No abstract

Using phase-stepped interferometry, we have measured full two-dimensional maps of the free-surface shape of a thin liquid film of water flowing over an inclined plate with topography. The measurement technique allows us to image automatically the shape of the free surface in a single field of view of about 2.4 by 1.8 mm, with a lateral resolution of 3.1 μm and a height resolution of 0.3 μm. By imaging neighbouring regions and combining them, complete two-dimensional free-surface profiles of gravity-driven liquid films with a thickness ranging between 80 and 120 μm are measured, over step, trench, rectangular and square topographies with depths of 10 and 20 μm, and lateral dimensions of the order of 1 to several mm. The experimental results for both one- and two-dimensional flows are found to be in good agreement with existing models, including a recent two-dimensional Green's function of the linearized problem by Hayes et al. This extends the applicability of simple models to cases with a high value of topography steepness and low-viscosity liquids as in our experiments. A corollary of the agreement with the linear two-dimensional model is that our experimental results behave linearly, a convenient property that allows the free-surface response to complex topographies to be worked out from knowledge of the response to an elementary topography like a square.

The complex morphologies of liquids on topographically structured substrates are exploited for liquid actuation in open microchannels. The liquid is either confined in prefabricated grooves, thus forming elongated filaments, or gathers in macroscopic drops without invading the grooves, depending on conditions. Using the electrowetting effect, we can reversibly switch between these two states. The length of the filaments is sensitive to the ionic content of the liquid and can be described quantitatively with an electrical model considering the voltage drop along the groove.