We start with a surprise absorption experiment.
Then we introduce basic models of transport with adsorption on porous surfaces and review the properties of scalar conservation laws which arise as mathematical models. For some adsorption isotherms called favorable the profiles of concentrations exhibit shocks, while for unfavorable isotherms the profiles are rarefaction waves. Correspondingly, we discuss weak solutions in L_1 and challenges to numerical approximation.
Next we discuss hysteresis in adsorption which can be modeled using a coupled differential inclusion; we discuss some prior and some current work joint with R. Showalter. The talk will be illustrated with numerical simulations for non-hysteretic case and for a regularized model of hysteresis.