(276d) Understanding the Break-through Curve Measurement When Adsorption Is Fast

The break-through curve measurement characterizes the relationship between bulk solute—solid properties and solute movement along a packed bed and is a fundamental aspect of large-scale adsorption separations. The bulk properties explain the mechanism of adsorption, while solute movement details the mechanism of separation. A more quantitative description of the relationship between bulk properties and solute movement can accelerate process intensification and high-throughput materials screening.

In this work, we investigate the relationship between an adsorption isotherm and the break-through curve measurement when ε is small, or when mass transfer into the solid is much faster than convection. To accommodate the large number and diversity of adsorbent materials that can be synthesized, we focus on an adsorption isotherm possessing a generic functional form (i.e., smooth, and strictly increasing). We consider a single-solute adsorbing isothermally with negligible axial dispersion. Regular and singular perturbation theory in the limit ε→0, or when mass transfer is much faster than convection, provide a more quantitative and generic interpretation of several popular theoretical approaches, as well as how they are connected. For example, while dispersive waves in equilibrium theory are realized as the leading-order approximation as ε→0, shock waves and linear waves are only valid at the point ε=0. More realistic descriptions of the latter waves in the measurement, where ε is positive, can be obtained using boundary layer theory. The influence of the rate expression on the constant-pattern boundary layer, as well as the time scales over which the behavior is dominant, are revealed. In contrast to previous approaches, validity can be assessed quantitatively by the value of ε for a given system of interest. To predict the time at which the center of the constant-pattern boundary layer breaks through the column, its evolution from short times must be resolved. The detailed investigation of the limit ε→0 also identifies new regimes of adsorption isotherms for which solute movement is not yet fully understood.

This work provides a more quantitative understanding of the break-through curve measurement when adsorption is fast. The boundary layer perspective sets the stage for extension to more complex systems and other separation processes, as it does not require extensive expertise with weak solutions.