where FG is the collision frequency due to gravitational separation, v is the Stokes creaming velocity of a particle with radius r¡, and Ap is the density difference between the droplets and the surrounding liquid. This equation indicates that the collision frequency increases as the difference between the creaming velocities of the particles increases. The rate of gravitation-ally induced flocculation can therefore be retarded by ensuring that the droplet size distribution is not too wide, decreasing the density difference between the oil and aqueous phases, decreasing the droplet concentration, or increasing the viscosity of the continuous phase. Equation 7.22 would have to be modified before it could be applied to systems which do not obey Stokes' law (Section 7.3.1). In addition, it does not take into account the fact that the droplets reach a position at the top or bottom of an emulsion where they cannot move any further and are therefore forced to encounter each other.
Collisions Due to Applied Shear Forces. Food emulsions are often subjected to various kinds of shear flow during their production, storage, and transport. Consequently, it is important to appreciate the effect that shearing has on their stability to flocculation. In a system subjected to Couette flow, the collision frequency is given by (Dickinson 1992, Walstra 1996a):
where FS is the collision frequency due to shear. Thus the frequency of shear-induced collisions can be retarded by decreasing the shear rate, increasing the droplet size, or decreasing the dispersed-phase volume fraction. It should be noted that the collision frequency is independent of the viscosity of the continuous phase.
Relative Importance of Different Collision Mechanisms. In general, each of the above mechanisms may contribute to the droplet collision frequency in an emulsion. In practice, one of the mechanisms usually dominates, depending on the composition and microstructure of the product and the prevailing environmental conditions. To effectively control the collision frequency, it is necessary to establish which mechanism is the most important in the particular system being studied. The ratio of the shear-to-Brownian motion collision frequencies (FS/FB) and the gravitational-to-Brownian motion collision frequencies (FG/FB) is plotted as a function of shear rate and particle size ratio (= r2 /r1) in Figure 7.9 for a typical emulsion. At low shear rates (G < 2 s-1), collisions due to Brownian motion dominate, but at high shear rates those due to mechanical agitation of the system dominate. Gravitationally induced collisions dominate those due to Brownian motion when the particle size ratio exceeds about 5, and thus it is likely to be important in emulsions which have a broad particle size distribution.
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