Modeling relaxation processes for fluids in porous materials using dynamic mean field theory: an application to partial wetting

We review a recently developed dynamic mean field theory for fluids confined in porous materials and apply it to a case where the solid-fluid interactions lead to partial wetting on a planar surface. The theory describes the evolution of the density distribution for a fluid in a pore that has contact with the bulk during a quench in the bulk chemical potential. In this way the dynamics of adsorption and desorption can be studied. By focusing on partial wetting situation we can investigate influence of a weaker surface field on the mechanisms of capillary condensation and desorption. We have studied the dynamics of pore filling in a quench of the chemical potential between two states either side of the pore filling step, tracking the density distributions during the process. The pore filling process features an asymmetric density distribution where a liquid droplet appears on one of the walls. The droplet spreads and grows in size and this is followed by the appearance of a liquid bridge between the pore walls (for longer pores two liquid bridges are seen). The density distributions obtained in the dynamics resemble those obtained from static mean field theory in the canonical ensemble for an infinite pore without contact with the bulk