In this chapter, a general energetic variational framework for modeling the dynamics of
complex fluids is introduced. The approach reveals and focuses on the couplings and …

We present a reduction-consistent and thermodynamically consistent formulation and an
associated numerical algorithm for simulating the dynamics of an isothermal mixture …

In this paper, the energy scaling behavior of the time-fractional phase field models is
investigated. We report a seminal observation that the effective free energy of the time …

We develop a numerical approximation for a hydrodynamic phase field model of three
immiscible, incompressible viscous fluid phases. The model is derived from a generalized …

Biological membranes are complex structures whose mechanics are usually described at a
mesoscopic level, such as the Helfrich bending theory. In this article, we present the phase …

We construct a formal gradient flow structure for phase-field evolution coupled to mechanics
in Lagrangian coordinates, present common ways to couple the evolution, and provide an …

When forces are applied to matter, the distribution of mass changes. Similarly, when an
electric field is applied to matter with charge, the distribution of charge changes. The change …

Abstract Energetic Variational Approach is used to derive a novel thermodynamically
consistent three-phase model of a mixture of Newtonian and visco-elastic fluids. The model …

Direct numerical simulations (DNS) of microscale fluid-structure interactions (mFSI) in
multicomponent multiphase flows pose many challenges such as the thermodynamic …

Complex fluids are those with internal microstructures whose evolution affects the
macroscopic dynamics of the material, especially the rheology. Examples include polymer …