Problem 2. Fick's 2nd Law from the conservation of species Consider a medium that is a binary mixture of species and B for which the staionary medium approiximation holds. That is, the mass transfer may be approximated as occuring only by diffusion (no advection, i.e., movement of material by the velocity of the fluid). n example would be a block of silicon with species being the silicon atoms and species B being vacancy defects. 1. Starting from the mass conservation equation for species, dtdMA=M,inM,out+MA,g, derive the continuity equation, dtdCA=JA+N,g where N,g is the rate of increase of the molar concentration of species ,=(x,y,z). Show all steps. Hint: Perform mass balance using the elementary control volume, xyz, and relate mass to concentration by using the molecular weight MW,, such that the density can be re-written as =MW,C. 2. Derive the Fick's 2 nd Law from the continuity equation (Eq. 2), dtdCA=D2CA, where =(x22+y22+z22). Show all steps and write your assumptions about DA and the total concentration C=CA+CB. 3. Derive an expression for the molar flux of species B in terms of species , i.e., JB=f(J). Figure 1: Leaching of by diffusion into a stagnant liquid film of B