Mathematical modeling of pulp washing on rotary drums and their numerical solution for various adsorption isotherms
The mechanism of the displacement washing of the bed of pulp fibers is mathematically modeled by the basic material balance equation. Linear as well as non-linear adsorption isotherms are used to describe the relationship between the concentration of the solute in the liquor and concentration of the solute on the fibers. In the present study, the numerical solutions are obtained of pulp washing model with different adsorption isotherms. For the numerical solution “pdepe” solver in MATLAB is applied on the axial domain of the system of partial differential equations. Numerical results thus obtained are compared with earlier workers analytically and numerically. The comparison shows that results are in good agreement with both analytically as well as numerically and also show the suitability of the isotherm coupling with the washing model. The technique used in the present investigation is simple, elegant and convenient for solving two point boundary value problems with varying range of parameters.
Continuous filter cake washing performance
A previous report (1) has presented the derivation of new filter cake washing equations. This report presents the procedure for their application and contains an example of application to a specific batch washing system. It also presents the adaption of the equations to permit their use in predicting the performance of a continuous rotary-drum filter.
A note on the “ Danckwerts ” boundary conditions for continuous flow reactors
Abstract A mathematical justification is given for the use of the “ Danckwerts ” boundary conditions for continuous flow reactors. It is shown that the apparent indeterminacy, which D anckwerts resolves intuitively, is caused by the use of a discontinuous coefficient of diffusion. By treating this as the limit of a continuous function and imposing continuity of the reactant concentration as the physically relevant boundary condition, the Danckwerts solution is obtained in the limit.