Geometric Consistency in Taylor Analogy Modeling of Droplet Deformation in the Small Deformation Regime

Abstract Taylor analogy deformation models are widely used to predict droplet deformation in planar extensional flows, where model performance is commonly evaluated using the Taylor deformation parameter. However, the agreement in the Taylor deformation parameter alone does not necessarily ensure accurate prediction of droplet geometry, because the droplet elongation and size are fundamentally governed by the droplet interface displacement. As a result, relying solely on the Taylor deformation parameter may conceal errors in droplet elongation, even when the apparent deformation is reasonably reproduced. In addition, the existing models show limited predictive capability at low viscosity ratios. In the present study, the geometric consistency of Taylor analogy modeling is examined in the small deformation regime using three-dimensional numerical simulations. The results show that the limitations of existing models originate from simplified geometric assumptions used to relate the droplet interface displacement to the Taylor deformation parameter. Based on these findings, a geometry-consistent formulation is proposed to improve the prediction of both droplet elongation and deformation across a wide range of viscosity ratios, including the low viscosity ratio regime.