Simulation of surfactant-mediated tipstreaming in a flow-focusing geometry

Simulations are performed of a surfactant-laden drop that is stretched by an imposed uniaxial extension flow at infinity with flow focusing provided by two transverse, coaxial, annular baffles placed symmetrically to either side of the drop. The geometry is axisymmetric, with additional symmetry in the transverse plane that contains the drop center. Under suitable conditions, the drop can enter a mode of drop breakup referred to as tipstreaming, in which a thin elongated filament or thread is emitted from the drop ends and which subsequently breaks up into small droplets via capillary instability. The influence that flow focusing has on the conditions required for tipstreaming and on quantities such as the thread radius are investigated by study of sample simulations and the extent of flow focusing is varied by changing the inner or aperture radius of the annular baffles. The surfactant is soluble and bulk-interface surfactant exchange is in the mixed-kinetic or finite-Biot-number regime. The boundary-integral method is used for the underlying two-phase Stokes flow solver, combined with a finite-difference scheme for evolution of adsorbed surfactant on the interface. The dynamics of dissolved bulk phase surfactant is resolved by a large-bulk-Péclet-number asymptotic approach. Results on the conditions for tipstreaming in the simulations are compared to separate experimental results on conditions for tipstreaming in a microfluidic flow-focusing device.