Dynamics of films and droplets spreading on porous substrates

This paper numerically investigates spreading and sorption of films and droplets on an unsaturated porous substrate, a mechanism taking place in paper-coating and ink jet printing. The dynamics of the fluid on the substrate surface are described by lubrication approximation. Fluid flow within the porous substrate, caused by the droplet penetrating into it, is treated with the Richards' equation, which models unsaturated flow in porous media and describes fluid transport in the porous layer after complete absorption of the film or droplet. Numerical results for sorption of an axisymmetric droplet into a substrate of finite thickness show that a sharp localization of the penetrating fluid, as required for fine printing resolution, can be achieved by a steep capillary sorption curve. The interaction of the fluid with the-impermeable bottom of the layer may drastically delay droplet absorption and thus require matching layer thickness and droplet volume to avoid limiting printing process speed.