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The effects of shear and vorticity on deformation of a drop

A fluid drop immersed in a second incompressible fluid is deformed by a motion which, far from the drop, varies linearly with distance. Deformation of the drop is then determined by both the rate of deformation and the vorticity of the continuous fluid phase far from the drop. Experiments are described in which the vorticity and rate of deformation were independently varied by means of an eccentric-disk rheometer field. It is shown that predictions from a small-parameter expansion to first order in ε = μ0Gb/σ are in good agreement with experiment to values of ε as large as 0·4, where μ0 is viscosity of the continuous phase, G a measure of the flow strength, b the drop radius, and σ the interfacial tension. Of the several terms which arise in the O(ε) expansion, only that one which contains a Jaumann derivative of the deformation parameter provides an important contribution beyond Taylor's original analysis of the problem. This fact greatly simplifies the computation of drop shape.