Two-Phase Displacement Flows

The displacement of a fluid by a second, immiscible, fluid is a phenomenon present in many applications including lung dynamics, oil recovery applications or when you try to drink the last bit of a drink using a straw. There the air is aspired pushing the last droplets of coke into your mouth and making a characteristic, rather disgusting, noise. Due to the problem complexity, studies of these flows in simple geometries are an established approach to gain insight but most of the previous investigations were performed in circular geometries. Thus, rectangular tubes have been proposed as a paradigm for flows in nonaxisymmetric geometries and are more common in applications such as microfluidic devices. Together with Anne Juel and Andrew Hazel at the University of Manchester (UK) we investigated the effect of the geometry (the shape of the straw) on these flows. We uncovered a new scaling law which implies that bulk features of the flows in any rectangular channel can be inferred from those in a square channel. The three-dimensional interfacial problem was later solved numerically using the object-oriented multi-physics finite-element library oomph-lib. The results agree with our previous experimental results to within the ±1% experimental error. Both our experimental and numerical results indicate that the classical two-dimensional model can accurately describe finger propagation in rectangular channels when the width is at least eight times the height.

In many practical applications, however, the geometry of the tubes is considerably more complex, with areas of local constriction. In our experiments, we observed that a centered constriction of the rectangular cross section can lead to fundamental changes in the nature of flow. Tuning the constriction geometry can cause a switchlike transition from centered to localized bubbles at a critical value of the capillary number, allowing the possibility of directing bubbles just by varying the flow-rate. We hope that these new insights can be applied for the design of clever 3D geometries in microfluidc devices.