We propose an extension of the phenomenological Maffettone-Minale (MM) model (Maffettone P. L. and Minale M. , J. Non-Newton. Fluid Mech. , 78 (1998) 227) to describe the time-dependent deformation of a droplet with interfacial viscosity in a shear flow. The droplet, characterised by surface tension σ, is spherical at rest with radius R and deforms into an ellipsoidal shape under a shear flow of rate G, described by a symmetric second-order tensor S. In addition to surface tension, the extended MM (EMM) model incorporates interfacial shear and dilatational viscosities, μs and μd, through the corresponding Boussinesq numbers Bq ₒ= ₒ/ R and Bq ₃= ₃/ R, where μ is the bulk viscosity. A central goal of this work is to quantify the parameter range over which the EMM model provides a realistic description of droplet deformation, as a function of the capillary number Ca= R G/ and the Boussinesq numbers. To this end, model predictions are systematically compared with fully resolved numerical simulations.
A 2026 study studied this question.