Effects of ultrafiltration permeation rates on the hydrodynamics of a minichannel/slit laminar flow

It is experimentally studied herein the effect on pressure drop of scaling down the characteristic length of laminar flows in impermeable rectangular minichannels, its height, to values ranging from 700 to 1200μm with the bottom wall possessing different roughness values. Results are compared to the analytical solution of the Hagen–Poiseuille flow confirming the presence of surface phenomena unobserved in macroscale flows. A fictitious viscosity, μroughμrough, dependent on the surface roughness may be used to model such surface phenomena. This viscosity is obtained from μrough=μapp-μμrough=μapp-μ, μappμapp being the apparent viscosity used in the theory that matches the experimental data. From the experiments and theory values of μroughμrough ranging from 0.516μ0.516μ to 0.915μ0.915μ are obtained. Additionally, effects of suction on pressure drop in the same minichannel, but with permeation through membranes with different roughness values, are also experimentally characterized and analyzed viewing the identification of its attenuating or amplifying trends. Results clearly show that suction reduces the effects of surface phenomena on the pressure drop approaching more closely the Hagen–Poiseuille flow solution. Also, the assumption of fully developed flow is assessed through the numerical calculation of the entrance lengths of the studied minichannel flows and the results elucidated that such hypothesis constitutes a fair approximation: for the most adverse operating conditions, the maximum entrance length is only 17.7% of the channel length.