Pore-scale analysis of the minimum liquid film thickness around elongated bubbles in confined gas-liquid flows

The fluid mechanics of elongated bubbles in confined gas-liquid flows in micro-geometries is important in pore-scale flow processes for enhanced oil recovery and mobilization of colloids in unsaturated soil. The efficiency of such processes is traditionally related to the thickness of the liquid film trapped between the elongated bubble and the pore's wall, which is assumed constant. However, the surface of long bubbles presents undulations in the vicinity of the rear meniscus, which may significantly decrease the local thickness of the liquid film, thus impacting the process of interest. This study presents a systematic analysis of these undulations and the minimum film thickness induced in the range Ca=0.001-0.5 and Re=0.1-2000. Pore-scale Computational Fluid Dynamics (CFD) simulations are performed with a self-improved version of the opensource solver ESI OpenFOAM which is based on a Volume of Fluid method to track the gas-liquid interface. A lubrication model based on the extension of the classical axisymmetric Bretherton theory is utilized to better understand the CFD results. The profiles of the rear meniscus of the bubble obtained with the lubrication model agree fairly well with those extracted from the CFD simulations. This study shows that the Weber number of the flow, We=CaRe, is the parameter that best describes the dynamics of the interfacial waves. When We < 0.1, a single wave crest is observed and the minimum film thickness tends to an asymptotic value, which depends on the capillary number, as We → 0. Undulations dampen as the capillary number increases and disappear completely when Ca=0.5. When We > 0.1, a larger number of wave crests becomes evident on the surface of the rear meniscus of the bubble. The liquid film thickness at the crests of the undulations thins considerably as the Reynolds number is increased, down to less than 60% of the value measured in the flat film region. This may significantly influence important environmental processes, such as the detachment and mobilization of micron-sized pollutants and pathogenic micro-organisms adhering at the pore's wall in unsaturated soil.