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We propose an extension of the Maffettone-Minale (MM) model to predict thedynamics of an ellipsoidal droplet in a shear flow. The parameters of the MMmodel are traditionally retrieved in the framework of the perturbation theoryfor 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 wedetermine the model parameters at finite capillary numbers ($\mbox{Ca}\sim{\cal O}(1)$) without relying on perturbation theory results, while retaining arealistic representation in creeping time and steady deformation attained bythe droplet for different realizations of the viscosity ratio $\lambda$ betweenthe inner and the outer fluids. This extended MM (EMM) model hinges on anindependent characterization of the process of droplet deformation vianumerical simulations of Stokes equations employing the Immersed Boundary -Lattice Boltzmann (IB-LB) numerical techniques. Issues on droplet breakup arealso addressed and discussed within the EMM model.

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