Numerical simulation of drop and bubble dynamics with soluble surfactant

Abstract

Numerical computations are presented to study the effect of soluble surfactant on the deformation and breakup of an axisymmetric drop or bubble stretched by an imposed linear strain flow in a viscous fluid. At the high values of bulk Peclet number Pe in typical fluid-surfactant systems, there is a thin transition layer near the interface in which the surfactant concentration varies rapidly. The large surfactant gradients are resolved using a fast and accurate "hybrid" numerical method that incorporates a separate, singular perturbation analysis of the dynamics in the transition layer into a full numerical solution of the free boundary problem. The method is used to investigate the dependence of drop deformation on parameters that characterize surfactant solubility. We also compute resolved examples of tipstreaming, and investigate its dependence on parameters such as flow rate and bulk surfactant concentration. C 2014 AIP Publishing LLC. [http://dx. Wang, Siegel, and Booty Phys. Fluids 26, 052102 (2014) alone. Under the simplification of low Reynolds number flow, the evolution can be described completely by interface quantities and solved by surface-based methods such as the boundary integral method. This is among the most accurate and efficient numerical methods for solving free and moving boundary problems. Boundary integral simulations of the effect of insoluble surfactant on the deformation and breakup of axisymmetric and 3D drops in an imposed flow have been given These characterize the dependence of drop deformation on the capillary number Ca = μ 2 GR 0 /γ 0 , where μ 2 is the suspending fluid viscosity, G is the imposed strain rate, R 0 is the undeformed radius of the drop, and γ 0 is the surface tension of a clean interface. Tipstreaming is observed in the boundary integral computations of Bazhlekov, Anderson, and Meijer, 12 and Eggleton, Tsai, and Stebe 13 when the ratio λ = μ 1 /μ 2 of drop to suspending fluid viscosity is small and the capillary number is above a critical value. To the best of our knowledge, these are the only numerical simulations that evoke the tipstreaming observed in experiments. Other boundary integral studies of drop and bubble evolution with insoluble surfactant are, e.g., Refs. 14-19. Volume of fluid numerical simulations 20, 21 of low viscosity ratio drops with insoluble surfactant in extensional flow also show droplets or small drop fragments emitted from pointed bubble ends. However, these are on the scale of the mesh spacing and are therefore not well resolved, so that tipstreaming may have been introduced as a numerical artifact.A soluble surfactant advects and diffuses in the bulk fluid, and there is an exchange or transfer between its dissolved form in the bulk and its adsorbed form on the interface. We adapt a "hybrid" numerical method for the study of surfactant solubility effects in interfacial flow that was introduced in Refs. 22 and 23. The method applies for small bulk diffusion of surfactant, or equivalently for large bulk Peclet number Pe. The value of Pe in ...

Stability and tip streaming of a surfactant-loaded drop in an extensional flow. Influence of surface viscosity

“…In fact, there is a widespread belief that surfactant is a necessary element to produce tip streaming in unbounded extensional flows. Tip streaming has been described from simulations of such systems (Eggleton et al 2001;Booty & Siegel 2005;Bazhlekov et al 2006;Wang, Siegel & Booty 2014).…”

“…The size of the ejected thread increases with the initial surfactant surface concentration. Wang et al (2014) studied the tip streaming numerically in a droplet covered with a soluble surfactant, placed in a uniaxial extension flow. They showed that the adsorption of a small amount of surfactant onto the interface produces tip streaming.…”

The role of soluble surfactants in the linear stability of two-layer flow in a channel

“…(i) Bi → 0, found when there is no desorption from the interface to the bulk, i.e. k d → 0 (Booty & Siegel 2010;Wang et al 2014). This condition is equivalent to setting the flux J b = 0 in (2.28) and (2.29);…”

Soluble surfactant spreading: How the amphiphilicity sets the Marangoni hydrodynamics

“…A large part of past studies deal with the spreading of soluble liquids (mostly alcohols) on water, i.e., systems without cmc and micelles [38][39][40][41][42][43]. When solutions of soluble surfactants are considered, mostly numerical simulations have been done [44][45][46], whereas experimental studies often focused on transient behavior, especially on front propagation [47][48][49]. Moreover, experimental results were often collected for very thin films (less than 1 mm in thickness), adding complexities such as the occurrence of fingering instabilities [50,51].…”