The effect of surface tension on free-surface flow induced by a point sink

Abstract

The steady, axisymmetric flow induced by a point sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface; but, as the surface tension increases, this is replaced by a tendency for the lowest point on the free surface to descend sharply as the Froude number is increased.2010 Mathematics subject classification: 0102.

Predicting transition from selective withdrawal to entrainment in two fluid stratified systems

“…The flow phenomena observed in this experiment is similar to the one observed by Lubin et al [2] and Hocking et al [8,9]. At a certain entrainment depth and at a certain flow rate a dip forms above the point sink on the surface of the lower fluid.…”

“…The critical drawdown Froude number based on the depth of the withdrawn fluid layer for conditions in which interfacial waves wer not a significant factor is approximately 1. Later, Hocking et al [9] included the surface tension effect due to the curvature of the interface and concluded that the Froude number, based on the sink depth from the interface, represented the complete flow phenomenon and the surface tension adds a resistance to the withdrawal force.…”