Diffuse-interface methods in fluid mechanics

Abstract

We review the development of diffuse-interface models of hydrodynamics and their application to a wide variety of interfacial phenomena. These models have been applied successfully to situations in which the physical phenomena of interest have associated with them a length scale commensurate with the thickness of the interfacial region, (e.g. near-critical interfacial phenomena or small scale flows such as those occurring near contact lines), and fluid flows involving large interface deformations and/or topological changes (e.g. breakup and coalescence events associated with fluid jets, droplets, and large-deformation waves). We discuss the issues involved in formulating diffuse-interface models for single-component and binary fluids. Recent applications and computations using these models are discussed in each case. Further, we address issues including sharp-interface analyses that relate these models to the classical freeboundary problem, computational approaches to describe interfacial phenomena, and models of fully-miscible fluids.

Level Set Method for Simulating the Interface Kinematics: Application of a Discontinuous Galerkin Method

“…3 Classical level set method [47]. 4 Particle level set method [47] is a notched disk with the radius R = 0.15, the slot length L Slot = 0.25 and the slot width W Slot = 0.5, centered at (x c = .5, y c = 0.75). The manually constructed signed-distance level set function of the interface is shown in the figure 13.…”

“…In the context of the continuum mechanics, an interface is represented as a geometrical surface with zero thickness which may result in mathematical singularities, see [3]. A common approach to overcome the singularity problem is to make a diffuse interface assumption according to which, the fluid properties are supposed to vary smoothly across the interface, see [4]. A major issue in the numerical simulation of the multiphase flows is the manner of representing the interface and simulating its kinematics.…”

Physics of Multiphase Microflows and Microdroplets

“…Several numerical methods have been developed to describe the complex evolution process of a multiphase system. These methods can be classified into two major categories: the interface tracking and the interface capturing (Hirt and Nichols (1981); Osher and Sethian (1988); Anderson and McFadden (1998); Tryggvason et al (2001)). The interface tracking method is a sharp interface approach, in which the interfaces are assumed to be infinitely thin i.e.…”

“…This type of approach is able to deal with topological changes in a natural way. The indicator function is generally chosen as the volume fraction of one of the two phases/components, as in the volume of fluid (VOF) method (Hirt and Nichols (1981)), the signed distance to the interface, as in the level-set method (Osher and Sethian (1988)), or the density/mass fraction of one phase or component (also called order parameter), as in the phase-field models (Anderson and McFadden (1998)). In this class of approach, the same set of governing equations (Eqs.…”

Pore-scale mass and reactant transport in multiphase porous media flows

“…These models converge to the continuum mass and momentum conservation for a slightly compressible multi-component mixture of fluids (Shan & Doolen 1995). All these models, however, belong to a more general class diffuse-interface methods (Anderson, McFadden & Wheeler 1998). For the case of an immiscible binary mixture, this means that when the equilibrium state is reached, the two fluids are separated by an interface of finite thickness δ.…”