Stokes ultrafiltration

Hydrodynamic. For a pressure driven process such as ultrafiltration the flow of solvent towards the membrane results in a drag which carries the solute in the same direction. This drag is a function of the distance of the solute from the pore entrance. At large distances it is equal to the isolated solute value (Stokes limit), but as the solute approaches and begins to enter the pore, the drag, for a constant filtration velocity, increases due to the restriction of solvent flow. This increase depends on the ratio of solute diameter to pore diameter. 

An evaluation of more than 40 different colloidal suspensions in our laboratories has indicated that the diffusion coefficient calculated from the ultrafiltrate flux using the Leveque or Dittus-Boelter relationships is generally from one to three orders of magnitude higher than the theoretical Stokes-Einstein diffusiv-ity. 

Similar discrepancies were noted by Blatt et al32 for colloidal suspensions such as skimmed milk, casein, polymer latexes, and clay suspensions. Actual ultrafiltration fluxes are far higher than would be predicted by the mass transfer coefficients estimated by conventional equations, with the assumption that the proper diffusion coefficients are the Stokes-Einstein diffusivities for the primary particles. Blatt concluded that either (a) the "back diffusion flux" is substantially augmented over that expected to occur by Brownian motion or (b) the transmembrane flux is not limited by the hydraulic resistance of the polarized layer. He favored the latter possibility, arguing that closely packed cakes of colloidal particles have quite high permeabilities. However, this is not a plausible hypothesis for the following reasons ... 

Film theory has had less success in microfiltration than ultrafiltration for predicting or correlating e7q>erimental data. Division coefBcients for molecules can be successfiilly calculated fi om the Stokes-Einstein equation, vriiereas those calculated for particles are extreme small The predicted flux rates, from Equation (10.18) are much smaller than... 

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