Coagulation of Bubbles in a Viscous Liquid

The dispersiveness of a Uquid-gas mixture can be characterized by a continuous volume distribution of bubbles n(V, t, P) at the moment of time f at the point P of the considered volume. The distribution n satisfies the kinetic equation, which, with due regard of the diffusion growth and coagulation, and neglecting the breakup of bubbles, takes the form  

The second term in the left-hand side is the convective transfer of bubbles, which is equal to the velocity of a bubble of volume V. We assume that bubbles are small enough, so that u = and a = lApg/i/ti for bubbles with 

If the expressions dV/dt)j and K o), V) are known, then, having solved Eq. (25.1), one can find the number and volume concentrations of bubbles, N and W, and also their average volume Vav = W/N. The expressions for (dV/dt)g were obtained in Section 22. In the present chapter, the expressions for K(eo, V) and some simple solutions of the kinetic equation will be obtained. 

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