Brackish water salt rejection by porous hyperfiltration membranes

A theory is developed for the rejection of multiple salts by a macroporous hyperfiltration membrane, modelled by cylindrical pores, whose interior surfaces acquire a constant potential when in contact with the salt ions. With three ion types and two valences the ion rejections are shown to depend on the ratio of Debye length to pore radius, a dimensionless wall potential, a filtration Peclet number, and the ratios of concentrations and charge numbers of two of the ions of different valence. Numerical solutions for the rejections are given for large Peclet number and analytic solutions when the Debye length is also large.