 9 Type IVb experiment

Fig 10 Type Va experiment Fig 11 Type Vb experiment

Fig 12 The deformation of the membranes during experiment Va

Fig 13 The mean principal stress during the consolidation for each experiment (X and Y stresses are averaged)

Figure 13 shows quite a large deviation between the measured consolidation stresses of the different experiments This could be due to changes in the filling of the powder This is done manually and could cause different consolidated samples for different experiments

Also the preshear step deviates per experiment The stresses in this step are more or less reaching a steady state as was expected because the volume of the sample is not changing

4.3 The occurrence of anisotropy

The results for the third step (figure 4 to 11) show a strong dependence of the measured stresses on the different types of deformation in this step

During the consolidation and preshear step a certain structure has been formed in the powder, which adapted itself to the combination of the X-walls moving inwards and the Y-

walls moving outwards Feise [3] calls this a favorable structure for this type of shear This structure causes the different reactions of the sample to the different types of deformation applied in the third step (figure 3)

If experiments I and II are compared (figure 4 and 5) it can be concluded that the powder is much weaker in the Y direction, that is the direction in which the minor stresses worked during the preshear For a different direction of shear this structure has not been built ideally This is why the principal stresses decrease when step three begins in experiment I (figure 4) and why they continue at approximately the same values as occurred in preshear in

experiment II (figure 5) This contributes to the idea that during the shear a certain pattern or structure is formed which is directed by the shear

Surprisingly the stresses in the same direction sometimes deviate from each other (for example figures 6 and 10) This difference between X1 and X3 in experiment IIIa and Va doesn't disappear during the remainder of the step This means that there are shear stresses on the walls The question is if they are caused by the FWBT or by the powder itself

The experiments are performed in a strain-controlled mode, which means that the X, Y and

Z axes are the principal axes of strain If the powder causes the differences in stress between X1 and X3 or between Y2 and Y4, then the principal axes of strain are not equal to the principal axes of stress

5 CONCLUSION

The Flexible Wall Biaxial Tester is a suitable machine to investigate powder on its flow properties because of the divergence in stress and strain patterns that can be applied on the sample The performed experiments showed that anisotropy is occurring in a consolidated and presheared powder The highest stresses are occurring in the direction in which the major stress occurred during the preshear step This is according to literature [3, 4] and is explained

by the formation of a certain structure in the powder

The second observation from these experiments is that it is doubted that the principal axes

of strain are in the same direction as the principal axes of stress This observation has not been found in literature

3 H.J Feise, Powder Technol., 98 (1998) 191-200

4 B Scarlett, M Van der Kraan and R.J.M Janssen, Phil Trans R Soc Lond A, 356 (1998) 2623-2648

5 J.R.F Arthur, T Dunstan and G.G Enstad, Int J Bulk Storage in Silos, 1, (1985) 7-10

6 Van der Kraan., Techniques for the measurement of cohesive powders, dissertation, Delft University of Technology, The Netherlands, 1996

7 R.J Akers, The certification of a limestone powder for Jenike shear testing, Community Bureau of Reference-BCR, CRM 116, Brussels, 1991

9 2001 Elsevier Science B.V All rights reserved 39

From discrete element simulations towards a continuum description of particulate solids

S Luding, M L~itzel and H.J Herrmann

Institute for Computer Applications 1, Pfaffenwaldring 27, 70569 Stuttgart, Germany

We propose a way to obtain averaged macroscopic quantities like density, momentum flux, stress, and strain from "microscopic" numerical simulations of particles in a two-dimensional ring-shear-cell In the steady-state, a shear zone is found, about six particle diameters wide, in the vicinity of the inner, moving wall The velocity decays exponentially in the shear zone, particle rotations are observed, and the stress and strain-tensors are highly anisotropic and, even worse, not co-linear From combinations of the tensorial quantities, one can obtain, for example, the bulk-stiffness of the granulate and its shear modulus

1 INTRODUCTION

The description of the behavior of particulate materials relies on constitutive equations, functions of stress, strain, and other physical quantities describing the system It is rather difficult to extract macroscopic observables like the stress from experiments, e.g in a two- dimensional (2D) geometry with photo-elastic material, where stress is visualized via crossed polarizers [6, 7] The alternative is, to perform discrete element simulations [2, 4] and to average over the microscopic quantities in the simulation, in order to obtain some averaged

macroscopic quantity The averages over scalar quantities like density, velocity and particle- spin are straightforward, but for the stress and the deformation gradient, one finds slightly different definitions in the literature [3, 8-11 ]

In the following, we will briefly introduce the boundary conditions for our model system, before presenting the averaging procedure Kinematic and dynamic quantities of the system are obtained from the simulation data and some material properties are determined as combinations of the observables

2 M O D E L AND AVERAGING STRATEGY

In the following, a two-dimensional (2D) Couette-shear-cell is used, filled with bidisperse disks of diameter d and height h, a snapshot of the system is displayed in Fig 1 The system is slowly sheared by turning the inner ring counter-clockwise about once per minute

The inner and the outer ring have a radius of Ri=0.1034 m and Ro=0.2526 m, respectively

In the experiment, the height of the system is h=0.006 m and it is filled with slightly smaller disks of diameters ds =7.42 mm and d1=8.99 ram, in order to avoid crystalization The results presented in this study stem from three simulation with N=Ns+N! particles These simulations, referred to as (1), (2), and (3) in the following, with N(1)=2555 +399, N(2)=2545+394, and N~3)=2511+400, correspond to an area coverage, or volume fraction of vi~)=0.8194, v(2)=0.8149, and v~3)-0.8084, respectively The angular frequency of the inner ring is

g2=-2rdT=0.1s -~ and the simulation is performed until t=-120s; for the averaging, the first rotation is disregarded For more details see Ref [9]

Fig 1: Snapshot from the model system (Left) Stress chains - dark particles feel low pressure, light particles are strongly compressed (Right) Contact network - each contact is plotted as a line

The averaging procedure, as applied in the following, can be formalized for any quantity

Q, keeping in mind that we first average over each particle and then attribute a fraction of each particle - and thus a fraction of Q - to the corresponding averaging volume An alternative approach, i.e to use the fraction of the center-center line of the particles instead of the volume [5], is not applied here Written as a formula our ansatz reads

The first important quantity to measure is the volume fraction

v = V

obtained by using QP=I, and disregarding the sum over the contacts The volume fraction

is related to the mass density via p(r)= ~ v , with the material's density pP=1060 kg m -3, paralleling the experiments [6, 7, 9] The next quantity of interest is the mean flux density

W = V p~V

obtained with QP=v p, the velocity of particle p We checked that Vr, the radial component

of the velocity vector, is approximately zero, in accordance with the assumption of a steady state cylindrical shear situation In Fig 2, the density v and the velocity vo are plotted against the distance from the center r

Fig 2: Snapshot (Left) Density v and (Right) scaled tangential velocity v,/Or, with the angular velocity Or of a solid body rotating with the inner ring, plotted against the distance from the center r The different symbols and lines correspond to different densities and we used 60 intervals for binning, here

We identify the shear zone with those parts of the system with large vo Like in the experiments, the material is dilated in the shear-zone near the inner, rotating wall and also in the vicinity of the outer boundary, whereas it is densified in the central part (due to mass conservation and the fixed volume boundary conditions) Particles are layered close to the walls, as indicated by the periodic wiggles in density, but no order effects are visible in the inner parts of the system The velocity decays exponentially from the inner ring over two orders of magnitude, before it reaches some noise-level The qualitative picture does not vary with the density; however, if the density would be reduced further below the value of simulation (3), the innermost particles would lose contact with the moving inner wall and the system would freeze

3 FABRIC, STRESS AND ELASTIC DEFORMATION

The fabric tensor, which describes the directed probability distribution to find a contact, involves the contact normal vectors n c, related to the so-called branch vectors lpC=(dP/2) n c

from the center of particle p with diameter d p to its contact c, so that

The static component of the stress tensor [8, 9] is defined as the dyadic product of the force

fc acting at contact c with the corresponding branch vector, where every contact contributes with ist force and its branch vector, if the particle lies in the averaging volume

~=g~

and the dynamic component of the stress tensor,

1 ~ w P V p p p v p |

has two contributions: (i) the stress due to velocity fluctuations around the mean and (ii) a stress due to the mean mass transport in angular direction In Fig 3, the static and the dynamic contributions are plotted In our system, the diagonal elements of the static stress are almost constant, whereas the off-diagonal elements decay proportional to r-2 The angular velocity in the shear zone strongly contributes to the stress due to mass flux, however, the dynamic stress is usually much smaller than the static stress

Fig 3: Components of the static stress (Left) and the dynamic stress (Right), and the fluctuation contribution pv, 2, plotted against the distance from the center r Note the different vertical axis scaling Only the dense simulation (1), solid symbols, is compared to the dilute one (3), open symbols Finally, the elastic deformation gradient [9,10] is defined as

c=l

(7)

where ArC=SCn c is the deformation vector of contact c, with the deformation 8 c, and A=F "1

is the inverse fabric tensor The elastic deformation gradient is a measure for the mean reversible deformation of the material and thus for the energy stored in the compressed granulate In the following, we extract some material properties from the quantities defined above

In Fig 4 the rescaled stiffness and some shear modulus of the granulate are plotted against the trace of the fabric Furthermore, the orientations of the tensors F, 6, and s are plotted against the distance from the inner ring The data for the bulk modulus from different simulations collapse on a master curve, except for the areas close to the walls The data for the shear modulus show a non-linear increase with tr(F); the denser system diverges at larger values than the dilute system, however, the data are strongly scattered The most remarkable result is the fact that the orientations ~ of the tensors are not co-linear, where ~ is defined as the orientation of the "major eigenvector", i.e the eigenvector corresponding to the major eigenvalue of T, with respect to the radial direction

In Fig 5, the mean total particle spin, o3, as obtained from the spin density

VO) F t,~v

is plotted, together with the continuum spin Wr~ and the excess or eigen-spin, o3*=o3-Wr~, as functions of r in the few innermost layers We remark that the rotation of the particles is a stable effect, independent of the density, at least in the range of densities examined here The particles in the innermost layer rotate clockwise and in the next layer, a counter-clockwise spin is evidenced; the particles in the innermost sheared layers roll over each other

Note that both the deformation rate Dr~ and the continuum spin Wr~ are obtained by addition and subtraction, respectively, of the velocity gradient's off-diagonal elements

where we compute the partial derivative with respect to r from the data of vr directly

Fig 4: (Left) Granulate stiffness 2rcE/kn=tr(o)/tr(E), plotted against tifF) (Middle) Scaled granulate shear resistance 2rtG/kn=dev(o)/dev(e), plotted against tifF) (Right) Orientation of the fabric-, stress-, and strain-tensors (from top to bottom) Here 150 binning intervals are used

Fig 5: (Left) Total particle spin co, which consists of the contiuum spin Wro (Middle) and an excess eigen-spin co (Right) Different symbols correspond to different densities; 150 binning intervals are used