On the non-linearity of osmotic flow

Abstract

The osmotic water flow and the solute flow through three different commercial cellulose acetate membranes were measured with different NaCl concentrations, hydrostatic pressures and module flow conditions. Based on the measurements, the concentrations on the surfaces of the selective layer of the membrane were theoretically calculated and the results applied to fit equations whose derivation is based on the theory of dimensional analysis. The results show that the frequently used linear forms of the osmotic transport equation do not satisfactorily describe the phenomenon. The proposed forms of a new transport equation for water flux are A w Δx s −B w Δp r 1+Φ x ̄ s or A w Δ x s −B w Δ p r where A w, B w and Φ are the transport coefficients, x s is the molar fraction of the solute, x ̄ s is the mean molar fraction and p r is the dimensionless pressure. The question of whether the non-linear phenomenon of osmotic water transport is much more general than hitherto expected, is raised. Criticism is provided on the assumption of internal concentration polarisation as an explanation of the apparent non-linearities appearing in the experiments. The two-coefficient linear equation was found sufficient to describe the measured solute flux. The one-coefficient linear equation for solute flux, relating the flux only to the solute concentration difference or molar fraction difference, was found to be inadequate.