Cox modified model to describe the time evolution of a drop deformation for high viscosity drops in simple shear flow. (June 2018) - Escalante-Velázquez, C.A.; Rosas, I.Y.; Reyes, M.A.H.; Geffroy, E.
Highlights: A modified Cox model which describes accurately the period of the oscillations during transient deformations observed for a highly viscous drop is presented. This modified model was constructed from the analysis of numerical simulations, experimental results in a two roll mill (2TRMs) device, as well as experimental data of drop deformation available in the literature. It is demonstrated that the oscillation period depends not only on the shear rate as predicted by Cox model but also on the viscosity ratio ( λ ). The expression founded for oscillation period coincides with the trend experimentally observed in the periods and also predicts a "critical value" for λ for which the oscillatory behavior disappears. Abstract: In this work a modification of Cox's model for the deformation of a highly viscous drop is presented, which describes accurately the period of the oscillations during transient deformations. It is demonstrated that the oscillation period depends not only on the shear rate as predicted by Cox model but also on the viscosity ratio. This modified model is obtained from the analysis of numerical simulations of drop deformation using the boundary element method, while the experimental results are those obtained in quasi-simple shear flow generated in a two roll mill (2TRMs) device, as well as experimental data available in the literature. The predictions of the periods match very well with experimental data.