Differential Separation of Multi-Componenet Mixtures

Consider the process of differential degassing of a quiescent volume of a multi-component liquid-gas mixture, in which the disperse phase consists of spherical bubbles of equal size. Assume that the volume concentration of bubbles is small and their mutual interaction can be neglected. The problem reduces to the analysis of mass exchange for a unit bubble of initial radius Rq placed in a multi-component solution. Assume that the process is isothermal the pressure above the mixture surface is maintained at a constant value. 

The distribution of component concentrations in the solution is described by the diffusion equation  

The condition of dynamic balance of the bubble surface with due consideration of inertial, viscous, and capillary forces is given by the equation 

Assuming that all parameters of the gas in the bubble are distributed uniformly but depend on time, we have the following equations  

To these equations, it is necessary to add the following initial and boundary 

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Differential Separation of Multi-Componenet Mixtures 731 and the volume concentration of bubbles is... 

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