Comparing free surface and interface motion in electromagnetically driven thin-layer flows

Two-dimensional fluid dynamics is often approximated experimentally using a thin fluid layer which is driven by electromagnetic forces. That approximation is most accurate when both the direction and magnitude of the flow are nearly uniform over the depth of the layer. In this study we test uniformity by measuring fluid motion at two depths simultaneously. We use a two-layer configuration with immiscible fluids and track particles at the free surface and the interface of the two layers for Reynolds numbers Re ≤ 400. We find that the flow direction is almost entirely independent of depth, though its slight misalignment grows as the Reynolds number increases. Similarly, we find that the ratio of speeds at the free surface and interface nearly matches a recent theoretical prediction, even for complex flows, but deviates systematically as Re increases. We find that flows with thinner fluid layers are better aligned and more nearly match the predicted speed ratio than flows with thicker layers. Finally, we observe that in time-dependent flows, flow structures at the interface tend to follow flow structures at the free surface via complicated dynamics, moving along similar paths with a short time delay.