Prediction of mass-transfer coefficient with suction in the applications of reverse osmosis and ultrafiltration

Sherwood-number relations for prediction of the mass-transfer coefficient for developing concentration boundary-layer have been obtained for laminar flow-regime from first principles. The common flow-modules, namely, rectangular channel, tubular and radial cross-flow are considered. The relationships developed include the effect of suction through the membrane. Relevant relations for estimation of mass-transfer coefficient for cross-flow reverse osmosis and ultrafiltration are formulated. The Sherwood-number relations developed are compared with the standard correlations to quantify the effect of the suction. The proposed Sherwood relations are used in conjunction with the osmotic-pressure model to predict the permeate flux in reverse osmosis and osmotic-pressure governed ultrafiltration.

[1]  R. Probstein,et al.  ON The PREDICTION OF LIMITING FLUX IN LAMINAR ULTRAFILTRATION OF MACROMOLECULAR SOLUTIONS , 1977 .

[2]  L. Lebrun,et al.  Diffusion of dextran through microporous membrane filters , 1994 .

[3]  R. L. Riley,et al.  Boundary-Layer Effects in Reverse Osmosis , 1964 .

[4]  P. Bhattacharya,et al.  LIMITING FLUX PHENOMENA IN ULTRAFILTRATION OF KRAFT BLACK LIQUOR , 1991 .

[5]  Vassilis Gekas,et al.  Mass transfer in the membrane concentration polarization layer under turbulent cross flow , 1987 .

[6]  S. Gupta,et al.  COMPARATIVE LIMITING FLUX ANALYSIS OF BLACK LIQUOR AND POLYETHYLENE GLYCOL IN ULTRAFILTRATION , 1990 .

[7]  P. Bhattacharya,et al.  ULTRAFILTRATION FLUX AND REJECTION CHARACTERISTICS OF BLACK LIQUOR AND POLYETHYLENE GLYCOL , 1989 .

[8]  Development of concentration profile and prediction of flux for ultrafiltration in a radial cross-flow cell , 1994 .

[9]  Clement Kleinstreuer,et al.  Laminar dilute suspension flows in plate- and frame ultrafiltration units , 1983 .

[10]  S. De,et al.  Flux prediction of black liquor in cross flow ultrafiltration using low and high rejecting membranes , 1996 .

[11]  C. Bhattacharjee,et al.  Flux decline analysis in ultrafiltration of kraft black liquor , 1993 .

[12]  A. Zydney,et al.  Diffusive and convective protein transport through asymmetric membranes , 1991 .

[13]  Ashutosh Sharma,et al.  Surface interactions in osmotic pressure controlled flux decline during ultrafiltration , 1994 .

[14]  C. A. Smolders,et al.  Hydrodynamic resistance of concentration polarization boundary layers in ultrafiltration , 1985 .

[15]  Pierre J. Carreau,et al.  Modeling of ultrafiltration : predictions of concentration polarization effects , 1994 .

[16]  P. Flory.  Principles of polymer chemistry , 1953 .

[17]  C. A. Smolders,et al.  Mass transfer coefficients in cross-flow ultrafiltration , 1989 .

[18]  H. K. Lonsdale,et al.  Synthetic membranes : science, engineering, and applications , 1986 .