Wettability is an important factor which controls the displacement of immiscible fluids in permeable media, with far reaching implications for storage of CO2 in deep saline aquifers, fuel cells, oil recovery, and for the remediation of oil contaminated soils. Considering the paradigmatic case of random piles of spherical beads, fluid front morphologies emerging during slow immiscible displacement are investigated in real time by X-ray micro–tomography and quantitatively compared with model predictions. Controlled by the wettability of the bead matrix two distinct displacement patterns are found. A compact front morphology emerges if the invading fluid wets the beads while a fingered morphology is found for non–wetting invading fluids, causing the residual amount of defending fluid to differ by one order of magnitude. The corresponding crossover between these two regimes in terms of the advancing contact angle is governed by an interplay of wettability and pore geometry and can be predicted on the basis of a purely quasi–static consideration of local instabilities that control the progression of the invading interface.

In this study, the dynamics of initially stationary liquid drops on smooth and topographic inclined silicon surfaces was investigated experimentally and by lattice Boltzmann simulations. The transient contact angles and the critical angle of inclination were measured systematically for different liquids, drop sizes, and surfaces having different wettability and surface roughness. In general, the critical angle of inclination is larger for hydrophilic than for hydrophobic surfaces, irrespective of the liquids, and increases with increasing contact angle hysteresis and decreasing drop sizes. A two-phase liquid-vapor lattice Boltzmann model based on the Shan and Chen approach was developed for two dimensions which incorporates the wetting and topographic characteristics of the surface. The simulation results matched the experimentally found features quantitatively and allowed one to explore the roll-off behavior even in cases that can hardly be accessed experimentally.

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