Dec., 1963
RHEOLOGICAL PROPERTIES OF EMULSIOXS
constant over a considerable composition range corresponding to adsorption of a monolayer a t the surface.’ As seen in Fig. 3, a linear relation does exist in this case for mole fractions less than 0.084 (because of the similar atomic weights, the mole fraction is approximately equal to the weight fraction). Analysis of the graph for this region yielded an excess surface concentration, rT1,of 1.78 X 10-lo mole/cni.2. The limiting concentration expected in a close-packed monolayer of thallium atoms with an atomic radius* of 1.99 8. is estimated to be 12 X 10-lo mole/cm.2. A comparison of these values suggests that either an imperfect monolayer is formed or that the assumption of close packing in the monolayer is incorrect. Thus, at concentrations less than 8.5 mt. %, the thallium appears to1 concentrate in a surface layer on the mercury with an accompanying reduction in the surface tension of the amalgam. The increase in surface tension for amalgams with the thallium content (7) W. D. Kingery, “Property Measurements a t H I F Temperatures,” ~ John Wiley and Sons, Inc., New York. N. Y . , 1959, p. 370. (8) N. A. Lange, “Handbook of Chemistry,” Tenth Ed., McGran-Hi11 Book Co., Inc., Xew York, I‘J. Y . , 1961, p. 108.
2531
greater than that of the eutectic composition is more difficult to explain. However, if the components form compounds which are less stable in the surface layer than in the bulk, the surface tension of the mixture may be higher than that of the pure component^.^,^^ It does appear that a compound (Hg,TI,) is formedzs3 which may be concentrated in the bulk of the amalgam. Formation of the compound would remove thallium atoms from the surface layers and thereby raise the surface tension values. The data for mercury-indium amalgams giwn in Table I1 are insufficient for detailed interpretation. As in the case of the mercury-thallium system, it is possible that the formation of a compound is responsible for the significant rise in surface tension with increasing indium content of the mercury-indium amalgams. Acknowledgment.-The authors express their appreciation to Dr. Robert E. Bunde for his interest and many valuable comments. (9) W.J. Moore, ibid., p. 503. (10) A. Bondi, Chem. Rev., 52, 417 (1953).
CHANGES IN THE RHEOLOGICAL PROPERTIES OF EMULSIOKS ON AGING, AND THEIR DEPENDENCE ON THE KINETICS OF GLOBULE COAGULATION BY P. SHERMAN T . Tl’all and Sons, Ltd., Acton, London W . S, England Received February I S , I963 Viscosity changes a t high rates of shear have been investigated for water-in-liquid paraffin emulsions and liquid paraffin-in-water emulsions stabilized by nonionic emulsifying agents and aged a t 20’. All the emulsions showed a narrow globule size distribution. The fall in viscosity with time is controlled by the increase in mean globule size, D,. D, exerted the same effect on the viscosity of aged emulsions as on the viscosity of freshly prepared emulsions of the same composition. Globule coalescence displaces into the continuous phase that area of the adsorbed emulsifier layer around adjacent globules where they make contact. The rate of increase in D, and the viscosity-& relationship for fresh emulsions are determined readily, and from these data viscosity changes over long aging periods can be predicted. The experimental values of the minimum veloc’ity gradient required to deflocculate globules completely in both types of eomulsionsuggest a value 4 X 10-13 erg for the van der TTaals constant in all cases, and a separation of -60 A. between flocculated globules in the liquid paraffin-in-water emulsions. The globules in the liquid paraffin-in-water emulsions were negatively charged, the magnitude of their mobility suggesting that stability is at least in part due to electrical repulsion forces.
Introduction When emulsions are aged, substantial changes are observed in the degree of dispersion of the discontinuous phase before it separates out in bulk. The accumulated data suggest the following sequence of events: globule flocculation leading to the formation of aggregates, thinning of the film of continuous phase separating adjacent globules withiii the aggregates, surmounting of the energy barrier, and finally globule coalescence. The net result is a progressive increase in globule size and, since emulsions are rarely monodisperse, the globule size distribution may become progressively broader also. It is nom well established that globule size and size distribution influence the rheological properties of emulsions,l so that the latter would be expected to change also when emulsions are aged. Freshly prepared emulsions exhibit an inverse relationship between viscosity a t such high rates of shear, (1) P. Sherman, Proc. Srd Intern. Congr. Surface Actzuzty, 2 , 696 (1960).
vm, that viscosity remains constant with further increase in rate of shear and mean globule size, D,, provided that their globule size distributions are not too broad.’I2 When the globules suffer little distortion under these conditions, which depends on globule size, the physical properties of the adsorbed film of emulsifier around the globules, and their distance of separation, this influence of D, on vm may be observed at volume concentrations of disperse phase (cp) as low as 0.15. These observations suggest a possible approach to the study of viscosity changes in emulsions when aged. Provided the only change involved is a gradual increase in D,, there being no appreciable change in the limits of globule size distribution, the decrease in v m as D, increases should be predictable from the vm-Dnlcurves for fresh emulsions of the same formulation, since the rate of increase in D ,can be determined readily from the kinetics of globule coale~cence.~The present study (2) P. Sherman, Food Technol., 1 6 , 394 (1961). (3) M. van den Tempel, Proc. Bnd. Intern. Congr. Surface Actiazty, 1, 439 (1957).
P. SHERMAN
2532
proves the validity of this conclusion. Accelerated aging by high speed centrifugation or exposure to elevated temperatures may lead to changes in D, that are quite different from those observed duriiig normal aging. The present investigation has not been extended to changes in emulsion viscosity a t very low rates of shear, 17, since 7-D, relationships are complicated by the superimposition of aggregation effects. Under these low shearing conditions an aged emulsion exhibits a much higher degree of globule flocculation than when it is first prepared. Furthermore, the contribution of these phenomena to r increases with aging time, so that the q-Dm curve for a fresh emulsion cannot be used to obtain information about changes in 11 on aging without precise knowledge of the rate of aggregation and its effect on 7. Experimental Preparation of Emulsions.-Deionized water (Elgastat Portable Deioniser) and liquid paraffin (b.p. medicinal grade; 1.56 poise viscosity a t 25”) were used throughout as the aqueous and oil phases, respectively. Sorbitan monooleate was the emulsifying agent used for the water-in-oil (w/o) emulsions, and sorbitan monolaurate for the oil-in-water (o/w) emulsions. These emulsifying agents were used in the commercially available form (Honeywill-Atlas Ltd.) at 1.5% (wt./wt.) concentration without further purification. They are stated to be of “at least 99% purity.” Sorbitan monooleate dissolved readily in the oil phase. Sorbitan monolaurate did not dissolve in the aqueous phase, but it dispersed readily on agitation. The emulsions were prepared by stirring followed by passage through a valve homogenizer. Emulsions were prepared over the p range 0.18-0.70 approximately with sorbitan monooleate, and 0.43-0.74 with sorbitan monolaurate. Aging was carried out at room temperature (67-68’F.) over several weeks in stoppered bottles. Determination of Mean Globule Size.-Immediately after was deterpreparation the mean volume globule diameter (Dm) mined. Further determinations were made at frequent intervals during the course of aging. The diameters of approximately 2000 globules were determined microscopically for each sample after dilution with the appropriate medium. D, was calculated from the relationship
D,
+-
-
dnlDla n&3 - - - n A 3 = nl n2- - n,
=
+
-
d c Zn
-
where nl, n ~- , - n5 are the numbers of globules with diameters D1, Dz, - - D,, respectively. The liquid paraffin-in-water emulsions were mixed gently with at least an equivalent weight of glycerol prior to sampling to reduce Brownian motion. For several emulsion samples D,,, was calculated indirectly also from counts of the number of globules in a preselected dilution of samples-6 introduced into a haemocytometer cell. These dilutions were far greater than those employed in the direct measurement of globule diameter, viz., 1000 or more times, depending on p, as compared with 10-20.
-
cp=-
aNDm3 6
(2)
Vol. 67
Inhomogeneity of Emulsion Samples.-The size distribution of globules within an emulsion is represented normally by an integral, or differential, distribution curve. Many attempts have been made to define such data by a single distribution equation. A review of this work led to a linear equation containing two parameters6
lnv, = l n v
+ x-z -x-z
(3)
where vz is the total volume below diameter x, v is the total volume of disperse phase, X i s the diameter of the largest globule, z represents the variable globule diameter, and 2 is the characteristic diameter. From the linear plot of In v, against x the two parameters 2 and X can be calculated. Application of eq. 3 to the present data indicated an appreciable deviation from linearity at small values of x (< 2 p). Size distribution data have been summarized, therefore, in terms of an inhomogeneity factor. The inhomogeneity, I , is defined as “the mean square deviation of the number distribution curve with respect to the diameter.” 7
I =
Jo’” (D - DJ2nldl Jo’- nldl
(4)
where D is the globule diameter, Dn is the number average diameter ZnDIZn, and nl is the rate of change in the number of particles with their diameter. On expansion eq. 4 reduces to
I = an/a - On2
(5)
where a, is the number average area Zna/Zn. I was calculated for all fresh and aged emulsions. Emulsion Viscosity.-The flow properties of the emulsions were investigated over a range of shear rates extending to 2000 sec.-l a t 21.0 i 0.1”. A variable pressure capillary viscometer,* based on that originally designed by Bingham and Green, was used to examine the w/o emulsions. A single capillary, of radius, R , 0.041 em., and length, L, 1.916 em., sufficed t o cover the rangeof viscosities encountered. The viscosities of the o/w emulsions were determined with a direct reading coaxial cylinder Couette viscometer (Portable Ferranti) in which the gap width could be varied from 0.075 to 0.455 cm. Sufficient emulsion of each type was prepared to allow a fresh sample to be taken every time a viscosity was determined. Sormally, about 2 kg. of fresh emulsion was prepared. The emulsions ranged from R’ewtonian to non-Kewtonian systems exhibiting pseudoplasticity, according to (o. For the emulsions showing non-Newtonian flow, the viscosity values adopted for correlation with D, were those at such rates of shear that further increase in shear rate did not alter the viscosity. The 7- values were calculated from
du -1 --_ qm
(6)
dS
where v and S are velocity gradient and stress, respectively.
S (at the capillary wall)
=PR
2L
(7)
where P is the applied pressure. iiccording to R.looneyQ
~
that D, = 3 v’6 p/N where N is the number of globules per cubic centimeter of emulsion. I n general, good agreement was obtained between the two methods for estimating D,. Direct measurement of globule diameter was preferred, however, since it was difficult to ensure that all globules had been accounted for when focusing at different depths of the haemocytometer cell in the alternative technique. Slight discrepancies then produced far greater inaccuracy in D, than by direct measurement. The most concentrated oil-in-water emulsions (p = 0.73) contained some globules with a multiple phase structure. 60
(4) A. S. C. Lawrence a i d 0. S . JIills, Divcussions Fnradag Sac., 18, 08 (1954). ( 5 ) 11. F. Cheesman, Biochem. .I., 160, 687 (1951). (6) N. Schwarz and C . Bezemor, Rollaid-Z., 146, 139, 14G (1906). (7) II. H. G . Jellinek, J . Sac. Chern. Ind., 69, 225 (1950). (8) A. de Waele and G. Dinnis, Phusics, 7, 426 (1935). (9) M. Rlooney, J . nheol., 2, 210 (1931).
Dec., 1963
RHEOLOGIC-4L PROPERTIES O F
EMULSIONS
2533
where Q is the volume (cc.) of sample extruded per see., so that
By drawing tangents at selected values of P on the P-Q curve, a second curve is derived that is related to the S-v plot, and which is linear at high values of v. The gradient of this latter portion, G is proportional to l / ~ - .
1
-=
FG
(10)
Vm
where
K (0.014) is the factor for converting flowmeter readings into units of Q , and CT is the density of mercury. Microelectrophoresis Cell.-The charge on the oil globules in freshly prepared o/w emulsions stabilized by sorbitan monolaurate was investigated using a cell based on the design of Smithand Lisse.'o It consisted of two equal sized Perspex compartments linked together by two glass capillaries of widely different diameters. These capillaries were selected so that the return electroosmotic flow of the aqueous phase of the emulsions took place along the wider capillary. The rate of flow of the oil globules along the axis of the narrower capillary, using the appropriate depth of focuts calculated from Henry's equation," was the true electrophoretic velocity. All tests were made a t 67-68°F. A field strength of 2.1 v./cm. was found to be suitable. Dilutions were prepared by mixing samples of each original emulsion with a further volume of its aqueous phase. A minimum number of 20 readings was taken for each emulsion dilution before the direction of flow was reversed and a further similar number of readings taken.
Results Changes in Emulsion Viscosity on Aging.-The rheological properties of the emulsions changed substantially on aging. The upper limit of globule size distribution in the w/o emulsions never exceeded 5.0 p, with a t least 80% of the total number of globules in any one sample not exceeding 1.5 p in diameter. For the o/w emulsions the upper limit never exceeded 18.0 p , with at least 810%of the total number of globules in any one sample not exceeding 4.0 p in diameter. I increased with aging time for both types of emulsion. The w/o emulsions showed very much lower values of I , and also slower rates of increase in I with time, than the o/w emulsions (Fig. 1 and 2 ) . With increasing rate of shear the aggregates of globules formed in an unaheared emulsion gradually disintegrate until the globules are redispersed. The mean distance (a,) then separating globules in the w/o emulsions can be calculated from
20
10
0
30 40 50 60 Aging period, days.
of change in the inhomogeneity of w/o emulsions.
Fig. 1.-Rate
8.0 i;
A7.0
.*
i=
f;6 . 0 4 0 H
5.0;
4.0f i_100
0
Fig. 2.-Rate
6.0
200
300 400 Aging period, hr.
.
4.0.
-e
0
3.0
0
(IO) >I. E. Smitlr and M. W. Lisse, J. Phgs. Cham., 40, 399 (1936). (11) D. C. Henr3, J. Chem. Soc., 977 (1938).
500
of change in the inhomogeneity of o/w emulsions.
2.0'
where pmaxis the optimum volume coiicentratioiz of disperse phase that can be incorporated in the emulsion. 1x1 this instance tpmctx corresponds to the theoretical value for equal sized spheres (0.74) arranged in a hexagonal lattice structure. By plotting the viscosity data so as to show the illfluence of a, on qpoll (vm/qO) it is clear that the change iii qrel resulting from an increase in a,,, is the same for both Ireshly prepared arid aged w/o emulsions. The
70
60
m w .
0.1
0.2
0.3
0.4
0.5 am,P. vrel for
0.6
0.7
Fig. 3.-The influence of a,,, on aged w/o emulsions: X, freshly prepared emulsions; 0, aged emulsions.
progressive increase iii D, is, therefore, the only aging process exerting a measurable effect on vlrl. Statistical analysis of these data indicates an equation of the form
Invrei
=
1.36 - 1.09 a,
(13)
where 1.36 = b r ~ q , ~atl tp +. pmax,thc rcgression coefficient ( r ) = 0.904, the standard deviation of scatter (a,) = 0.074, and the 95% confidelice limits = 10.15
P. SHERMAN
2534
VOl. 67
46/0 '
is ail overlap of hydrodynamic disturbances generated by adjacent globules, these deformations may produce \ noticeable increases in rrel since it is well established 40 that prolate ellipsoids show a higher vre] than the same volume concentration of spherical particles. A relationship of the eq. 13 type was derived for some of the o/w emulsion data (cp = 0.4352 and 0.6339), the approximate a, values being calculated from eq. 12. The true qo values of these emulsions, in which sorbitan monolaurate passes from the water phase to the oil phase during emulsification, were estimated by analysis of coagulated emulsion^.'^ The I A? viscosity data for both freshly prepared and aged einulsions were found to coincide over this range of p (Fig. 4). When the plot was extended to include the data for the most concentrated emulsions, the experimentally determined rrelvalues fell well beIow those calculated, the discrepancy increasing with aging time. Globules with a multiphase structure were found in these latter emulsions. It is possible that for these emulsions pmax should have a somewhat lower value than 0.74. I n the extreme case it mould be -0.53, i.e., the theoretical 0 0.1 0 . 3 0.3 0.4 0.5 0.6 0.7 0 . 8 0.9 pmaxfor prolate ellipsoids. If this assumption is coram, B. a, should be rect, the11 for any particular value of rZe1, Fig. 4.-The influence of a, on vrel for aged o/w emulsions: smaller than the value calculated, as was observed. X, freshly prepared emulsions; 0 , aged emulsions. The Influence of Olobule Flocculation on the Rheo(units of Invrel). Thirty-nine of the 41 results available logical Characteristics of Aged Emulsions.-The aggrefell within the 95yoconfidence limits. gation of globules was less marked in the o/w emulsions The viscosity data for the o/w emulsions are more than in the w/o emulsions. For both types of emulsion difficult to interpret. It is unlikely that the globules the number of globules in any single aggregate increased are surrounded by a plastic solid film,' so that there is with aging time. no barrier to the transmission of normal and tangential The thickness of the diffuse double layer (l/x) in stresses across the interface to the internal phase fluid. w/o eniulsions is several p, so that the potential energy I n dilute emulsions this can lead to circulation of fluid of repulsioii ( V R )decreases much more slowly with inwithin the globules, and also to globule deformation at creasing separation of the globules (So)than in o/w sufficiently high rates of shear.12 The former effect, emulsions. I n calculating VR for w/o emulsions it is which may reduce the emulsion viscosity, depends on necessary, therefore, to allo~vfor the superimposed the ratio qJq0 where q i is the viscosity of the internal interaction effects between several globules in close phase. For o/w emulsions this ratio is very high (>125, proximity'* rather than consider the repulsive forces if one allows for migration of emulsifier from the conbetween two isolated globules, which normally suffices tinuous phase to the internal phase on emul~ification~~) for o/w emulsions. so that there should not be any appreciable circulation The amended expression for VR in oil continuous of fluid within the globules. medial4 allows for the interaction between twelve globProvided globule deformation under shear is small, it ules situated on a spherical shell of radius 81, where can be calculated from12
IB
where 1 11 and B are the dimensions of ihe major and minor axes. I n the present study D, ranged from 3.5 to 5.7 p , y = 2.86 dyne~/cm.-~, so that M B/M B varied from 3.5 X to 5.7 X when v = 1000 see.-'. This corresponds t o an increase in M / B of 0.9-1.27,. It should be remembered, however, that some globules ranged in size up to 18.0 p, and that their number in relation to the total number of globules in any emulsion increased as p increased, and also with the aging period. Consequently, a very small, but progressively increasing, percentage of the globules underwent an increase in M / B extending up to about 3.5Yo. Deformations of this magnitude would presumably exert little effect on vrel in dilute emulsions, where urnis large. I n more coiicentrated emulsions, such that there
-
+
(12) G . Taylor, Proc. Roy. Soc. (London), A146,501 (1934). (13) P. Sherman, paper presented a t the British Society of Rheology's
symposium, "Rheology of Emulsions," October, 1962.
Taking ail average value of 0.53 for p, R, = 2.24 p. For very small values of Ho, the potential energy of attraction (VA) is calculated from
v*=-- AD, 24Ho where A is the van der Waals constant. The calculated values of V Arequire correction for retardation effects.15 The energy barrier to flocculation, V , for the w/o emulsions is found to be 2 kT when Dm = 2.0 p, and 1 kT when Dm = 1.0 p, when A is taken as 10-la erg (Fig. 5). Irrespective of the value chosen for A the magnitude of V is too small to prevent flocculation. Also, the increase in on aging will not retard globule flocculation to any significant extent. (14) W. Albers and J. T. G. Overbeek. J . Colloid Sei., 16,489, 510 (1960).
(15) J. T. G. Overbeek, "Colloid Science," Vol. I, H. R. Iiruyt, Zd.. Elsevier Publishing Co., Amsterdam, 1952.
Dee., 1963
RHEOLOGICKL PROPERTIES OF EMULSIOSS
The average mobility of oil globules in the o/w emulsions (cp = 0.4352) was -Z&/sec./v./crn. I n the absence of emulsifies oil globules dispersed in water show a mobility of -- 4.35 p/sec./v./cni. a t 25°.16 The relatively high mobrlity of the oil globules in the o/w emulsions may be due to the 0.5% soap impurity coiitained in the sorbitan monolaurate. By means of the standard equations for V Rand VA as applied to aqueous continuous media,16 the net potential energy barrier preventing close approach of the globules in o/w emulsioiis can be calculated, and also the distance separating oil globules in the aggregate. At the low concentration of soap involved, it is unlikely that the potential drop across the globule surface (#) exceeds the ( potential (35 mv.) by more than approximately 10%. Taking l / x = lo7 cm., A = erg, and # = 40 mv., the distance separating equal sized globules with D,n = 3.0-6.0 p is about 60 b. (Fig. 6). Even if one assJimes that # = 80 mv. this distance does not exceed 80 A.. Evaluation of the van der Waals Constant from Rheological Data.--When globules in an emulsion flocculate, part of the continuous phase is immobilized within the aggregates which form. Each aggregate behaves as if it had a volume greater than the sum of the volumes of the individual globules from which it is constituted,l7~ l8 and a t very low shearing stress it rotates about its center of mass like a single globule.1Q With increasing rate of shear, the aggregates break down, the final stage in this process involving basically the separation of residual pairs of globules. The globules separate when the van der Waals attraction is exceeded by the opposing hydrodynamic flow tension which tends to force the globules apart. The velocity gradient (v,,,,) whicli effects the deflocculatioii can be calculated14 provided the emulsions are reasonably monodisperse and the globules are not deformed.
Fig. 5.-Potential
M
kT (e'9s)
I
I
I Fig. 6.--Potential
energy curves for o/w emulsions.
TABLE I VALUES OF vmin CALCULATED FOR WATER-IX-LIQKID PARAFFIN EXCLSIONS STABILIZED WITH SORBITAY MOXOOLEATE vmln, see-.'--
,---
____ N =40&.-
F---
H
= 25
b.--
A =
A = 10-12 erg
x
5
2 0
A = 10 '2erg
io-ia erg
682 500 375
1.5
(19) R. R t . J. Xlanley and $. G. Mason, Cnn. J. Chem., 31, 763 (lY54). (20) >I. J. Vold, J . C o l h d Sa., 16, 1 (1961).
D,-30, Dm=60y
60
1.1
(1G) J. Powney avid L. J. IVood, T r x n a . Farndag Sor., 36, 57 (1940). (17) V. Vand. J . I'hus. Coiiofd Chem., 6 2 , 277 (1948). (18) J. Robinson, zbzd., 82, 1042 (1948).
energy curves for w/o emulsions.
1
Dm P
where H is the distance separating globules in the residual aggregate, and ox (-30") is the critical angle between the line joining the centers of the two globules and the direction of shear a t the time when the aggregate undergoes disruption. Table I gives some theoretical values of v,,,, calculated for the w/o emulsions for three selected values of D,,and two possible values of A. I n view of the influence of the adsorbed emulsifier layer on the attraction between globules,20it is unlikely that A will have a value higher than those quoted. The precise value of H is not known, so two possible values have been selected. One of these assumes that the c18 hydrocarbon chains of the sorbitan monooleate molecules are fully extended into the oil phase, while the lower value assumes a certain degree of kink. By comparing these data with the experirnental values of vn,in an approximate evaluation of A has been made. The experimentally determined values of Omin for moderately concentrated w,/o emulsions ( p = 0.2733
2535
332 238 185
5
A = 10
x
1%
erg
1690 1239 929
845 620 465
and 0.4703) lie within the range 750-1100 set.-' for = 1.1-2.0 p. No definite pattern was established for the influence of D, on vmln as the changes in D, were relatively small. The order of magnitude for A should be, therefore, 0.5 X 10-l2 to 2 X erg, depending on whether H = 40 A. or somewhat less. Previously it was shown that the globules in o/w emulsions of medium concentration deform only slightly when subjected to high rates of shear, so that it should be possible to calculate vmin for these systems from eq. 17. Table I1 shows v,in calculated for values of D, = 3.5-6.0 ,u a t selected values of A taking H as 60 and 80
D,
A.
TABLE I1 VALUESOF urnin CALCULATED FOR LIQVIDPARAFFIN-IN-WATER EMULSIONS STABILIZED WITH SORBITAN MONOLAURATE timrn.
H = 60 A =
Dm, A
= 10 I S 5 X 10
w
erg
erg
3 6 4 5 6.0
4621 3593 2937
2311 1797 1469
see.-I-
b.---
-----I€
A
1 0 - 1 3 A = 10 ' 2 5 X
I-
= 80
d
A = 13
= PI
!!
462 359 294
10-1d
--
A
=
10
el R
erg
el R
2599 2021 1652
1300 1011 826
260 202 165
1J
P.SHERMAN
2536
Vol. 67
Dt3 = Do3
8lcTqt +exp( - E / R T ) V
no
A
A
n
~=02?53
n
2.0
0
10
20
30 40 Aging period, days.
50
Fig. 7.-W/O emulsions-comparison of experimental and calculated changes in yrel on aging: 0,experimental data; A, calculated data.
30
I
(p-0.4352
0 1 0
10 15 Aging period, days.
5
20
Fig. 8.--O/W emulsions-comparison of experimental and calculated changes in v r p l on aging: 0,experimental data; A, calculated data.
The X u curves for the o/w emulsions (p = 0.4352) indicate that umin lies between 1000 and 1300 sec.-l, with vmln decreasing as D , increases. Taking H as 60 8.,ie., the position of the secondary minimum in the net potential energy curve (Fig. 6), A should be slightly erg. less than 5 X Kinetics of Globule Coalescence,-If one assumes that the rate of slow coalescence, C, is governed wholly by the probability of rupture of the thin film of continuous phase between flocculated globule^,^ and by the rupture of H bonds between molecules in the adsorbed emulsifier film
N,
=
N o exp(-Ct)
(18)
where No is the original number of globules per unit, volume and N t is the number after any aging time t. It follows that
I n D , = InDo
+ Ct/3
(19)
where D t and Do are the mean diameters a t zero tinit-! and after any aging time t, respectively. Since only a fraction of the collisions bctwceii colliding globules result in coalescence4
O
where k is the Boltzmann constant, T is the absolute temperature, and E is the energy barrier to coalescence whichdepends on the charge on the globules, the rheological properties of the emulsifier layer, etc. I n the development of eq. 19 and 20 it is assumed that E is independent of D,, and that C is independent 01" N . These conditions apply to only part of the present coagulation data. A complete analysis of the kinetics of globule coalescence associated with this study will not be presented here. Only those details which are relevant to the discussion are given. Many emulsions of both types did not coalesce a t a uniform rate throughout the whole of the aging period. An initial phase of rapid coalescence, which occasionally lasted for several days, was followed by a second phase of slow coalescence which extended over the remainder of the aging period. Some of the emulsions exhibited slow coalescence only. Rapid coalescence, in its present connotation, does not imply that all globules coalesced immediately after flocculation. It merely indicates a somewhat faster rate than for slow coalescence. In general, rapid coalescence was found only a t such large values of the total surface area that the adsorbed emulsifier molecules were unable to establish a fairly compact film around the globules. As the total surface area decreased due to coalescence, the molecules in the film packed more closely together and a more effective barrier to coalescence developed. These observations were subsequently confirmed by varying the emulsifier concentration and initial total surface area.21 This led eventually to the phase of slow coalescence with E = 6-7 kcal. mole-l. Those emulsions with a relatively smaller initial total surface area showed only slow coalescence. Both the w/o and o/w emulsions creamed to no significant extent during the first few days of aging so that rapid coalescence cannot be attributed to this phenomenon. Equations 19 and 20 apply only for slow coalescence. During rapid coalescence the globules coalesce more rapidly than is suggested by these equations since many more factors are involved. Because of this the Dt3-t or In D-t plots should be continued until such time as their linearity is well established if changes in vrel are to be predicted accurately. This should take oidy a few days at the most, and it provides all the information relevant to rapid and slow coalescence, if both occur. From the latter E and C are determined. The values of D , for longer aging periods can then be calculated. During slow coalescence, C was 17.7 x 10-8 sec.-l for the W/O emulsions, and 31.9 x sec.-l for the o/w emulsions. Predicting Viscosity Changes on Aging.-The value of vrel corresponding to any value of D t is derived from Fig. 3 and 4. Values of rrelobtained in this way compare favorably with values determined experimentally over long aging periods (Fig. 7 and 8). Discussion Little is known about the mechanism whereby nonionic emulsifiers stabilize o/w emulsions, e.g., whether 22 steric hindrance is involved as for TV,/O cniulsion~,'~ (21) P. Sherman, unpublished data.
or whether a repulsion force of sufscicnt magnitude is developed to provide an adcquate poteiitial energy barrier to globult. coaiescence. The stability of negative silver iodide sols coiitaining pure lionionic detergent (polvosycthyleiic glycol moiioalkyl ether) is attributed to a combination of both electrical and iionelcctrical repulsion forws, the latter arising by solvation of the ethylciie oxide groups of the adsorbed deteigcnt ?i Thc o w emulsions may be stabilized by a similar mechaiiism, although the sorbitan residue should uiidcrgo less solvation than the polyoxycthylcne chain. Thc position of the "secondary minimum" in the iict potential energy curve (P'ig. 6) rical repulsion forces contribute to 111sof liquid parslffin iii water, containing no emulsifier, have a higher charge than the globules iii these eniulsioii~,and yct they coalesce a t a much faster rate. Litleast oiie otlicr factor must be iiivol~ed,therefore, g., the physical properties of the c>niulsificrfilm around the globules. ,lgcd t.inulsions should show a higher viscosity a t low i~atcsof shear than comparable fresh einulsions with the ~ a i n eI),,, , because of the larger proportion of aggregates ill the former. However, globules within the aggregates coalesce, thereby introducing aii opposing tendency which reduces qll,l. The net change in qlel will dcpeiid 011 which of t htw two phenomena predominates. For the intcrprctatioii of viscosity data derived at high rates of shear, only globule coalescence requires consideration. Coalesceiice is preceded by emulsifier d e s o r p t i o ~ i . ~ " ~In~ the ahsence of desorption the thickness of the emulsifier film, Ar: would increase as globules coalesccd. For example, the iiiitial Ar for w/o emulsions stsbiliztd by sorbitan nionooleate is approxi1.3 p coalesced, mately 'LO A. If two globules with D,,, AT would increase to 31 A. if all the emulsifier inolccules were retained a t the iiitcrfacc, and if this enlarged globule then coalesced with another of D,,, 1.3 1, Ar would increase furthcr to $2 ,is a result a, would respectively. The corresponddecrease by 22 arid 44 A., ing changes for o/w emulsions stabilized by sorbitan nioiiolaurate would be about half these values. Any effect which small changes in a,, exert on vrrl shonld be iioticcahlc in the most concentrated emulsions, particularly the m/o emulsions, since A 7 decreased to about two-fifths of its original value by the end of the aging period. Figures 3 and 4 do not suggest that aged concentrated emulsioiis show higher vrrl values than the correspoiiding fresh emulsioiis, so that Ar remains u11changed irrespective of the degree of coagulation within the emulsion. The rate of decrease in vrcl for both w;o aiid olw emulsioiis depends on the rate of increase in DTn, Sirice the latter is determined readily, the change in vrel on aging for any given time can be predicted without$ resort to dubious accelerated aging techniques. (1
a.
( 2 2 ) 11 I~OPIIIIILIIL. a n d .J. T. G Overbe?k. Discusrzons Fuiudul, Soc., 18,
c ~ i l l I
