Numerical Study of Surfactant-Laden Drop-Drop Interactions

Abstract

In this paper, we numerically investigate the effects of surfactant on drop-drop interactions in a 2D shear flow using a coupled level-set and immersed interface approach proposed in (Xu et al., J. Comput. Phys., 212 (2006), 590-616). We find that surfactant plays a critical and nontrivial role in drop-drop interactions. In particular, we find that the minimum distance between the drops is a non-monotone function of the surfactant coverage and Capillary number. This non-monotonic behavior, which does not occur for clean drops, is found to be due to the presence of Marangoni forces along the drop interfaces. This suggests that there are non-monotonic conditions for coalescence of surfactant-laden drops, as observed in recent experiments of Leal and co-workers. Although our study is two-dimensional, we believe that drop-drop interactions in three-dimensional flows should be qualitatively similar as the Maragoni forces in the near contact region in 3D should have a similar effect.

Coalescence of surfactant-laden drops by Phase Field Method

“…Coalescence is favoured when droplets are less deformed (Clean at Ca = 0.10 and case A) and is prevented when droplets are more deformed (cases B-C-D and Ca = 0.12). The behaviors of the deformation parameter D obtained are in good agreement with previous experiments [24] and numerical studies [6,61,77].…”

“…After the initial approaching stage, a thin liquid film forms between the droplets. If the liquid film thickness decreases below a critical threshold, the attractive van der Waals forces draw the interfaces even closer and the two droplets coalesce [12,13,14,26,40,77,82]. The presence of a surfactant can drastically affect the interaction: indeed, the increased deformability and the tangential stresses at the interface hamper the draining of the thin liquid film and alter the interaction outcome [13].…”

A level-set continuum method for two-phase flows with insoluble surfactant

“…There are very few numerical simulations in surfactant-laden drop-drop interactions, see [6,41] for two surfactant-laden drop simulations in shear flows governed by Stokes equations. In the set-up, two surfactant-laden drops are initially circles with the radii of 0.5, centered at (À1, 0.25) and (1, À0.25), respectively.…”

“…This approach was applied to simulating surface phase separations in [24] and surfactant-laden dropdrop interactions in 2D Stokes shear flow in [41]. This approach was extended to 3D interfacial flows with insoluble surfactant in [45].…”

A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant

“…As for interfacial flows with surfactant, an approach was proposed in [28], which coupled the IIM as the flow solver and an Eulerian level-set method as the surfactant solver. This approach was applied to the simulation of surface phase separations in [18], and the surfactant-laden drop-drop interactions in [29]. All these works were in 2D.…”