Mass transfer in the vicinity of a separation membrane—the applicability of the stagnant film theory

Abstract

In membrane separation cells, the permeate velocity is usually predicted applying the stagnant film equation with mass transfer data from impermeable systems, Sh I. In this paper, the applicability of the stagnant film equation is discussed. Laminar momentum and solute transport equations are numerically solved in a permeable parallel plate cell and in a conical cell with a laminar jet impinging vertically to the membrane surface. Membrane surface concentration and permeate velocity predictions are applied to stagnant film equation to obtain Sh I. Sh I data are compared with Sherwood data from impermeable systems with uniform mass production at the wall, and with Sherwood data from impermeable systems with uniform concentration at the wall. This analysis is done for a wide range of the dimensionless numbers characterizing the membrane separation process: Schmidt, Reynolds (or Peclet for the parallel plate cell), Π v and Π π 0 numbers. The stagnant film equation is a quite accurate equation to predict permeate velocity, and the type of impermeable data that must be used depends on the dimensionless groups. The conclusions are identical for both cells.