Dynamic contact angle of a liquid spreading on an unsaturated wettable porous substrate

TL;DR

This paper investigates how a liquid spreads on an unsaturated porous substrate, revealing that the effective dynamic contact angle is uniquely determined by solution existence conditions, unlike on impermeable solids.

Contribution

It introduces a novel approach to defining the dynamic contact angle on porous substrates based on solution regularity, unlike traditional boundary condition methods.

Findings

Effective contact angle depends on solution existence criteria.

Identifies a critical velocity where flow regime transitions occur.

Describes a regime where surface spreading stops but internal wetting continues.

Abstract

The spreading of an incompressible viscous liquid over an isotropic homogeneous unsaturated porous substrate is considered. It is shown that, unlike the dynamic wetting of an impermeable solid substrate, where the dynamic contact angle has to be specified as a boundary condition in terms of the wetting velocity and other flow characteristics, the `effective' dynamic contact angle on an unsaturated porous substrate is completely determined by the requirement of existence of a solution, i.e. the absence of a nonintegrable singularity in the spreading fluid's pressure at the `effective' contact line. The obtained velocity dependence of the `effective' contact angle determines the critical point at which a transition to a different flow regime takes place, where the fluid above the substrate stops spreading whereas the wetting front inside it continues to propagate.