Emulsion flocculation rate

There appear to be two stages in the collapse of emulsions flocculation, in which some clustering of emulsion droplets takes place, and coalescence, in which the number of distinct droplets decreases (see Refs. 31-33). Coalescence rates very likely depend primarily on the film-film surface chemical repulsion and on the degree of irreversibility of film desorption, as discussed. However, if emulsions are centrifuged, a compressed polyhedral structure similar to that of foams results [32-34]—see Section XIV-8—and coalescence may now take on mechanisms more related to those operative in the thinning of foams. 

There are two approaches to the kinetics of emulsion flocculation. The first stems from a relationship due to Smoluchowski [52] for the rate of diffusional encounters, or flux ... 

For example, van den Tempel [35] reports the results shown in Fig. XIV-9 on the effect of electrolyte concentration on flocculation rates of an O/W emulsion. Note that d ln)ldt (equal to k in the simple theory) increases rapidly with ionic strength, presumably due to the decrease in double-layer half-thickness and perhaps also due to some Stem layer adsorption of positive ions. The preexponential factor in Eq. XIV-7, ko = (8kr/3 ), should have the value of about 10 " cm, but at low electrolyte concentration, the values in the figure are smaller by tenfold or a hundredfold. This reduction may be qualitatively ascribed to charged repulsion. 

The preceding treatment relates primarily to flocculation rates, while the irreversible aging of emulsions involves the coalescence of droplets, the prelude to which is the thinning of the liquid film separating the droplets. Similar theories were developed by Spielman [54] and by Honig and co-workers [55], which added hydrodynamic considerations to basic DLVO theory. A successful experimental test of these equations was made by Bernstein and co-workers [56] (see also Ref. 57). Coalescence leads eventually to separation of bulk oil phase, and a practical measure of emulsion stability is the rate of increase of the volume of this phase, V, as a function of time. A useful equation is... 

Viscosity Increase. The flocculation rate of an emulsion is iaversely proportional to the viscosity of the continuous phase and an iacrease of the viscosity from 1 mPa-s (=cP) (water at room temperature) to a value of 10 Pa-s (100 P) (waxy Hquid) reduces the flocculation rate by a factor of 10,000. Such a change would give a half-life of an unprotected emulsion of a few hours, which is of Httle practical use. 

Emulsion stability of SEDDS is usually good because the droplets are small and have narrow size distributions. However, stability can be measured by determining the flocculation rates, degree of separation, or changes in the diameter of droplets formed on dilution over time during storage under various conditions. 

Fig. 9 Zeta potential and flocculation rate of a parenteral emulsion in the presence of a non-specifically adsorbing electrolyte (A) and a specifically adsorbing electrolyte (B).

Where is the phase volume ratio of the 0/W emulsion and n is the number of drops for mean volume, Vm, at time, t, is the flocculation rate constant. 

The present paper deals with kinetics of coagulation of Phthallylsulfathiazole stabilized xylene in water emulsion in the presence of some cationic detergents. Rate of flocculation, rate of coalescence and rate of creaming have been determined. To estimate the stability of the present systems their zeta potentials have been measured and stability factors calculated. Temperature effect on the system was also studied. 

Figure 3 Relative change in the total number of droplets vs. time initial number of primary particles Njq = 1 x 10 cm flocculation rate constant Kp= 1 x 10 cmVs curve 1, the numerical solution ofthe set Eq. (37) curve 2, the model of Borwankaref al. (38) for diluted emulsions curve 3, the model of van den Tempel (71) (a) coalescence rate constant = 1 x iQ- s" (b) = 1 x iQ - s" (c) Kg =...

In a flocculating concentrated emulsion, K, and the contribution of unreacted primary partieles is negligible. A rapid flocculation rate relative to the rate of coalescence is given by Van den Tempel (216) ... 

Further reviews of coalescence and flocculation kinetics were reported by Becher (211), Tadros and Vincent (90), and Hartland (217). For all practical purposes the above treatments usually suffice in crude-oil studies. Extensive treatments of coalescence and flocculation kinetics were modeled as required for various other emulsion applications. Borwanker et al. (218) developed a mathematical model to account for flocculation and coalescence kinetics occurring simultaneously. They modified Van den Tempel s treatment for coalescence to include coalescence occurring in small floes. They showed how the rate-controlling mechanism could change from coalescence-rate controlling to flocculation-rate controlling during an emulsion hfetime. They further extended the model for concentrated emulsions. 

Figure 22 The total number of constituent drops in a flocculating emulsion, decreases with time, t, because of a parallel process of coalescence. The curves are calcualted for the following parameter values initial number of constituent drops iiq = lO cm coalescence rate constant F = 10 s h Curve 1 is a numbeiical solution to Eq. (121) Curves 2 and 3 are the results predicted by the models of Bor-wankar et al. (194) and van den Tempel (193), respectively. The values of the flocculation rate constant are (a) ar= 10 " cmVs (b) ar=...

W emulsions are formed at low electrolyte concentrations, < 0.3M NaCl, and W/0 emulsions are formed at high electrolyte concentrations, > 0.3M NaCl. The continuous phase at 0.3M NaCl was indeterminable, by the simple method previously discussed. This emulsion phase collapsed to a value of V /Vm of 0.1 between 10,000 minutes (limit of time scale of Figure 11) and 15,000 minutes (last observation point) all the other emulsion phases formed with univalent alkalis at high pH s flocculated to V /Vrj. = 0.5 over the observation period. The flocculation rate of the W/O emulsions is faster than the 0/V7 emulsions because of double layer effects (25). The W/O emulsions flocculated but did not coalesce because of the presence of interfacial films discussed by Wasan et al. (17). The relative rates of flocculation of either the O/W or the W/O emulsions appear to depend on the concentration of electrolyte however, the data are insufficient to make a more definitive statement at this time. 

Coalescence requires that the molecules of liquid within two or more emulsion droplets coming into direct contact. Droplets therefore need to be in close proximity, which is for example the case in highly concentrated emulsions, flocculated emulsions, or creamed layers. In a subsequent step, a disruption of the interfacial membrane must occur to allow the liquid molecules to come into direct contact. The rate at which coalescence proceeds, and the physical mechanism by which it occurs, is thus highly dependent on the nature of the emulsifier used to stabilize the system. Improving the stability of an emulsion to coalescence may... 

Fig. XIV-9. Effects of electrolyte on the rate of flocculation of Aerosol MA-stabilized emulsions. (From Ref. 35.)...

Studies of flow-induced coalescence are possible with the methods described here. Effects of flow conditions and emulsion properties, such as shear rate, initial droplet size, viscosity and type of surfactant can be investigated in detail. Recently developed, fast (3-10 s) [82, 83] PFG NMR methods of measuring droplet size distributions have provided nearly real-time droplet distribution curves during evolving flows such as emulsification [83], Studies of other destabilization mechanisms in emulsions such as creaming and flocculation can also be performed. 

A reduction in the electrical charge is known to increase the flocculation and coalescence rates. Sufficient high zeta potential (> — 30 mV) ensures a stable emulsion by causing repulsion of adjacent droplets. The selection of suitable surfactants can help to optimize droplet surface charges and thus enhance emulsion stability. Lipid particles with either positive or negative surface charges are more stable and are cleared from the bloodstream more rapidly than those with neutral charge [192, 193]. 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

From a pharmaceutical perspective, phospholipids-stabilized emulsions are remarkable. For example, they are relatively stable, with shelf lives of 18 months to 2 years being obtained after the initial heat sterilization. They resist the increased shear rates as the bottles are transported from producer to user and they can tolerate the addition of a wide variety of monovalent electrolytes for at least short periods prior to administration. However, they cannot resist freezing and changes in droplet size following exposure to freeze-thaw cycles can be used as a measure of the stability of the emulsion system. Most injectable emulsions are sensitive to multivalent cations such as calcium or magnesium salts, which rapidly flocculate the phospholipids-stabilized systems. 

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