Computational and experimental analysis of dynamics of drop formation

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Abstract
Dynamics of formation of a drop of a Newtonian liquid from a capillary tube into an ambient gas phase is studied computationally and experimentally. While this problem has previously been studied computationally either (a) using a set of one-dimensional equations or (b) treating the dynamics as that of irrotational flow of an inviscid fluid or creeping flow, here the full nonlinear, transient Navier–Stokes system subject to appropriate initial and boundary conditions is solved in two dimensions to analyze the dynamics at finite Reynolds numbers. The success of the computations rests on a finite element algorithm incorporating a multiregion mesh which conforms to and evolves with the changing shape of the drop. The new algorithm is able to capture both the gross features of the phenomenon, such as the limiting length of a drop at breakup and the volume of the primary drop, and its fine features, such as a microthread that develops from a main thread or a neck in a viscous drop approaching breakup. The accuracy of the new calculations is verified by comparison of computed predictions to old and new experiments. With the new algorithm, it is shown for the first time that the interface of a viscous drop can overturn before the drop breaks. Calculations have also been carried out to determine the range of parameters over which algorithms that treat the drop liquid as inviscid and the flow inside it as irrotational can accurately predict the dynamics of formation of drops of low viscosity liquids. Limiting lengths of drops and primary drop volumes are computed over a wide range of the parameter space spanned by the relevant dimensionless groups.