Abstract

Pressure-driven flows in channels are considered when one or both walls are structured with a large number of parallel micro grooves that are aligned longitudinally with the flow. The grooves have finite depth and are typically filled with gas, enabling the liquid in the channel to flow in an almost shear-free configuration known as a ``plastron”. This leads to some interesting two-phase mathematical problems with mixed boundary conditions – no slip on solid surfaces and zero shear at liquid gas menisci that are allowed to have arbitrary curvature. Due to the imposed pressure gradient the meniscus curvature changes as we traverse the channel and in general a fully 3D flow ensues. This talk will be in three parts: (i) a complete description of solutions in the 2D case assuming the flow to be parallel; (ii) allowing 3D effects through slow longitudinal variations of the meniscus curvature leading to a semi-analytical construction; (iii) the hydrodynamic bi-global instability characteristics of such flows at arbitrary Reynolds numbers. All numerical work is constructed to be spectrally accurate and is coupled with singularity removal at boundary discontinuities. The stability results will also be compared with experimental observations.