Capillary imbibition in lubricant-coated surfaces

We describe spontaneous imbibition processes in lubricant-coated surfaces. This geometry represents a simplified version of experimental realisations like slippery liquid-infused porous surfaces (SLIPS) and lubricant-impregnated surfaces (LIS), where the lubricant eliminates direct contact of both invading and displaced fluids with the solid. We combine a theoretical and computational analysis to clarify the dissipation mechanisms that governs the dynamics of imbibition. The asymmetric distribution of dissipation among the fluid phases results in two limit regimes: When the dissipation is more relevant in the displacing fluid, we find a diffusive advancing of the front, which corresponds the well-known limit in which invading and displaced fluids are in direct contact with the solid. If dissipation takes place preferentially in the lubricant, we find a linear advancing of the front through the entire channel.

A simplified mathematical modelling is presented, which captures these regimes. The analysis allows to characterise the corresponding crossovers between the limiting cases, and generalise the dynamics to imbibition when there is an external forcing.

Our work paves the way into experimental scenarios of similar systems, like SLIPS or LIS, and also towards characterisation of lubricant-coated surfaces in more general channel geometries like wegdes or sinudoidal shapes.