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An analytical-numerical model is developed to calculate the deformation and spreading of axisymmetric and two-dimensional liquid drops in a gas stream for small Ohnesorge numbers and large Reynolds numbers. The model is based on an approximate series solution of the Navier-Stokes equations written for the interior flow of the drop and assuming a quasi-static gas flow. The pressure distribution on the drop surface is provided using a perturbation analysis about a trivial zeroth-order solution. The axisymmetric formulation is used for calculating the deformation of the spherical droplets, and the two-dimensional formulation is used to develop a model for predicting the spreading of the cross section of liquid jets in crossflows. The penetration of the liquid jet in the gas flow is calculated, and the results are compared with experimental and empirical results.
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Mashayek et al. (2009) studied this question.
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