Immiscible displacement of oil by water in a microchannel: Asymmetric flow behavior and nonlinear stability analysis of core-annular flow

The immiscible displacement of oil by water in a circular microchannel was investigated. A fused silica microchannel with an inner diameter of 250 μm and a length of 7 cm was initially filled with a viscous silicone oil. Only water then was injected into the channel. We describe our flow observations based on the two-dimensional images captured in the middle of the channel. The water finger displaced the oil and left an oil film on the channel wall. While the oil was being displaced at the core, the flow resistance decreased, which resulted in increases in water flow rate and inertia. Eventually, the water finger reached the channel exit and formed a core-annular flow pattern. The wavelength of the waves formed at the oil-water interface also increased with the increase in inertia. The initially symmetric interfacial waves became asymmetric with time. Also, the water core shifted from the center of the channel and left a thinner oil film on one side of the microchannel. Under all flow rates tested in this study, as long as the water was continuously injected, the water core was stable and no breakup into droplets was observed. We also discuss the flow stability based on nonlinear and linear stability analyses performed on the core-annular flow. Compared to the linear analysis, which ignores the inertia effects, the nonlinear analysis, which includes the inertia effects, predicts longer interfacial wavelengths by a factor of 1/sqrt[1-a(o)/2(We(w) + We(o)a(o)(2)/1-a(o)(2))] where We(w) and We(o) are the Weber numbers of the water and the oil phases, respectively, and a(o) is the unperturbed water core radius made dimensionless by the channel radius.