Simulating surfactant effects in phase-transforming fluids

TL;DR

The paper develops a thermodynamically consistent phase-field model based on the isothermal Navier-Stokes-Korteweg equations to simulate surfactant effects on liquid-vapor transformations. It introduces a reconstructed interfacial chemistry via a reconstructed chemical potential $\mu^{\text{rc}}(\rho,c)$, coupled to Langmuir adsorption, and decouples interface thickness from surfactant concentration using a diffuse-domain approach and $\lambda$-scaling. The model reproduces the observed SDS surface-tension trend up to the CMC, predicts interface oscillation frequencies consistent with theory, and captures surfactant-assisted deformation, inhibited coalescence, and delayed condensation in bubble populations. Overall, the framework provides a versatile, thermodynamically grounded tool for studying surfactant dynamics in non-equilibrium phase-change flows and points to future work on complex surface chemistries and acoustic responses.

Abstract

Surfactants are critical in natural processes and engineering, but measuring their concentrations in non-equilibrium conditions and in the presence of flow is difficult. Therefore, computational methods are a key tool for improving our understanding. Predicting the effect of surfactants on liquid-vapor transformations is particularly challenging due to (1) simultaneous mass transfer, non-equilibrium thermodynamics and Marangoni stresses, and (2) the phenomenological assumptions underlying many liquid-vapor phase-change models. Starting from the Navier-Stokes-Korteweg equations, a first-principles approach to liquid-vapor phase transformations, we developed a model of liquid-vapor flows with surfactants. We performed simulations of bubbles under equilibrium and liquid-vapor interface oscillations to demonstrate that the model successfully reproduces surfactant-mediated reductions in surface tension. We also investigated the mechanisms whereby surfactant affects bubble coalescence and condensation. Overall, this work provides a new framework for studying the effect of surfactants on liquid-vapor transformations and suggests multiple areas for future research, including the impact of complex surface chemistries on flow around bubbles and the acoustic response of bubbles with surfactants.

Figures (6)

• Figure 1: Original (black) and reconstructed (green) chemical potential in the interfacial region.
• Figure 2: (A) Surface tension obtained from simulation (red line) and experiments (gray markers) Zhang2014-zp as a function of SDS concentration. (B) Spatial variation of the density for different values of the surfactant concentration, showing that the density profile does not change with surfactant concentration.
• Figure 3: (A) Computational domain showing liquid water at the bottom and water vapor at the top. The initial interface has a sinusoidal shape. The red box highlights the region of interest, whose time evolution is shown on the right for different values of $c_l$. (B) Oscillation frequency of the interface as a function of surfactant concentration.
• Figure 4: (A) Density contours at equilibrium, illustrating the deformation of a single bubble in shear flow. The bubble deforms into an elliptical shape, characterized by a major axis diameter $l$, a minor axis diameter $d$, and an angle of inclination $\beta$. (B) Contour of velocity magnitude. Color arrows are scaled by local velocity magnitude and indicate the flow direction. The black solid line represents the vapor-liquid interface.
• Figure 5: (A) Top: time evolution of the inclination angle $\beta$ of the bubble in shear flow for different values of $c_l$; Bottom: Time evolution of $D$ for different values of $c_l$. (B) Comparison of $\beta$ (top) and $D$ (bottom) using theoretical estimates (dashed line) and simulation results (circular markers).