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Spontaneous imbibition, also known as capillary filling, occurs when one fluid displaces a second one from a solid porous medium due to its preferential affinity to wet the solid. The standard case corresponds to a liquid displacing a gas with negligible viscosity in a uniform porous medium. The viscous friction of the invading liquid increases with penetration length, leading to the slowing down dynamics of Washburn’s law, l(t)~t-1/2. How is this dynamic law modified if we introduce a thin lubricant layer? Here, simulate such a system and vary systematically the lubricant viscosity. For large lubricant viscosities, we observe Washburn law. Strikingly, we find a new dynamic regime in the limit of small lubricant viscosities where the front invades the channel linearly in time, suggesting that the viscous friction is constant through all the simulation. We derive a simplified theoretical model that agrees with the simulations and explains both limit dynamic regimes. We demonstrate that by decreasing the lubricant viscosity, dissipation takes place in the lubricant layer, instead of the invading front, leading to a constant friction force in time. The theoretical model predicts an exponential growth of the front when a constant, external force is imposed in the invading liquid. We validate this result and obtain excellent agreement between the simulations and the model. Finally, we use a similar theoretical analysis to study how the capillary number affects the deformation of a liquid interface for drops moving in such a lubricant coated channel, compared to the conventional solid case, where the Cox-Voinov law is to be applied.
Sergi G. Leyva is a phD student in the UBICS (University of Barcelona Institute of Complex Systems) at the University of Barcelona, under the supervision of Prof. Ignacio Pagonabarraga. He studied Physics and obtained a Master degree in Atomistic and Multiscale Computational Modelling in Physics, Chemistry and Biochemistry at the University of Barcelona. Since 2018 he’s been actively working with Prof. Pagonabarraga, in topics as diverse as Active Matter, Magnetic Colloids, Electrolyte flows in nanochannels and Capillary driven problems. His interests lay in combining simple theoretical models with all sort of computational modelling, whatever it might be for unveiling the fundamental laws of non-equilibrium thermodynamics in active matter, fluid transitions due to electrokinetic coupling with hydrodynamics in nanometric channels, or fluids imbibing channels coated with lubricants. He’s currently staying for three months at University of Edinburgh under the supervision of Dr. Rodrigo Ledesma for achieving the international PhD mentorship.