Fourier series solution for multistage countercurrent cake washing and segregated wash effluent circulation

A Fourier series solution method was developed for solving a multistage countercurrent cake washing problem, so that the solute concentration gradient inside a cake between washing stages was preserved. The cake washing process was described by the advection–dispersion equation. The solution method was employed to explore the multistage countercurrent cake washing in a segregated and a non-segregated wash effluent circulation. The segregated wash effluent circulation gave better solute recovery than the non-segregated wash effluent circulation especially when the wash ratio was around one.