The effect of surfactant on the stability of a liquid thread

The surface-tension-driven motion of a surfactant-coated liquid thread in inviscid surroundings is investigated using linear stability theory as well as one-dimensional nonlinear approximations to the governing Navier–Stokes equations. Examination of analytic limits of the linear dispersion relationship demonstrates that surfactant acts as a distinct mechanism for long-wavelength cut-off, instead of inertia, if the surfactant effects exceed a critical value, β = ½, where β is a dimensionless surface-tension gradient. Two different long-wavelength regimes can be identified, depending on the degree of tangential stress, with β = 1 characterizing a transition from extensionally dominated inertial flow to shear-dominated viscous flow. One-dimensional nonlinear models are formulated which capture the changes in behaviour with variation of β by inclusion of the necessary high-order terms. Scaling close to breakup shows that surfactant is swept away from the pinching region and then has little effect.