Particle accretion and release in flows of suspensions

We consider a pressure-driven, one-dimensional, advective flow of a suspension through a porous domain. Suspended particles are filtered out, changing the porosity. These changes affect the filtration velocity through a porosity-dependent permeability factor. The reaction mechanism includes an accretion term and a term which allows trapped particles to return to the mobile phase. We obtain numerical solutions on a bounded domain and illustrate both contamination and remediation effects, and we consider the existence of traveling wave fronts in an infinite domain. For the latter, accretion rates are characterized that permit such fronts.