Thermodynamically consistent modelling of two-phase flows with moving contact line and soluble surfactants

Abstract

Droplet dynamics on a solid substrate is significantly influenced by surfactants. It remains a challenging task to model and simulate the moving contact line dynamics with soluble surfactants. In this work, we present a derivation of the phase-field moving contact line model with soluble surfactants through the first law of thermodynamics, associated thermodynamic relations and the Onsager variational principle. The derived thermodynamically consistent model consists of two Cahn–Hilliard type of equations governing the evolution of interface and surfactant concentration, the incompressible Navier–Stokes equations and the generalized Navier boundary condition for the moving contact line. With chemical potentials derived from the free energy functional, we analytically obtain certain equilibrium properties of surfactant adsorption, including equilibrium profiles for phase-field variables, the Langmuir isotherm and the equilibrium equation of state. A classical droplet spread case is used to numerically validate the moving contact line model and equilibrium properties of surfactant adsorption. The influence of surfactants on the contact line dynamics observed in our simulations is consistent with the results obtained using sharp interface models. Using the proposed model, we investigate the droplet dynamics with soluble surfactants on a chemically patterned surface. It is observed that droplets will form three typical flow states as a result of different surfactant bulk concentrations and defect strengths, specifically the coalescence mode, the non-coalescence mode and the detachment mode. In addition, a phase diagram for the three flow states is presented. Finally, we study the unbalanced Young stress acting on triple-phase contact points. The unbalanced Young stress could be a driving or resistance force, which is determined by the critical defect strength.

Effect of salinity on oil production: review on low salinity waterflooding mechanisms and exploratory study on pipeline scaling

“…It has been applied to solidification dynamics, viscous fingering, fracture dynamics, vesicle dynamics, etc. The method substitutes boundary conditions (matching conditions) at the interface by a partial differential equation for the evolution of an auxiliary field (the phase field) that acts as an order parameter [100][101][102]. A phase-field model is usually constructed in such a way that in the limit of an infinitesimal interface width (the so-called sharp interface limit), the correct interfacial dynamics are recovered.…”

A unified apparent porosity/permeability model of organic porous media: Coupling complex pore structure and multi-migration mechanism

“…SEM images from Eagle Ford shale samples showed that pores are mainly round, angular, and slitshaped pores (Afsharpoor and Javadpour, 2016;Song et al, 2019). In conventional oil and gas reservoirs, using circular pores approximation to represent actual pore type is reasonable because the pore surface-to-volume ratio in conventional reservoirs is small (Zhu et al, 2019). In shale reservoirs, pores have a large surface-to-volume ratio.…”

Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities

“…We can directly obtain chemical potentials through variational derivatives of the free energy functional with respect to two phase-field variables. Two Cahn-Hilliard-type equations can be adopted to describe the evolutions of two phase-field variables (Liu et al, 2018;Zhu et al, 2019c). The hydrodynamics coupled phase-field surfactant model can be obtained if two Cahn-Hilliard-type equations are further coupled to the Navier-Stokes equation.…”