Diffusion into a Rectangular Parallelepiped from a Well-Stirred Fluid
M. O’Keeffe · Journal of Applied Physics · 1966
It is shown that the solution to the problem of the fractional uptake mIII(a1, a2, a3), at time t, by a rectangular parallelepiped of dimensions 2a1×2a2×2a3 from a well-stirred fluid is given by 1−mIII(a1, a2, a3)=[1−mI(a1)][1−mI(a2)][1−mI(a3)],where mI(ai) is the well-known solution for the fractional uptake by an infinite plane sheet of thickness 2ai, viz. 1−mI(ai)= ∑ n[2α(1+α)/(1+α+α2qn2)] exp(−Dqn2t/ai2).Here α is the ratio of number of moles in the fluid phase to the number of moles in the solid phase, D is the diffusion coefficient, λ and the qn are the nonzero roots of tan qn=−αqn.