Dynamics of a surfactant-laden viscoelastic thread in the presence of surface viscosity

Abstract

As is known, the presence of surfactants can profoundly influence the dynamics of Newtonian viscous threads. Also, it is known that non-Newtonian viscoelastic threads behave differently from Newtonian ones, particularly in the nonlinear regime. A naturally arising question is how surfactants affect the dynamic behaviour of non-Newtonian viscoelastic threads. To gain some insights into it, we build a one-dimensional model for an Oldroyd-B/finitely extensible nonlinear elastic-Peterlin approximation (FENE-P) viscoelastic liquid thread covered with an insoluble surfactant monolayer based on the slender body theory. A parametric study is performed to examine the effects of the dimensionless numbers related to the surfactant, including the initial concentration, the Marangoni number, the surface Péclet number, the shear Boussinesq number and the dilatational Boussinesq number. It is found that the formation of the beads-on-a-string structure can be greatly delayed by the surfactant. At large values of the surface Péclet number, the exponential thinning of the Oldroyd-B viscoelastic thread is little influenced, but the surfactant may lead to the disappearance of secondary droplets. At moderate values of the surface Péclet number, the surfactant induces the formation of secondary droplets. The primary droplets are axially stretched by the Marangoni or surface viscous stresses and evolve into a prolate or a more singular shape eventually. The surfactant can delay the pinch-off of the FENE-P viscoelastic thread to a great extent, but it affects little the decrease in the minimum thread radius prior to pinch-off when the surface Péclet number is large.