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This study presents droplet dynamics in a rough capillary channel. Prior studies investigating the effect of roughness on fluid flow have mainly considered a continuous phase whose behavior is different from a discontinuous phase, i.e., an oil slug. To explore the dynamic behavior of droplet motion across a rough channel, a direct numerical simulation of in a three-dimensional channel is performed. Three models have been considered: model A had a rough surface only on the bottom walls, model B on both the bottom and top walls, and model C on all walls. The results show that in contrast with common observations, roughness promotes droplet mobility in comparison with smooth walls. The presence of roughness results to an additional energy required to move the droplet, and the degree of confinement increases with the roughness; thus, the difficult of mobilization increases with the increase in roughness. Different roughness parameter effects have been investigated. The results have shown that the critical pressure increases with the increase in the pillar's height and decreases with the pillars spacing. The offset leads to a decrease in flow resistance for larger contact angles. We noted also that it is more difficult to mobilize a discontinuous phase in a neutral-wet surface condition. Furthermore, discontinuous pillars in the lateral direction led to much higher resistance. Through our comprehensive numerical study, we provide valuable insights into the impact of roughness in capillary channels. These findings can be used as guidelines for designing droplet flow on complex and rough surfaces, such as microfluidic devices, and hold significant relevance in the optimization of droplet control strategies in enhanced oil recovery methods. [ABSTRACT FROM AUTHOR]

Conditions of release of trapped droplets in constricted channels are of great significance in various domains, including microfluidic development and enhanced oil recovery. In our previous studies, a detailed and quantitative analysis of the threshold pressure needed to release a droplet from a constricted channel has been performed. However, droplets may exist in real applications as long droplets, which may exhibit different behavior than finite droplets. Therefore, in this study, direct numerical simulations, combining the fluid flow equations and the phase-field method, have been conducted on three-dimensional constrained channels to investigate discrepancies in release conditions of finite droplets and long droplets. The results have shown that for a finite droplet, the maximum pressure increases with the increase in the contact angle, whereas for a long droplet, the maximum pressure is almost the same both in the water-wet and neutral-wet conditions. Effects of droplet size on the release pressure have also been studied. For the finite droplet and at the water-wet condition (θ = 45°), the minimum release pressure increases linearly with the droplet length, while for the long droplet at similar conditions, the minimum release pressure does not change much as the length of the droplet increases. Furthermore, the release pressure decreases with the increased tapering angle. [ABSTRACT FROM AUTHOR]