Kinetics of Emulsion Drop Coalescence in a Turbulent Flow

Kinetics of Emulsion Drop Coalescence in a Turbulent Flow 

consider the dynamics of integration of drops with fully retarded surfaces in the absence of electric field. If drops are uncharged, the kernel of the kinetic equation is given by the relation (13.100), namely 

Let us use the method of moments to solve the kinetic equation (11.1). Then, in view of (13.135), we obtain from (11.15) the following equation for zeroth moment, which has the meaning of the number concentration of drops 

There are fractional moments appearing in the right-hand side of (13.136). To determine them, recall the method of interpolation of fractional moments through the integer ones (see Section 11.1). Using two-point interpolation, one can express the fractional moments in terms of two moments mo and mi according to (11.20). Then 

Since only the coalescence is being considered, the volume concentration of drops does not change with time and mi(t) = 1. Then the solution of Eq. (13.137) with the initial condition mo(t) = 1 has the form 

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