Rework the learning problem from 18B.8, but this time include the contribution from the radius of the spherical particle as you perform your shell balance.
In studying the rate of leaching of a substance A from solid particles by a solvent B, we may postulate that the rate-controlling step is the diffusion A from the particle surface through a stagnant liquid film of thickness ( out into the main stream (illustranted in Fig. 18B.8). The molar solubility of A in B is cA0, and the concentration in the main stream is CA(.

Fig.18B.8 Leaching of A diffusion into a stagnant liquid film of B.
Shell Mass Balances and Concentration Distribution in Solids and in Laminar Flow
(a) Obtain a differential equation for as a function of z by making a mass balance on A over a thin slab of thickness Δ z. Assume that DAB is constant and that A is only slightly soluble in B. Neglect the curvature of the particle.
(b) Show that, in the absence of chemical reaction is the liquid phase, the concentration profile is linear.
(c) Show that the rate of leaching is given by

CAS Solid particle containing ! Main Liquid film i liquid | stream of A and B 2= 8 DAs(C10 Cas NA