Title: Transient flows in active porous media,
Abstract: Stimuli-responsive materials that modify their shape in response to changes
in environmental conditions -- such as solute concentration, temperature, pH,
and stress -- are widespread in nature and technology. Applications include
micro- and nanoporous materials used in filtration and flow control. The
physiochemical mechanisms that induce internal volume modifications have been
widely studies. The coupling between induced volume changes and solute
transport through porous materials, however, is not well understood. Here, we
consider advective and diffusive transport through a small channel linking two
large reservoirs. A section of stimulus-responsive material regulates the
channel permeability, which is a function of the local solute concentration. We
derive an exact solution to the coupled transport problem and demonstrate the
existence of a flow regime in which the steady state is reached via a damped
oscillation around the equilibrium concentration value. Finally, the
feasibility of an experimental observation of the phenomena is discussed.
Please note that this version of the paper has not been formally peer reviewed,
revised or accepted by a journal.