Abstract
Frequently the concentrations in the opposing flows in a countercurrent exchange device satisfy linear partial differential equations with prescribed boundary and initial conditions, and interest centers on the transients in the exiting concentrations. A method is proposed for numerically determining these transients. It does not require determining the behavior at internal points. The method involves the transformation of two point boundary value problems into Cauchy systems, and the numerical inversion of Laplace transforms. It depends strongly on the ability of modern computers to integrate large systems of ordinary differential equations with known initial conditions.
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