2025/12/17 by Guglietta, Fabio, Taglienti, Diego, Sbragaglia, Mauro
Engineering · Chemical Engineering · #Fluid Dynamics and Heat Transfer #Fluid Dynamics and Thin Films #Rheology and Fluid Dynamics Studies
paper · doi:10.48550/arxiv.2512.15616
We propose an extension of the phenomenological Maffettone-Minale (MM) model (P.L. Maffettone and M. Minale, J. Non-Newton. Fluid Mech. 78, 227-241 (1998)) 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 morphological tensor \boldsymbolS. In addition to surface tension, the extended MM (EMM) model incorporates interfacial shear and dilatational viscosities, μs and μd, through the corresponding Boussinesq numbers Bqs=μs/μR and Bqd=μd/μR, 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=μR G/σ and the Boussinesq numbers. To this end, model predictions are systematically compared with fully resolved numerical simulations.