PRINCIPLES OF EMULSION FORMATION

Chemical Engimavfng Science Printed in Great Britain Vol 48 No 2, pp 333-349 PRINCIPLES OCW-2507/93 Is.OO+O.KI Pergamon Press Ltd 1993 OF EMULSION Pieter FORMATION 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 facilitating break-up) and preventing tension (and thereby 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 information, literature listed most without referring to there Since this review was written - in 1978 - new results and some of these and considerations have become available, 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 is energy needed? first be deformed and Why In order to break up a droplet it must this is opposed by the Laplace pressure, 333 PIETER WA~STRA 334 which is the difference in pressure between the convex concave side of a curved interface and is given by and the 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 = 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 pressure implies a very large 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 small needed to deform and break up droplets, very much energy has to be dissipated in the liquid with a radius of urn have to be Assume that oil droplets formed in water and that the volume fraction of oil = 0.1 and y = 0.01 N m-l, we obtain a specific surface area A of x lo5 m-' and the net surface free energy needed to create that surface Ay = kJ rnm3 In practice, we need about 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 immediate most essential one, which is to prevent the formed This will be recoalescence of the newly drops discussed further on We will consider first the break-up of This can be achieved in laminar flow due to shear drops inertial effects stresses, or in turbulent flow, where (pressure fluctuations) are predominant, although shear For inertial stresses may be of importance in some cases for instance caused by ultrasonic effects due to cavitation, refer earlier review; since, some new waves, we to our literature has appeared (e.g Li and Fogler, 1978; Reddy and Fogler, 1980) DROPLET BREAK-UP IN LAMINAR FLOW flow field equals The stress exerted on a drop in a laminar gradient and qC the viscosity of slcG, where G is the velocity This is counteracted by the the continuous phase stress Laplace pressure and the ratio is called the Weber number: We = q, G r / Y Principles of emulsion formation 335 We,, Fig number for disruption of critical The Weber droplets in simple shear flow (curve, results by average resulting for the Grace, 1982) and size in a colloid mill (hatched area, droplet 1990) as a function of the results by Ambruster, 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 has been well studied and ,some to the shear rate) results are shown as the curve in Fig These results agree well with theory Others have often found somewhat different results, WeGr showing the same trend but being at a slightly probably is that lower or at a higher level; the explanation 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) (2) shows that for a low viscosity of the continuous Eq phase, deformation of requires small drops extremely high if y = 0.005 N m-l and ?jC = velocity gradients For example, s-1 to obtain low3 Pa s (water), it would need G = 25*106 gradients can droplets of r = 0.2 urn (We_ = 1) Such velocity usually not be produced except over very small distances It is also seen that no break-up occurs for qo/qC > The explanation is roughly that the drop cannot deform as fast as the simple shear flow induces deformation Deformation time of stress a drop is proportional to its visaosity over the applied, time according that is %/rlcG, whereas the deformation to the flow would be l/G So if rlo/qC >> 1, the drop does but the deformed drop starts rotating deform to some extent, 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: it can deform to a consequently, 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 PIETER WALSTRA 336 In elongational flow shear, velocity gradient in the (no 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 a spread in droplet size will Anyway, 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 and concentration of type 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 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 boundary (which is a droplet 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 realize high becomes difficult to elongational velocity have been gradients These aspects 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 Principles of emulsion formation the fluctuations often are characterized by u', i.e the rootmean-square average difference between u and the overall flow If the turbulence is isotropic (which is more or velocity less the case if the Reynolds number is high and the length the flow can be characterized in a scale considered small), There is a according to the Kolmogorov theory simple way, they are the higher spectrum of eddy sizes, and the smaller so high that their velocity gradient (u'/x), until it becomes the eddies dissipate their kinetic energy into heat; the size scale and of the smallest eddies x0 is called the Kolmogorov droplets smaller than this are usually not greatly deformed are called energy-bearing eddies and Somewhat larger eddies For these they are mainly responsible for droplet break-up eddies we have u’(x) = c El/3 x1/3 p-1/3 where x is eddy size (or distance over which u' is considered), 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 main characterizing the volume, is the parameter turbulence The eddies cause pressure fluctuations of the order of p{u'(x)j2 and if these are larger than the Laplace 4y/x of a neighbouring droplet of diameter x, the pressure 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/sy3/5 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 holds (4) mostly 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 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 -0.4, slope of predicted by eq (4): here power density is proportional to consumption In homogenizer the the net energy 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 331 338 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 20 lJltm Tut-t-ax (batch 10 ) 0.5 - Fig 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 oilin-water emulsions produced In various machines From Walstra, 1983 (4) predicts that changing qc does not result In a change Eq 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 breakpresumably, the flow is similar to up: type of plane hyperbolic flow If this is the mechanism, resulting the relation is (5) If the situation is in between true inertial and true viscous forces, viscosity thus have some effect Increasing may viscosity also means decreasing Reynolds number, hence less intense turbulence, hence on average larger eddies, hence more Principles of emulsion formation shear This would also imply that the spread in conditions, for spread in droplet size, becomes larger hence the this has indeed been observed increasing viscosity, and the effect of viscosity of the (Walstra, 1974) Nevertheless, continuous phase on the resulting droplet size distribution is mostly slight this If a soluble polymer is added to the continuous phase, of causes some increase in qC, but it also has the effect smaller eddies are turbulence depression: especially the This results in a larger average removed from the spectrum 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 phase (q:, _in Effect of viscosity of disperse mPa s) on average droplet size (d,,, in pm) for various machines (turbomfxer, circles; ultrasonic generator, crosses; homogenizers, other symbols) From Walstra, 1974 (4) also predicts no effect of the viscosity of the Eq disperse phase on the resulting droplet size, and this is clearly not in agreement with experiments Fig 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 339 mETEIt 340 d max = c E-2/5 (y WhLSTRh lj,u'/4)3'5P-1'5 + This equation does not agree with the constant and virtually parallel Slope8 in Fig 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 In other stress 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, additional the term is of the same form as Laplace the 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"' - 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 are depicted in Fig It should be noticed 5; some results that eq (6) is different from the one given before: rdeI = the latter relation is based on the qDd/y (Walstra, 1983); 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 yields t time = eddy x of / u an ’ ( x eddy ) r x2/3 can fe3 be derived p1’3 from eq (3), which (7) several Results are shown in Fig 4, which gives emulsification process characteristic times throughout the the finally resulting drop (ever decreasing droplet size); It is seen size according to eq (4) would be about 0.3 pm time is mostly that for a relatively low v&, the deformation shorter than the life time of the eddies of the size of the which would imply that the pressure fluctuations last droplet, long enough for the droplets to be disrupted by these eddies this is not any more the case For higher droplet viscosities, This implies that larger eddies are responsible for droplet break-up Hence, for a larger droplet viscosity the resulting of the greater drops are on average larger and - because Principles of emulsion formation 341 spread in flow conditions for larger eddies - show more spread This has indeed been observed (Walstra, 1974) It in size quantitative theory along would be useful to develop a more these lines and, of course, test it droplet diameter (pm1 time specific Fig THE ROLE surface area (m-‘I Calculated characteristic times for deformation duration of surfactant, adsorption of droplets, during of eddies and rate of droplet encounters, emulsification process (decreasing droplet the from turbulence size) Calculated isotropic theory for E = 10" W m-', qc = mPa s, qn = 0.1 or F = 10 Pa s, cp = 0.2, m, = the cmc (corresponding mol m-j 2.5 umol m-', and y mN m-l) or initially (broken lines); y without surfactant = 35 mN m-l Surfactant is sodium dodecyl sulphate OF THE SURFACTANT During emulsification three main processes occur: Droplets are deformed and possibly broken up and adsorbed onto the Surfactant is transported to deformed and the newly formed droplets Droplets encounter each other and possibly coalesce It these processes occur should be realized that simultaneously and also that they each occur numerous times during emulsion formation, which implies that a steady state is not necessarily reached In other words, if emulsification would be continued, smaller droplets may possibly result Of fairly course, conditions change during emulsification and a PETER WALSTRA 342 obvious change is that area - the concentration - due to the increasing droplet surface of surfactant in solution decreases The surfactant has two main roles to play: it lowers interfacial tension, thereby facilitating droplet break-up: and it prevents (to a varying degree) recoalescence Moreover, if surfactant concentration is high and the resulting interfacial tension very low, it may under some conditions cause nspontaneous emulsification" due to strong the interfacial tension gradients induced Such a droplet break-up without putting in much mechanical only of energy is importance in the earlier stages of emulsion formation and has little to with the final droplet size obtained, unless emulsification is achieved by simple shaking or when we come into the realm of microemulsions These aspects will not be considered here Different surfactants lower y to a different degree and this should affect the final droplet size according to eq (2) or For a surfactant giving a lower y less energy is thus eq.(4) needed to obtain a certain droplet size As seen in Fig 5, obtained in the predicted relations are indeed roughly turbulent flow, provided that there is of surfactant Similar relations have been foundanin ezczloid mill (Ambruster, 1990) But there are some exceptions (e.g Ambruster, 1990) and the course of the curves in Fig is not readily explained Naturally, for a lower total surfactant concentration, speaking the the surface excess l? (loosely concentration of surfactant in the interface) during break-up will be lower and correspondingly the effective y higher, but that does not explain the different shapes of the curves droplet surface area/pm-’ “non-ionic.” IS- -G Ucrm -6 ‘Ol.?Ira~P l.O- -8 - IO o.s- -15 -30 0 I , 10 I [surfactantl/kg.mb3 Fig Effect of total surfactant concentration on the resulting average droplet size, other conditions Interfacial tension at high being equal; = 0.2 concentration for the non-ionic 2, caseinate 10 and the PVA's 20 mN.m", approximately Approximate results from various sources Principles of emulsion formation Fig Diagram of the Gibbs-Marangoni effect acting on two approaching droplets during emulsification Surfactant molecules indicated by Y See text There must therefore be differences in the degree of recoalescence .That recoalescence can occur, also in the case of polymer surfactants, has been shown in experiments where after emulsification the surfactant concentration is lowered emulsion is then again subjected to the same and the emulsifying treatment: the average droplet size is indeed observed to increase Prevention of coalescence of newly formed drops is presumably due to the Gibbs-Marangoni effect This is illustrated in Fig If two drops move towards each other (which happens very frequently) and if they still are they will acquire more insufficiently covered by surfactant, surfactant at their surface during their approach, but the amount of surfactant available for adsorption will be lowest where the film between the droplets is thinnest This leads to an interfacial tension gradient, r being highest where the film is thinnest The gradient causes the surface to move in the direction of the highest y or, in other words, surfactant moves in the interface towards the site of lowest surface excess This gradient causes streaming of the liquid along the surface (the Marangoni effect), thus will drive which the droplets away from each other stabilizing Hence, a self mechanism Note that the mechanism only works if the surfactant is in the continuous This phase must be the explanation of Bancroft's rule: when making an emulsion of oil, water and surfactant, the phase in which the surfactant is (best) soluble becomes the continuous one; and, in turn, the fact that Bancroft's rule is never violated (unless is extreme) is a indication strong that the Gibbs-Marangoni 343 DETER WALSTRA 344 effect is responsible for preventing recoalescence Note also that the mechanism only works in a non-equilibrium situation: after the available surfactant molecules are evenly distributed over the droplet surface (as in a "finished" emulsion) it does not act Then, the colloidal interaction forces primarily determine the coalescence stability Whether the Gibbs-Marangoni effect is strong enough depends on the Gibbs elasticity E of the film between the approaching droplets E is defined as twice the surface dilational modulus (E=2dy/dlnA, where A is surface area) and is given by (Lucassen, 1981) E= -2dy/dlnr 1+ (h/2)dm,/dr (8) where h is film thickness If E is high, the stabilizing mechanism works - because now a strong interfacial tension gradient can develop and if it is low, it may be insufficient A sample calculation for E as a function of the molar surfactant concentration in the continuous phase m, is given in Fig It follows that E Is higher if h is smaller and, for most situations, if m, is higher For most polymers, E is much lower than for small molecule surfactants This is because for the same mass concentration the molar concentration of a polymer is much lower, which also implies that IY (expressed in moles per unit surface area) is mostly low during emulsification, which, in turn, causes -dy/d lnr to be almost zero In fact, the values of -dy/d 1r-C obtained from experimental results will be too high, because these have been obtained at equilibrium conditions f (mN.m-‘I Fig Effect of sodium dodecyl concentration of sulphate in the liquid on the Gibbs elasticity of a film of urn thick (after Lucassen, 1981) The broken line roughly indicates the relation for a mixture of surfactants From Walstra, 1989 Principles According to state for approximation Yo - of emulsion formation and Benjamins (1982) in an interface de Feijter surfactants given by 345 the is equation of in first (9) Y =I-RT/(l 8)2 meaning and is the where yO is y for l? = 0, RT has its usual surface fraction covered by surfactant, e-ggiven by nnr', where n is the number of molecules per unit surface area and r a polymer molecule, their radius If say a protein, is adsorbed it changes conformation, thereby commonly its increasing the effective r, thus increasing 8, thus decreasing effect may be considerable (de Feijter and Benjamins, Y: the the magnitude of the Gibbs elasticity, 1982) Consequently, and thereby the extent to which recoalescence is prevented, on the time scale of the rearrangement of the will depend molecule in interface This dependence Will polymer the polymers, undoubtedly but at present no vary among experimental results seem to be available In the author's this effect and the molecular weight of the polymer opinion, may be the main variables causing differences among polymer in the resulting average droplet size, if the surfactants polymer is present in a relatively low concentration If its "equilibrium" concentration is high, value of y will be the determinant, and differences polymers in resulting among droplet size are indeed far smaller; see Fig It is consider needed useful to the time for the also surfactant to reach the droplet surface, This not =&I%* at the prevailing conditions of very determined by diffusion; high velocity gradients or very intense turbulence, transport droplet is almost towards the entirely determined by convection (Levich, 1962) This implies, in author's the that experiments in which the decrease in surface opinion, tension at a macroscopic surface above a solution of the surfactant is measured as a function of time, are irrelevant emulsification to That correlations are sometimes found between the rate of lowering y and the effectivity of the surfactant in producing small droplets, is presumably due to the fact that high molecular weight surfactants diffuse more slowly to the interface in the tests performed, while they also give rise to a relatively low Gibbs elasticity under the conditions of emulsification The actual situation may be more complicated because of the association of many surfactants in solution, especially the formation of micelles It may be that in some cases the rate of dissociation of individual molecules from a micelle is rate determinant; on the other hand, it cannot be ruled out that micelles as such collide with the droplet, considering the strong inertial forces in turbulent flow We will here only consider free molecules being transported by convection and we then obtain approximately in laminar flow =ad, and in ~20 turbulent r/dm, flow G (loa) 346 PIETER WALSTRA T rd - 10 I' II,"~ / d m, @I2 (lob) Some results are given in Fig It is seen that in turbulent flow, 'cadsis definitely longer than fdci, the more so as the droplets become smaller and for surractant concentration Similar relations hold f% l~~~~ification in laminar flow Consequently, during droplet break-up r will be lower and r higher than their "equilibrium" values This points to the Gibbs-Marangoni effect being essential and also to a situation in which break-up and coalescence go along for some time until the smallest droplet size is attained: even then, break-up and coalescence presumably go on, balancing each other Fig also gives some results for the average time elapsing before a droplet encounters another one, assuming them to be randomly oriented throughout the available volume The relation is in isotropic turbulence ‘cnc tl d= l p1'3 / 15 E1'3 (11) It is seen that for high and small droplets, T,,, becomes (much) shorter than 'G,~ This certainly points to coalescence then becoming important Some authors hold that break-up would be a first order rate process and coalescence second order, and that the change in the number of globules N would be given by dN/dt = K,N - K,N', but such a relation is usually not in agreement with experimental results In the authors opinion, most of the recoalescence occurs with newly formed drops, that probably originate from one parent drop, and are thus close to each other anyway In other words, for these drops r_ is even shorter than shown in Fig log (d,/pm) -0.2 -0.4 1.4 loq(pHIPa) Effect of homogenizing pressure the (P) on resulting average droplet size (a,,) when varying fraction of oil (indicated on the the volume continuous phase (a curves) and leaving the protein solution) the same From Walstra, 1988 0.6 Fig Principles of emulsion formation Nevertheless, at higher volume fractions, recoalescence is probably more important Fig gives some results from the author's laboratory (Walstra, 1988) Qualitatively, the higher average droplet size at a higher 4, and the relatively larger effect of for a higher power density, are probably due to - the smaller amount of surfactant available per unit surface this causes a higher effective y and a lower area created: Gibbs elasticity (more coalescence); - the higher encounter frequency of droplets, particularly of droplets onto which yet little surfactant has adsorbed: this causes more frequent coalescence; - turbulence depression, causing droplet break-up to be less efficient CONCLUSION The break-up of drops in laminar and turbulent flow is reasonably well understood, although quantitative explanation of the effect of the viscosity of the disperse phase in the case of turbulence would need further study It appears as if droplet disruption due to cavitation (in an ultrasonic generator) is much like that in turbulent flow To achieve a high efficiency it is necessary to dissipate the available mechanical energy in the shortest time possible The role of the surfactant is qualitatively understood, but quantitative relations are hardly available, especially for polymer surfactants, like proteins The development of simulation models for adsorption of surfactant and for the phenomena occurring during a close approach of droplets, would be very useful The role of the Gibbs elasticity needs further study, especially its dependence on time scale (of the order of microseconds) for different surfactants LIST : E G m, P r I ie X Y r E rlc tlD P t cp OF FREQUENTLY USED SYMBOLS constant (-) droplet diameter (m) Gibbs elasticity of film (N m-l) velocity gradient (s-l) concentration of surfactant (mol mm3 or kg m-') pressure (Pa) radius (m) average velocity in turbulent eddy (m s-l) Weber number (Pa Pa-') distance, such as eddy size (m) interfacial tension (N m-l) surface excess (mol rnm2) power density (W rnm3) viscosity of continuous phase (Pa s) viscosity of disperse phase (Pa s) mass density (kg rnm3) characteristic time (5) volume fraction of disperse phase (m3 m-') 347 PIETERWALSTRA 348 REFERENCES zum kontinuierlichen Ambruster, H (1990) Untersuchungen Emulgierprozef3 in Kolloidmtihlen unter Berucksichtigung spezifischer Emulgatoreigenschaften und der Strbmungsverhaltnisse im Dispergierspalt Ph.D University of Karlsruhe dissertation, Chin, H.B and C.D Han (1979) Studies on droplet deformation in extensional and breakup I Droplet deformation flow J Rheol 23, 557-590 Chin, H.B_ and C.D Han (1980) Studies on droplet deformation and break-up II Breakup of a droplet in nonuniform shear flow J, Rheol 24, l-37 Davies, J.T (1972) Turbulent Phenomena Academic Press, New York related to Davies, J.T (1985) Drop sizes of emulsions turbulent energy dissipation rates Chem Eng sci 40, 839-842 de Feijter, J.A and J Benjamins (1982) Soft particle model of compact molecules at interfaces J Colloid Interface Sci 90, 289-292 phenomena in high viscosity Grace, H.P (1982) Dispersion immiscible fluid systems and application of static mixers as dispersion devices in such systems Chem Eng Commun l4, 225-227 study of Han, C.D and K Funatsu (1978) An experimental droplet deformation and breakup in pressure-driven flows through converging and uniform channels J Rheol 22, 113-133 Hydrodynamics PrenticeLevich, V.G (1962) Physicochemical Cliffs Hall, Englewood Li, M-H and H.S Fogler (1978) Acoustic emulsification Part Breakup of the large primary oil droplets in a water emulsion J Fluid Mech 88, 513-528 properties of free liquid films Lucassen, J (1981).Dynamic Chemistry of Surfactant and foams In: Physical Ed.), Dekker, New Action (E.H Lucassen-Reynders, York, pp 217-266 stability of Reddy, S.R and H.S Fogler (1980) Emulsion acoustically formed emulsions J Phys Chem 84, 1570-1575 Schubert, H and H Ambruster (1989) Prinzipien der Herstellung und StabilitSit von Emulsionen, Chem.Ing -Tech 61, 701-711 Torza, S., R.G Cox and S.G Mason (1972) Particle motions in and steady sheared suspensions XXVII Transient deformation and burst of liquid drops J Colloid Interf Sci 38, 395-411 of rheological properties of Walstra, P (1974) Influence both phases on droplet size of O/W emulsions obtained by homogenization and similar processes Dechema Monogr 77, 87-94 of Emulsions In: Encyclopedia Walstra, P (1983) Formation Vol.1 Basic Theory (P of Emulsion Technology Becher, Ed.), Dekker, New York, pp 57-127 Principles of emulsion formation Walstra, P (1988) The role of proteins in the stabilisation of emulsions In: Gums and Stabilisers for the Food Industry (G.O Phillips et al., Eds.), IRL Press, Oxford, pp 323-336 Walstra, P (1989) Principles of foam formation and stability In: Foams: Physics, Chemistry and Structure (A.J Wilson, Ed.), Springer, London, pp 1-15 349 [...]... Encyclopedia Walstra, P (1983) Formation Vol.1 Basic Theory (P of Emulsion Technology Becher, Ed.), Dekker, New York, pp 57-127 Principles of emulsion formation Walstra, P (1988) The role of proteins in the stabilisation of emulsions In: Gums and Stabilisers for the Food Industry 4 (G.O Phillips et al., Eds.), IRL Press, Oxford, pp 323-336 Walstra, P (1989) Principles of foam formation and stability In:... von Emulsionen, Chem.Ing -Tech 61, 701-711 Torza, S., R.G Cox and S.G Mason (1972) Particle motions in and steady sheared suspensions XXVII Transient deformation and burst of liquid drops J Colloid Interf Sci 38, 395-411 of rheological properties of Walstra, P (1974) Influence both phases on droplet size of O/W emulsions obtained by homogenization and similar processes Dechema Monogr 77, 87-94 of Emulsions... Acoustic emulsification Part 2 Breakup of the large primary oil droplets in a water emulsion J Fluid Mech 88, 513-528 properties of free liquid films Lucassen, J (1981).Dynamic Chemistry of Surfactant and foams In: Physical Ed.), Dekker, New Action (E.H Lucassen-Reynders, York, pp 217-266 stability of Reddy, S.R and H.S Fogler (1980) Emulsion acoustically formed emulsions J Phys Chem 84, 1570-1575 Schubert,.. .Principles of emulsion formation Fig 6 Diagram of the Gibbs-Marangoni effect acting on two approaching droplets during emulsification Surfactant molecules indicated by Y See text There must therefore be differences in the degree of recoalescence .That recoalescence can occur, also in the case of polymer surfactants, has been shown in experiments... fact, the values of -dy/d 1r-C obtained from experimental results will be too high, because these have been obtained at equilibrium conditions f (mN.m-‘I Fig 7 Effect of sodium dodecyl concentration of sulphate in the liquid on the Gibbs elasticity of a film of 1 urn thick (after Lucassen, 1981) The broken line roughly indicates the relation for a mixture of surfactants From Walstra, 1989 Principles According... shorter than shown in Fig 4 log (d,/pm) 0 -0.2 -0.4 1.4 loq(pHIPa) 8 Effect of homogenizing pressure the (P) on resulting average droplet size (a,,) when varying fraction of oil (indicated on the the volume continuous phase (a curves) and leaving the protein solution) the same From Walstra, 1988 0.6 Fig 1 Principles of emulsion formation Nevertheless, at higher volume fractions, recoalescence is probably... role of the surfactant is qualitatively understood, but quantitative relations are hardly available, especially for polymer surfactants, like proteins The development of simulation models for adsorption of surfactant and for the phenomena occurring during a close approach of droplets, would be very useful The role of the Gibbs elasticity needs further study, especially its dependence on time scale (of. .. C.D Han (1979) Studies on droplet deformation in extensional and breakup I Droplet deformation flow J Rheol 23, 557-590 Chin, H.B_ and C.D Han (1980) Studies on droplet deformation and break-up II Breakup of a droplet in nonuniform shear flow J, Rheol 24, l-37 Davies, J.T (1972) Turbulent Phenomena Academic Press, New York related to Davies, J.T (1985) Drop sizes of emulsions turbulent energy dissipation... the rate of lowering y and the effectivity of the surfactant in producing small droplets, is presumably due to the fact that high molecular weight surfactants diffuse more slowly to the interface in the tests performed, while they also give rise to a relatively low Gibbs elasticity under the conditions of emulsification The actual situation may be more complicated because of the association of many... Feijter, J.A and J Benjamins (1982) Soft particle model of compact molecules at interfaces J Colloid Interface Sci 90, 289-292 phenomena in high viscosity Grace, H.P (1982) Dispersion immiscible fluid systems and application of static mixers as dispersion devices in such systems Chem Eng Commun l4, 225-227 study of Han, C.D and K Funatsu (1978) An experimental droplet deformation and breakup in pressure-driven