PRINCIPLES OF EMULSION FORMATION

DROPLET BREAK-UP IN LAMINAR FLOW The stress exerted on a drop in a laminar flow field equals slcG, where G is the velocity gradient and qC the viscosity of the continuous phase... 1 The

PRINCIPLES OF EMULSION FORMATION

Pieter Walstra Department of Food Science, Wageningen Agricultural

University, Wageningen, the Netherlands

ABSTRACT

The phenomena occurring during emulsion formation are briefly reviewed Droplet break-up in laminar and in turbulent flow is discussed and quantitative relations are given The roles of the surfactant are considered, i.e lowering the interfacial tension (and thereby facilitating break-up) and preventing recoalescence (via the Gibbs-Marangoni effect), in relation to the time scales of the various processes occurring

INTRODUCTION

This article concerns the formation of classical emulsions, so not micro-emulsions, multiple emulsions or high-internal phase emulsions ( HIPEs) This subject was reviewed earlier in some detail by the author (Walstra, 1983), from which we will take most information, without referring to literature listed there Since this review was written - in 1978 - new results and considerations have become available, and some of these will be given here, in addition to reviewing briefly the most salient points

To make an emulsion, we need oil and water (or more general an oily and an aqueous phase), a surfactant and energy The essential characteristics of the resulting emulsion are:

- The emulsion type: oil-in-water or water-in-oil This is primarily determined by the type of surfactant (see further on)

- The droplet size distribution, since smaller droplets are nearly always more stable against creaming, coalescence and often also flocculation It is easy to make droplets (gentle shaking suffices), but it may be difficult to make the droplets small enough This means that the essential process

is not droplet formation but droplet break-up Moreover, newly formed droplets may coalesce again during emulsification, and this should be avoided as much as possible

ENERGY RELATIONS

Why is energy needed? In order to break up a droplet it must first be deformed and this is opposed by the Laplace pressure,

333

334 PIETER WA~STRA

which is the difference in pressure between the convex and the concave side of a curved interface and is given by

PL = y (l/R, + l/R,)

where y is the interfacial tension and R, and R, are the principal radii of curvature For a spherical drop of radius r

we thus have pL = 2 y / r and taking, for example r = 0.2 urn (which is often desired) end y = 0.01 N m-l (which is a reasonable value), we have a Laplace pressure of 10' Pa (1 bar) In order to deform the drop, a larger external stress has to be applied; this implies a very large pressure gradient, since the stress difference has to occur over a distance of the order of r The stress can be due to a velocity gradient and then is a shear stress, or it can be due

to a pressure difference arising from inertial effects (chaotic motion of the liquid)

To achieve the very high shearing stress or the very intense velocity fluctuations needed to deform and break up small droplets, very much energy has to be dissipated in the liquid Assume that oil droplets with a radius of 1 urn have to be formed in water and that the volume fraction of oil 4 = 0.1 and y = 0.01 N m-l, we obtain a specific surface area A of 3 x lo5 m-' and the net surface free energy needed to create that surface Ay = 3 kJ rnm3 In practice, we need about 3 MJ ma3 to make the emulsion, which means that by far the greatest amount

of the energy supplied is dissipated into heat

It is seen from eq (1) that the stress - and consequently the amount of energy - needed to deform and thereby break up the droplets is less if the interfacial tension is lower, which can be achieved by adding a sufficient amount of a suitable surfactant This is one role of the surfactant, but not the most essential one, which is to prevent the immediate recoalescence of the newly formed drops This will be discussed further on We will consider first the break-up of drops This can be achieved in laminar flow due to shear stresses, or in turbulent flow, where inertial effects (pressure fluctuations) are predominant, although shear stresses may be of importance in some cases For inertial effects due to cavitation, for instance caused by ultrasonic waves, we refer to our earlier review; since, some new literature has appeared (e.g Li and Fogler, 1978; Reddy and Fogler, 1980)

DROPLET BREAK-UP IN LAMINAR FLOW

The stress exerted on a drop in a laminar flow field equals slcG, where G is the velocity gradient and qC the viscosity of the continuous phase This stress is counteracted by the Laplace pressure and the ratio is called the Weber number:

We = q, G r / Y

We,,

Fig 1 The critical Weber number for disruption of

droplets in simple shear flow (curve, results by Grace, 1982) and for the resulting average droplet size in a colloid mill (hatched area, results by Ambruster, 1990) as a function of the viscosity ratio disperse to continuous phase

If We exceeds a critical value We_ (of the order of one), the drop bursts We_ depends on the type of flow and on the ratio

of the drop viscosity to that of the continuous phase r),/l), Break-up of single droplets in simple shear flow (velocity gradient in the direction normal to that of the flow and thus equal to the shear rate) has been well studied and ,some results are shown as the curve in Fig 1 These results agree well with theory Others have often found somewhat different results, WeGr showing the same trend but being at a slightly lower or at a higher level; the explanation probably is that break-up of the drop also depends on the rate at which G is attained and on the time during which G lasts (Torza et al., 2972)

Eq (2) shows that for a low viscosity of the continuous phase, deformation of small drops requires extremely high velocity gradients For example,

low3 Pa s (water),

if y = 0.005 N m-l and ?jC =

it would need G = 25*106 s-1 to obtain droplets of r = 0.2 urn (We_ = 1) Such velocity gradients can usually not be produced except over very small distances It

is also seen that no break-up occurs for qo/qC > 4 The explanation is roughly that the drop cannot deform as fast as the simple shear flow induces deformation Deformation time of

a drop is proportional to its visaosity over the stress applied, that is %/rlcG, whereas the deformation time according

to the flow would be l/G So if rlo/qC >> 1, the drop does deform to some extent, but the deformed drop starts rotating

at a rate of G/2 (For a low viscosity drop, the liquid in it rotates while the drop keeps its orientation with respect to the direction of flow: consequently, it can deform to a greater extent.) The viscosity ratio above which no break-up occurs how ever large We, turns out to be 4, both from theory and experiment

336 PIETER WALSTRA

In elongational flow (no shear, velocity gradient in the direction of the flow) no rotation is induced, and even very viscous drops can be deformed and broken up, if the velocity gradient lasts long enough; the latter may be a problem since

in most situations elongational flow is a transient phenomenon For the range of viscosity ratios given in Fig 1, and for plane hyperbolic flow, We,, is almost constant at about 0.3 Thus, elongational flow is more efficient in breaking up drops, especially at a high viscosity ratio

Up till fairly recently, the theory for droplet disruption in simple shear had only been tested for the deformation and burst of single drops In practice, however, drops will be disrupted many times until they have reached a critical size and conditions, i.e We_, will vary within the apparatus and during the process Anyway, a spread in droplet size will result The theory has now been tested in a colloid mill, made

in such a way as to cause true simple shear: conditions as to composition of both phases and type and concentration of surfactant were varied widely (Ambruster, 1990; Schubert and Ambruster, 1989) The average droplet size rX2 (being the third over the second moment of the frequency distribution of r) was determined and used for calculating We_ Results are indicated

in Fig 1 and it is seen that a reasonable agreement with prediction was obtained Break-up was observed at somewhat higher values of the viscosity ratio than 4, up to qD/qc = 10 This may have been due to some elongational component in the flow in the apparatus, but another explanation may be the presence of a surfactant This allows the development of an interfacial tension gradient on the surface of a sheared drop The latter causes the tangential stress to be not any more continuous across the droplet boundary (which is a prerequisite in the theories applied to drop disruption in laminar flow) and this hinders the development of flow of the liquid in the drop This may, in turn, make deformation and thereby break-up easier It would be useful to study this aspect in more detail

Up till now, we have tacitly assumed that both liquids are Newtonian If they are visco-elastic, the situation becomes much more complicated If the disperse phase is visco-elastic, droplet break-up is in general more difficult, especially if the relaxation time is considerable If the continuous phase

IS visco-elastic, it becomes difficult to realize high elongational velocity gradients These aspects have been studied in some detail fairly recently (Han and Funatso, 1978; Chin and Han, 1979, 1980)

DROPLET BREAK-UP IN TURBULENT FLOW

It will be clear from the previous section that laminar flow

is mostly not suitable for breaking up drops suspended in water or another low viscosity liquid Flow conditions have to

be (intensely) turbulent In turbulent flow (see e.g Davies, 1972), the local flow velocity u varies in a chaotic way and

the fluctuations often are characterized by u', i.e the root- mean-square average difference between u and the overall flow velocity If the turbulence is isotropic (which is more or less the case if the Reynolds number is high and the length scale considered small), the flow can be characterized in a simple way, according to the Kolmogorov theory There is a spectrum of eddy sizes, and the smaller they are the higher their velocity gradient (u'/x), until it becomes so high that the eddies dissipate their kinetic energy into heat; the size

of the smallest eddies x0 is called the Kolmogorov scale and droplets smaller than this are usually not greatly deformed Somewhat larger eddies are called energy-bearing eddies and they are mainly responsible for droplet break-up For these eddies we have

u’(x) = c El/3 x1/3 p-1/3

where x is eddy size (or distance over which u' is con- sidered), p is mass density and C a constant of the order of unity The power density E (often called the energy density), i.e the average amount of energy dissipated per unit time and unit volume, is the main parameter characterizing the turbulence The eddies cause pressure fluctuations of the order of p{u'(x)j2 and if these are larger than the Laplace pressure 4y/x of a neighbouring droplet of diameter x, the droplet may be broken up_ This results in a largest diameter

of droplets that can remain in the turbulent field of

d PaX = xmax = C ~-2/s y3/5 p-1/5

The turbulent field is mostly not quite homogeneous and the resulting droplets will thus show a spread in size Since in many oases the resulting droplet size distribution has a fairly constant shape for variable E, eq (4) mostly holds also for an average droplet size (e.g d,,), albeit with a different constant It is a very useful equation that has been shown to hold remarkably well for a wide range of conditions, provided that recoalescence of droplets is limited; see the earlier review, where also some additional conditions are discussed

Some results are given in Fig 2 It is seen that the stirrer

is much less effective than the high pressure homogenizer (although the stirrer would have produced smaller droplets for the same energy consumption in a flow-through arrangement, presumably by a factor of about 5) This is because the homogenizer dissipates the energy in a much shorter time, thus causing E to be higher The stirrer dissipates much energy at

a level where it cannot break-up small droplets Note that the stirrer and the ultrasonic transducer (which also produces pressure fluctuations) show the expected slope of -0.4, predicted by eq (4): here power density is proportional to energy consumption In the homogenizer the net energy consumption is given by the homogenizing pressure p, but here the power density is proportional to p312, since the time during which the energy is dissipated is inversely

338 PlETER WALSTRA

proportional to the liquid velocity through the homogenizing valve, which is, in turn, proportional to pl" Consequently, the slops of log droplet size versus log energy input is -0.6,

an additional reason why high-pressure homogenizers are very effective in producing very small droplets

lJltm Tut-t-ax

(batch 2 min )

1

20

10

5

2

1

0.5

Fig 2

- lqP(MJ t+ :

Average droplet diameter xgg as a function of net energy input P (varied by varying intensity, not duration of treatment) for dilute paraffin oil- in-water emulsions produced In various machines From Walstra, 1983

Eq (4) predicts that changing qc does not result In a change

in droplet size This is indeed often roughly the case, but there are some exceptions, in that a slight dependency is observed, average droplet size mostly somewhat decreasing with increasing viscosity Presumably, pressure fluctuations may not in all cases be the only cause for droplet break-up On a droplet caught between eddies with a size S> droplet size, shear stresses will act and these may be sufficient for break- up: presumably, the type of flow is similar to plane hyperbolic flow If this is the mechanism, the resulting relation is

(5)

If the situation is in between true inertial and true viscous forces, viscosity may thus have some effect Increasing viscosity also means decreasing Reynolds number, hence less intense turbulence, hence on average larger eddies, hence more

shear This would also imply that the spread in conditions, hence the spread in droplet size, becomes larger for increasing viscosity, and this has indeed been observed (Walstra, 1974) Nevertheless, the effect of viscosity of the continuous phase on the resulting droplet size distribution is mostly slight

If a soluble polymer is added to the continuous phase, this causes some increase in qC, but it also has the effect of turbulence depression: especially the smaller eddies are removed from the spectrum This results in a larger average droplet size (up to a factor 2) and a narrower droplet size distribution, If a liquid contains many particles, they also depress turbulence, but the effect on emulsion formation has -

to the author's knowledge - not been studied, It may well be, however, that turbulence depression is one of the reasons why

a high internal phase volume fraction causes larger droplets

to be formed: nevertheless, other factors are probably more important (see the next section)

Fig 3 Effect of viscosity of disperse phase (q:, _in

mPa s) on average droplet size (d,,, in pm) for various machines (turbomfxer, circles; ultrasonic generator, crosses; homogenizers, other symbols) From Walstra, 1974

Eq (4) also predicts no effect of the viscosity of the disperse phase on the resulting droplet size, and this is clearly not in agreement with experiments Fig 3 shows some results and it is seen that for constant E, log average droplet size versus log I), gave straight lines with a slope of 0.35 to 0.39 The viscosity effect has been discussed by Davies (1985) He added in the derivation of eq (4) a viscous stress term = q&'/d to the Laplace pressure 4y/d, where d = droplet diameter This leads to

340

This equation does not agree with the constant and virtually parallel Slope8 in Fig 3 D&vies assumed the flow velocity in the droplet to be equal to the external u' and this may not be true anymore for q >> q, and it is certainly not the case in the presence of surfactant, which makes that the droplet surface can withstand a certain shearing stress In other words, the viscous stress term to be added should not contain

U' but the internal velocity Us, Because u,,/d equals the external stress over qn and because this stress is at the prevailing conditions of the order of the Laplace pressure, the additional term is of the same form as the Laplace pressure and the result is merely a different constant in eq (4) independent of Q~

In this connection, it is useful to consider the time needed for deformation of the droplet rdcf, which may be defined as q,, over the stress The latter equals the external stress minus the Laplace pressure We thus obtain

=dmi J q, / (C E2'3 d"' p"' - 4 y/d) (6) The constant C is unknown, but in order to obtain reasonable values for the resulting droplet size, we have taken it to be 5; some results are depicted in Fig 4 It should be noticed that eq (6) is different from the one given before: rdeI = qDd/y (Walstra, 1983); the latter relation is based on the spontaneous relaxation of the droplet shape after it has been deformed, but this is not realistic The dependence of the deformation time on d is according to eq (6) even reversed: now the smaller the droplet becomes, the longer the deformation time This is because - according to the Kolmogorov theory - the size of a droplet disrupting eddy is roughly the same as that of the drop, and the pressure difference caused by an eddy increases with size All these relations only hold within certain bounds and are not quite exact, but they serve to illustrate trends

The life time of an eddy can be derived from eq (3), which yields

t eddy = x / u ’ ( x ) r x2/3 fe3 p1’3 (7)

Results are shown in Fig 4, which gives several characteristic times throughout the emulsification process (ever decreasing droplet size); the finally resulting drop size according to eq (4) would be about 0.3 pm It is seen that for a relatively low v&, the deformation time is mostly shorter than the life time of the eddies of the size of the droplet, which would imply that the pressure fluctuations last long enough for the droplets to be disrupted by these eddies For higher droplet viscosities, this is not any more the case This implies that larger eddies are responsible for droplet break-up Hence, for a larger droplet viscosity the resulting drops are on average larger and - because of the greater

spread in flow conditions for larger eddies - show more spread

droplet diameter (pm1 time

specific surface area (m-‘I

342 PETER WALSTRA

droplet surface area/pm-’

Ucrm

-8

-15 -30

[surfactantl/kg.mb3