The convective model of cross-flow microfiltration is not inconsistent

The approximate analytical equations of the convective model and of the model of Romero and Davis are compared. Introducing the approximations used by Romero and Davis in the convective model gives the same functional dependence of the average filtration flux, 〈ν〉, on particle radius and solute volume fraction and a different dependence on the shear rate, γ_s. The convective model gives an explicit dependence of 〈ν〉 on transmembrane pressure and non-Newtonian ‘apparent’ viscosity of the cake. It is shown that the pseudoplastic rheological behaviour of concentrated colloidal solutions (cakes) rationalizes the experimentally established dependence 〈nu;〉 ∼ γ^m_s with 0.4 < m < 1.5.