Prof. Mohammad Asif Room 2B45, Building 3 Department of Chemical Engineering King Saud University Separation Processes – I CHE 316 Prof. Mohammad Asif Room 2B45, Building 3 http://faculty.ksu.edu.sa/masif Tel: +966 1 467 6849

External Mass Transfer Resistance For given bulk fluid concentrations, the presence of external mass transfer resistances reduces the driving force for mass transfer across the membrane which lowers the trans-membrane flux. External mass transfer resistance is commonly neglected for gas permeation as solution-diffusion mechanism for gas permeation is quite slow compared to diffusion in the gas boundary layers or film adjacent to the membrane. Because diffusion in liquid boundary layers and films can be slow, external mass transfer resistance cannot be neglected in membrane processes that involve liquids, such as dialysis, reverse osmosis, and pervaporation. The need to consider the effect of concentration polarization is of particular importance in reverse osmosis, where the effect can reduce the water flux and increase the salt flux. At steady state, rates of mass transfer of a penetrating species, i, through the three resistances are as follows: where kiF and kip are mass-transfer coefficients for the feed-side and permeate-side boundary layers or films. The three terms in the denominator of the right-hand side are the resistances to the mass flux. In general, the mass-transfer coefficients depend on fluid properties, flow channel geometry, and flow regime (turbulent or laminar).

Typical mass-transfer coefficients for channel flow are obtained from the general empirical film-model correlation: where dH is hydraulic diameter, v is velocity. The constants a, b, and d are as shown in the table. Here, w is width of channel, h is height of channel L is length of channel. A dilute solution of solute A in solvent B is passed through a tubular membrane separator, with the feed flowing through the tubes. At a certain location, the solute concentrations are 5.0 X 10-2 kmol/m3 and 1.5 X 10-2 kmol/m3, respectively, on the feed and retentate sides. The permeance of the membrane for solute A is 7.3 X 10-5 m/s. If the tube-side Reynolds number is 15,000, the feed-side solute Schmidt number is 500, the diffusivity of the feed-side solute is 6.5 X 10-5 cm2/s, and the inside diameter of the tube is 0.5 cm, estimate the flux of the solute through the membrane if the mass-transfer resistance on the permeate side of the membrane is negligible.