EFFECTS OF PRESSURE AND CROSSFLOW VELOCITY ON ULTRAFILTRATION FLUX

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Abstract
Ultrafiltration in a channel is considered for fluids having power-law viscous models dependent on concentration approximately in exponential fashion. A simple concentration solution profile is made to apply using mass conservation in a steady-state element. The solution applies to pre-gel and gel conditions. The viscous model is shown to affect the results in profound ways. A few observations are made concerning the meaning of gel. The average flux for a membrane channel is predicted to depend on pressure systematically. The flux for a gel-dominated channel is predicted to respond to the shear stress by the fluid on the membrane and thusly on the crossflow velocity. Values of the exponent In(flux)/Invelocity) are 1/3 for laminar flows of all fluids. The exponent exhibits larger values for turbulent flows, being increased for shear-thinning materials. Data for a synthetic polymer and a natural polymer substantiate the predictions. This is the first known publication predicting the form of pressure effect and the first to explain values of the flux-velocity exponent as large or larger than unity.