# Numerical Approximation of a Phase-Field Surfactant Model with Fluid Flow

@article{Zhu2019NumericalAO, title={Numerical Approximation of a Phase-Field Surfactant Model with Fluid Flow}, author={Guangpu Zhu and Jisheng Kou and Shuyu Sun and Jun Yao and Aifen Li}, journal={Journal of Scientific Computing}, year={2019}, volume={80}, pages={223-247} }

Modeling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of two Cahn–Hilliard-type equations and incompressible Navier–Stokes equation. With the introduction of two auxiliary variables, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi…

## 25 Citations

### Decoupled and Energy Stable Time-Marching Scheme for the Interfacial Flow with Soluble Surfactants

- EngineeringICCS
- 2020

This work develops an efficient energy stable scheme for the hydrodynamics coupled phase-field surfactant model with variable densities and rigorously proves that the proposed scheme is unconditionally energy stable.

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

- Physics
- 2020

In this work, we present a hydrodynamics coupled phase-field surfactant model with variable densities. Two scalar auxiliary variables are introduced to transform the original free energy functional…

### A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant

- PhysicsComputational Geosciences
- 2021

The proposed scheme is shown to decay the total free Helmholtz energy at the discrete level, which is consistent with the continuous model dynamics, and recovers the Langmuir adsorption isotherms at equilibrium.

### Efficient energy-stable schemes for the hydrodynamics coupled phase-field model

- Computer ScienceApplied Mathematical Modelling
- 2019

### A BDF2 energy‐stable scheme for the binary fluid‐surfactant hydrodynamic model

- PhysicsMathematical Methods in the Applied Sciences
- 2021

A second‐order time stepping scheme is developed for the binary fluid‐surfactant phase‐field model coupled with hydrodynamics by using the scalar auxiliary variable approach and pressure correction…

### Fully-discrete, decoupled, second-order time-accurate and energy stable finite element numerical scheme of the Cahn-Hilliard binary surfactant model confined in the Hele-Shaw cell

- MathematicsESAIM: Mathematical Modelling and Numerical Analysis
- 2022

We consider the numerical approximation of the binary fluid surfactant phase-field model confined in a Hele-Shaw cell, where the system includes two coupled Cahn-Hilliard equations and Darcy…

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

- PhysicsJournal of Fluid Mechanics
- 2019

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…

### Improving the Accuracy and Consistency of the Scalar Auxiliary Variable (SAV) Method with Relaxation

- Computer ScienceJ. Comput. Phys.
- 2022

### Stabilized Energy Factorization Approach for Allen–Cahn Equation with Logarithmic Flory–Huggins Potential

- Computer Science, MathematicsJ. Sci. Comput.
- 2020

This paper proposes a novel energy factorization approach with the stabilization technique, which is called stabilized energy factorsization approach, to deal with the Flory–Huggins potential and shows that all nonlinear terms can be treated semi-implicitly and the resultant numerical scheme is purely linear and easy to implement.

### An energy-stable method for a phase-field surfactant model

- EngineeringInternational Journal of Mechanical Sciences
- 2022

## References

SHOWING 1-10 OF 85 REFERENCES

### Numerical Approximations for the Cahn–Hilliard Phase Field Model of the Binary Fluid-Surfactant System

- MathematicsJ. Sci. Comput.
- 2018

This paper develops two linear and decoupled, first order and a second order time-stepping schemes using the so-called "invariant energy quadratization" approach for the double well potentials and a subtle explicit-implicit technique for the nonlinear coupling potential.

### Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model

- Mathematics
- 2017

### Linear, Second order and Unconditionally Energy Stable schemes for a phase-field moving contact line Model

- Mathematics
- 2017

In this paper, we consider the numerical approximations for solving a hydrodynamics coupled phase field model consisting of incompressible Navier-Stokes equations with generalized Navier boundary…

### Simulating binary fluid-surfactant dynamics by a phase field model

- Physics
- 2012

In this paper, the dynamics of a binary fluid-surfactant system
described by a phenomenological phase field model is investigated
through analytical and numerical computations. We first consider …

### Decoupled, energy stable schemes for a phase-field surfactant model

- MathematicsComput. Phys. Commun.
- 2018

### Efficient energy-stable schemes for the hydrodynamics coupled phase-field model

- Computer ScienceApplied Mathematical Modelling
- 2019

### Analysis of finite element approximations of a phase field model for two-phase fluids

- MathematicsMath. Comput.
- 2007

It is shown that the proposed numerical methods satisfy a discrete energy law which mimics the basic energy law for the phase field model and the convergence to the phaseField model and to its sharp interface limiting model are established.

### Regular Article: Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling

- Physics
- 1999

Phase-field models provide a way to model fluid interfaces as having finite thickness. This can allow the computation of interface movement and deformation on fixed grids. This paper applies…

### A hybrid numerical method for interfacial fluid flow with soluble surfactant

- PhysicsJ. Comput. Phys.
- 2010