Stability of surfactant-laden droplets with surface viscosity in shear flow

The theoretical description of surfactant-laden interfaces with surface viscosity is challenging and, despite the importance of surface viscosity on the interface behaviour, the influence of surface viscosity is frequently neglected in theoretical and computational studies. Recent work on the deformation of surfactant-laden droplets in shear flow demonstrates a non-trivial influence of both surface shear and dilatational viscosities on the surfactant distribution and, consequently, the droplet shape [Luo et al., J. Fluid Mech. 858 (2019), 91]. Using a front-tracking method in conjunction with the Boussinesq-Scriven model, we study numerically the stability of drops laden with insoluble surfactants in an incompressible shear flow. Our study focuses on the influence of the constitutive parameters (surface pressure, surface shear viscosity, surface dilatational viscosity) of the Boussinesq-Scriven model on the critical capillary number above which the droplet breaks up and the influence of the surface rheology on the evolution of this instability.