Analytical Solution of the Simplified Symmetric Model

Let us start the analysis by finding the analytical solution for the simplified symmetric problem ci = C2 = 1/2 (ci is the mean concentration of a component 

Xip = kiRt ), and the concentration of component B in the /S-solution hg on the moving interphase 1-/3. Let the coefficients of interdiffusion in the /3 solution, D, and in phase 1, Dj, be constant. Then, the equations of balance and expressions for fluxes will be as follows  

Here is the flux of component B in /3-solution Iq is the flux of component C in /3-solution d%R/dt is the rate of motion of a boundary between the phase 1 and /3 solution dxi/dt is the rate of motion of the boundary between phase 1 and A. 

The solution of the system of Equations 9.31-9.34, together with the diffusion equation in the /S solution gives the following results  

Let us now compute the boundary concentration hg. For that, let us determine the flow of B in the /S phase near the moving boundary xr in terms of bg  

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