Self-Similar Draining near a Vertical Edge
Nan Xue, Howard A. Stone
Abstract
When a liquid film drains on a vertical plate, the film becomes nonuniform near the vertical edge. Here we experimentally report the three-dimensional (3D) self-similar shape of this film. Based on the well-known 2D self-similar solution of a draining film far from the edge, we identify a new 3D self-similar scaling, which converts the partial differential equation for the film thickness with three independent variables into an ordinary differential equation. Interferometry is performed to measure the film thickness as a function of position and time, and the results are in excellent agreement with the theoretical predictions.
Topics & Concepts
Enhanced Data Rates for GSM EvolutionOpticsScalingOrdinary differential equationMeasure (data warehouse)Partial differential equationMaterials sciencePosition (finance)InterferometryMathematical analysisFunction (biology)PhysicsDifferential equationGeometryMathematicsComputer scienceTelecommunicationsEconomicsEvolutionary biologyBiologyFinanceDatabaseFluid Dynamics and Thin FilmsFluid Dynamics and Heat TransferPlant Water Relations and Carbon Dynamics