The effects of surface tension on the initial development of a free surface adjacent to an accelerated plate

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Colleges, School and Institutes

Abstract

When a vertical rigid plate is uniformly accelerated horizontally from rest into an initially stationary layer of inviscid incompressible fluid, the free surface will undergo a deformation in the locality of the contact point. This deformation of the free surface will, in the early stages, cause a jet to rise up the plate. An understanding of the local structure of the free surface in the early stages of motion is vital in many situations, and has been developed in detail by King & Needham (J. Fluid Mech., vol. 268, 1994, pp. 89-101). In this work we consider the effects of introducing weak surface tension, characterized by the inverse Weber number W, into the problem considered by King & Needham. Our approach is based upon matched asymptotic expansions as W →. It is found that four asymptotic regions are needed to describe the problem. The three largest regions have analytical solutions, whilst a numerical method based on finite differences is used to solve the time-dependent harmonic boundary value problem in the last region. Our results identify the local structure of the jet near the vicinity of the contact point, and we highlight a number of key features, including the height of this jet as well as its thickness and strength. We also present some preliminary experimental results that capture the spatial structure near the contact point, and we then show promising comparisons with the theoretical results obtained within this paper.

Details

Original languageEnglish
Pages (from-to)37-73
Number of pages37
JournalJournal of Fluid Mechanics
Volume776
Early online date30 Jun 2015
Publication statusPublished - 10 Aug 2015

Keywords

  • interfacial flows (free surface), jets, wakes/jets