\(\text{Pe}\sim 0\ \)indicates that the bulk liquid is well mixed
leading to homogeneous liquid composition throughout the bed. For\(\text{Pe}<30\), the effect of axial dispersion on bed performance is
significant, while the bed operates under near plug flow conditions for\(\text{Pe}>100\), and the bed operates under plug flow conditions for\(\text{Pe}\sim\infty\).
In Eq. (1), \(J_{k}\) represents the mass transfer rate between the bulk
liquid and resin. By considering the solid phase resistance in the film
model assumption, mass transfer driving force for component \(k\) is
expressed as a function of the solid phase loading as follows: