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.
All Science Journal Classification (ASJC) codes
- Applied Microbiology and Biotechnology
- Mass transfer