Year: 2026
Type: preprint
Abstract: Viscous dissipation in a deforming drop arises from internal velocity gradients, and so direct measurement has therefore required optical or computational access to the drop interior. For sessile drops undergoing predominantly single-mode oscillations, we show the volumetric viscous dissipation rate is proportional to the time rate of change of a scalar measure of silhouette deformation. The dissipation rate per unit volume is proportional to the dynamic viscosity and the square of the rate of change of the drop silhouette deformation. We obtain this result by decomposing the silhouette deformation into data-driven modes and reconstructing the associated interior strain-rate field. We validate our theoretical approach against measured ring-down dissipation over a 33-fold range of viscosity. For a steady, oscillatory forcing, an energy balance combined with a base-excited oscillator analogy and a Stokes boundary-layer correction predicts the power transmitted from a vibrating substrate. The model reproduces measurements for a withheld fluid in the drop pre-resonance regime. We identify the ratio of Stokes penetration depth to drop height as the parameter governing volumetric energy transfer from the vertically oscillating substrate into the drop, and predict transfer is non-monotonic in both viscosity and drop size. A thin shear layer engages too little of the drop, while a layer spanning the drop height homogenizes the velocity field and suppresses shear. Cantilever ring-down experiments confirm our predictions. Our measurement approach, which requires only the drop silhouette, estimates the bulk dissipation that inviscid sessile-drop theory structurally omits in systems where the interior is optically or practically inaccessible.
Source: Research Square
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212280977