Simulation and experiments of droplet deformation and orientation in simple shear flow with surfactants

Abstract

The deformation and orientation behavior of three-dimensional (3D) viscous droplets with and without surfactants is studied in simple shear flow using simulations and experiments. Two added amounts of surfactants are considered, along with a range of viscosity ratios and capillary numbers. The numerical method couples the boundary integral method for interfacial velocity, a second-order Runge–Kutta method for interface evolution, and a finite element method for surfactant concentration. The algorithm assumes a bulk-insoluble, nonionic surfactant, and uses a linear equation of state to model the relationship between the interfacial tension and the surfactant concentration on the drop surface. The algorithm was validated by comparison with other numerical results and good agreement was found. The experiments are performed in a parallel-band apparatus with full optical analysis of the droplet. The simulated and measured 3D steady-state shape of the ellipsoidal drops and their orientation are in reasonably good agreement. It was found that the surfactants have a greater effect on drop geometry for smaller viscosity ratios and that the deformation increases as the transport of surfactant becomes more convection dominated. It was also found that surfactants cause the drops to align more in the flow direction and that, for both clean and surfactant-covered drops, this alignment increases with viscosity ratio. Finally, simulations showed a wider distribution of surfactant on the interface for smaller viscosity ratios.