A modified generalized continuous surface tension force model for the N-component immiscible and incompressible fluid flows by phase-field method

Abstract

In this work, we present a novel continuous surface tension force model for the phase-field model for N-component immiscible and incompressible fluid flows. The multi-phase Cahn-Hilliard-Navier-Stokes phase-field system is used to describe the evolutions of interfaces, velocities, and pressure. In phase-field model, the concentration of fluid smoothly changes from one fluid to other fluids, this transition region has finite thin thickness across fluid interface. Within the transition region, the surface tension force works. The force magnitude is assumed to be proportional to the interfacial curvature times a smoothed Dirac delta function, the force direction is determined by the unit normal vector to interface. With the fluid concentration (or phase-field function), we derive the associated signed-distance function from the equilibrium interface condition. The curvature is accurately calculated with the signed-distance function instead of the phase-field function. Moreover, the unit normal vector to interface and smoothed Dirac delta function are also calculated based on the signed-distance function. The proposed model is general in the sense that the interactions between arbitrary N components can be achieved without specific criterions. Compared with the continuous surface tension model based on phase-field function, the present model can significantly suppress the evolution of spurious velocity as the thickness of diffuse interface becomes sharp. The numerical simulations, such as pressure jump, spurious velocity, liquid lens, rising bubble in a four-component fluid system, and droplet impacting on a thin liquid film, are implemented to validate the capability of the proposed model.

Document Type: Original article

Cited as: Su, S., Yang, J. A modified generalized continuous surface tension force model for the N-component immiscible and incompressible fluid flows by phase-field method. Computational Energy Science, 2025, 2(2): 1-17. https://doi.org/10.46690/compes.2025.02.01 

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