Mathematical model of a countercurrent flow multi-fibre dialyser

The closed form solution to a distributed parameter mathematical model of a countercurrent flow dialyser is presented. The model consisting of a bundle of hollow fibres in a shell accounts for axial convection and radial diffusion. The proposed model relates the fractional removal of a solute to mass transfer parameters such as Sherwood number, length Peclet number and system geometry. Excellent agreement with experimental beer dialysis data is demonstrated for the removal of alcohol using 8-μm thick 200-μm diameter cuprophane hollow-fibre membrane fibres. Potentially, this model could be very helpful in designing new processes involving dialysis. For example, removal efficiency better than 90% is achievable in systems operating with a Sherwood number of 2.0, length Peclet number of 5 × 10⁵, unit tube-side/shell-side volumetric flow and length-to-diameter ratio of 5000. Results were obtained in this work from only the first eigenvalue and the case of no solute in the incoming dialysate stream.