Performance of one- and two-dimensional models for a slow flow system in a long, permeable tubule

A radially symmetric slow flow system in a long cylinder with moderate wall leakage is considered, with physical parameters taken from the renal proximal tubule. Dimensional analysis yields a simplified system which, under certain assumptions, is well-posed, and possesses a unique solution if a solution exists. A lumped parameter analysis generates a one-dimensional model identical to a typical one-dimensional model in a special case. The one- and two-dimensional models agree well in the situations examined. When the wall fluxes are of a certain class, the concentration to which the solution tends as the fluid proceeds down the tubule can be computed algebraically.