(419e) Boundary Layer Theory in Fixed-Bed Adsorption

Boundary layer theory is employed to improve the quantitative interpretation of break-through curve measurements. Small ε, or fast adsorption relative to convection, is considered, focusing on non-linear equilibria adsorbing with a linear-driving force. We demonstrate that perturbation theory provides an unambiguous interpretation of the so-called “local-equilibrium theory” or “solute-movement theory,” which is the leading-order approximation in small ε. The shock waves, or moving discontinuities, associated with the former problem can be interpreted as boundary layers. After suitable scaling transformations, we observe that the form of the problem inside the boundary (shock) layer is identical to that describing the so-called “constant pattern” wave previously only studied in infinite domains. This is a unification of the concepts of local-equilibrium and constant-pattern wave. By matching the boundary layer solution to the leading-order solution, we construct a composite solution to predict the shape of break-through curve within Ο(ε). We further argue that a short-time boundary layer exists and is associated with the release from carrier fluid as the solute begins to adsorb. In order to predict the break-through time to within Ο(ε), we show that the short-time boundary layer needs to be matched to the long-time boundary layer described previously. Numerical simulations assess the validity of the approach. While the work is primarily centered on the case of isothermal, constant concentration dynamics with one adsorbing solute, we anticipate that similar boundary layers will exist in the large number of processes found to exhibit shock waves in equilibrium theory.