The effect of surfactant on the transient motion of Newtonian drops

Abstract

The effect of dilute, insoluble surfactant on the deformation and breakup of a viscous drop is examined. Two cases are considered: the deformation and stretching of a drop in a uniaxial extensional flow and the surface-tension-driven motion of an elongated drop in a quiescent fluid. Aside from rescaling the mean capillary force through an average decrease in the interfacial tension, surfactants alter the motion of a viscous drop through gradients in interfacial tension. The effects of surfactants are found to be most pronounced for small viscosity ratios, where Marangoni stresses substantially retard the interfacial velocity and cause the drop to behave as though it were more viscous. Surfactants are found to facilitate the formation of pointed ends during drop stretching, and this may explain the observation of tip streaming in experiments with viscoelastic drops. Surfactant gradients also allow drops to be elongated to a larger degree without producing end pinching.

Droplet behavior in the presence of insoluble surfactants

“…8 Therefore, the effect of surfactant is smaller for higher viscosity ratios. 4,[9][10][11]17,18 In contrast to previous studies, where the focus was mainly on the determination of the critical capillary number and the behavior of droplets in subcritical flows ͑steady droplet shape and tip streaming͒, this study focuses on the time-dependent deformation of droplets in a supercritical elongational flow (Caϭ1.1 Ca c ). Droplet deformation and breakup as a function of the Péclet number is determined with a finite element method.…”

“…As it became clear a few years later, 3,4 this new mode of breakup was actually due to the influence of interfacially active materials. These surfactants reduce the interfacial tension coefficient, and may introduce Marangoni stresses if the surfactant concentration gradient along the interface is large.…”

“…Therefore, a low viscosity ratio droplet will behave as if its viscosity ratio was much larger. 4,[9][10][11] Whether the upper bound ⌫ ϱ is reached, depends on the surfactant coverage ⌫/⌫ ϱ and the Péclet number Pe, which is the ratio between convection and diffusion along the droplet interface. 12 For low surfactant coverage, the upper bound is not reached by far, and the droplet deformation will be higher than in the case of a clean droplet.…”

Microscale tipstreaming in a microfluidic flow focusing device

“…Modeling this process is not trivial since a detailed model for the problem involves simultaneous solutions of the Stokes equations in each liquid together with velocity and stress boundary conditions at the interface. [25][26][27][28] The normal and shear stress boundary conditions couple the velocity field with variations in the surface tension along the interface, and additional equations are also needed in order to couple surface tension with surface concentration, and surface concentration with diffusion, adsorption, and desorption processes for mass transfer of molecules from the bulk onto the interface.…”

“…These numerics are based upon a boundary integral formulation that was extended to include surfactant dynamics by Stone and Leal 26 and Milliken et al 27 While Eggleton and co-workers focused on elongational flow, recent work by Bazhlekov et al 28 using similar numerical methods has also shown similar behavior in droplets subject to shearing flows, also using insoluble surfactants. It is worth noting that this recent work reproduces numerically an experimental result reported by Grace 29 showing that below a critical viscosity ratio, surfactants lead to a sharp reduction in the critical capillary number for breakup of sheared droplets, and that this critical capillary number is independent of viscosity ratio below the critical value.…”