Nanofiltration flux and selectivity depend on the mass transfer through the nanometric pores. Among other factors, including charges and dielectric constant for the charged species, viscosity is of crucial relevance. Here we study how viscosity changes in confined media in the nanometric range. The models found in the literature, that assume that the ratio of the viscosity of water on the pore walls over that in bulk water is a constant, are totally unsatisfactory to predict the dependence of the Darcy constant on temperature.
Pure water flux is studied as a function of temperature for three commercial ceramic membranes. For these membranes, we fit flow versus temperature with a quite good fitting assuming that the first layer of water on the cylindrical pore walls move with a viscosity . If the flow is assumed to follow a Carman-Kozeny equation, according to its more realistic granular nature, the resulting porosity and mean grain size are in accordance with the data known and measured by atomic force microscopy (AFM).
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