Selective withdrawal from a viscous two-layer system

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Abstract
When fluid is withdrawn from a body of stratified fluid the surfaces of constant density are deformed towards the region of withdrawal. The equations describing the flow caused by withdrawal through a point sink in a two-layer unbounded system in which viscous forces dominate are formulated using the boundary-integral representation of Stokes flow. It is shown by dimensional and analytic arguments that surface tension between the layers is a necessary condition for the stability of an interfacial equilibrium in which only one fluid is withdrawn. The critical flow rate above which both fluids are withdrawn is determined numerically as a function of the capillary number. When the flow is supercritical a small adaptation of the numerical scheme allows the proportion of fluid withdrawn from each layer to be found. The various analyses and conclusions further our understanding of the physical processes that determine the compositional output of volcanic eruptions that tap an underlying stratified reservoir of magma.

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