Mass transfer in the filtration membrane covering from macroscale, multiscale to nanoscale

The analytical results are presented for the mass transfer in a cylindrical pore covering from the macroscale, multiscale to nanoscale owing to the variation of the inner diameter of the pore. When the thickness <i>hbf</i> of the physically adsorbed layer potentially fully formed on the pore wall is comparable to but less than the inner radius <i>R0</i>. of the pore, the multiscale flow occurs consisting of both the nanoscale non-continuum adsorbed layer flow and the macroscopic continuum liquid flow; When <i>R0</i> &le; <i>hbf</i>, the flow in the whole pore is essentially non-continuum; When <i>R0</i> is far greater than <i>hbf</i>, the flow in the whole pore can be considered as macroscopic and continuum and the adsorbed layer effect is negligible.