The Influence of Surfactant on the Deformation and Breakup of a Viscous Drop: The Effect of Surfactant Solubility

Droplet behavior in the presence of insoluble surfactants

“…Whether the surfactant should be soluble in the droplet phase or in the matrix phase depends on various factors. According to Milliken and Leal, 9 the effect of surfactants which are soluble in the matrix phase on the droplet deformation is similar to the effect of insoluble surfactants. The effect of solubility in the droplet phase is not yet studied.…”

“…The surfactant is assumed to be insoluble, which is a good approximation if the bulk concentration is dilute 12 or if the migration to and from the bulk is slow. 18 In fact, the study by Milliken and Leal 9 shows that in almost all cases, the droplet deformation and breakup in the presence of soluble surfactants fall between the results for insoluble surfactant and those for a clean interface.…”

“…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.…”

“…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.…”

A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface

“…In the context of surfactants, a boundary integral method for studying the effect of insoluble surfactants on drop deformation was developed in [82]. This method was extended to arbitrary viscosity ratios in [67], and to soluble surfactants in [66]. Another tracking method is the front-tracking method, where a fixed grid is used to compute the flow, while a set of connected marker particles is used to track the interface and any interfacial quantities.…”