A reduced model for droplet dynamics in shear flows at finite capillary numbers

Abstract

We propose an extension of the Maffettone-Minale (MM) model to predict the dynamics of an ellipsoidal droplet in a shear flow. The parameters of the MM model are traditionally retrieved in the framework of the perturbation theory for small deformations, i.e., small capillary numbers ($\mbox{Ca} \ll 1$) applied to Stokes equations. In this work, we take a novel route, in that we determine the model parameters at finite capillary numbers ($\mbox{Ca}\sim {\cal O}(1)$) without relying on perturbation theory results, while retaining a realistic representation in creeping time and steady deformation attained by the droplet for different realizations of the viscosity ratio $\lambda$ between the inner and the outer fluids. This extended MM (EMM) model hinges on an independent characterization of the process of droplet deformation via numerical simulations of Stokes equations employing the Immersed Boundary - Lattice Boltzmann (IB-LB) numerical techniques. Issues on droplet breakup are also addressed and discussed within the EMM model.