Role of surface viscous stresses in pinch-off of liquid threads

Surfactants are routinely used in diverse applications involving free surface flows with interface pinch-off such as inkjet printing, crop spraying and atomization coating because of their ability to adsorb onto and lower the surface tension of water-air and water-oil interfaces. In addition to lowering surface tension, surfactants may induce surface tension gradients (Marangoni stresses) and cause surface rheological effects. Although much attention has been paid to date to the influence of solutocapillarity and Marangoni stresses on jet/drop breakup, the effect of surface viscous stresses has been inadequately studied given the difficulty in measuring surface viscosities due to the presence of surfactants. We examine their effect on thread breakup by asymptotic analysis and 1D simulations using the slender-jet approximation. We obtain analytical expressions for thinning rate that explicitly depend on surface rheological parameters, thereby also providing a simple new route for measuring surface viscosity. The results obtained with the 1D algorithm are confirmed by direct comparison against predictions made with a 3D but axisymmetric free surface solver.