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 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 free-boundary problem, computational approaches to describe interfacial phenomena, and models of fully miscible fluids.

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Diffuse-interface methods in fluid mechanics

Our aim is to propose a theory which goes beyond the classical formulation of thermodynamics. This is achieved by enlarging the space of basic independent variables, through the introduction of non-equilibrium variables, such as the dissipative fluxes appearing in the balance equations. The next step is to find evolution equations for the dissipative fluxes. Whereas the evolution equations for the classical variables are given by the usual balance laws, no general criteria exist concerning the evolution equations of the dissipative fluxes, with the exception of the restrictions imposed on them by the second law of thermodynamics.

https://iopscience.iop.org/article/10.1088/0034-4885/51/8/002/pdf

Extended irreversible thermodynamics

The scalable and sustainable manufacture of thick electrode films with high energy and power densities is critical for the large-scale storage of electrochemical energy for application in transportation and stationary electric grids. Two-dimensional nanomaterials have become the predominant choice of electrode material in the pursuit of high energy and power densities owing to their large surface-area-to-volume ratios and lack of solid-state diffusion1,2. However, traditional electrode fabrication methods often lead to restacking of two-dimensional nanomaterials, which limits ion transport in thick films and results in systems in which the electrochemical performance is highly dependent on the thickness of the film1-4. Strategies for facilitating ion transport-such as increasing the interlayer spacing by intercalation5-8 or introducing film porosity by designing nanoarchitectures9,10-result in materials with low volumetric energy storage as well as complex and lengthy ion transport paths that impede performance at high charge-discharge rates. Vertical alignment of two-dimensional flakes enables directional ion transport that can lead to thickness-independent electrochemical performances in thick films11-13. However, so far only limited success11,12 has been reported, and the mitigation of performance losses remains a major challenge when working with films of two-dimensional nanomaterials with thicknesses that are near to or exceed the industrial standard of 100 micrometres. Here we demonstrate electrochemical energy storage that is independent of film thickness for vertically aligned two-dimensional titanium carbide (Ti3C2T x ), a material from the MXene family (two-dimensional carbides and nitrides of transition metals (M), where X stands for carbon or nitrogen). The vertical alignment was achieved by mechanical shearing of a discotic lamellar liquid-crystal phase of Ti3C2T x . The resulting electrode films show excellent performance that is nearly independent of film thickness up to 200 micrometres, which makes them highly attractive for energy storage applications. Furthermore, the self-assembly approach presented here is scalable and can be extended to other systems that involve directional transport, such as catalysis and filtration.

Thickness-independent capacitance of vertically aligned liquid-crystalline MXenes.

This review covers the recent advances in studies of the volume phase transition and critical phenomena of polymer gels mostly carried out in our group from 1973 to the present. We aimed here to discuss intensively (i) the basic understanding of the transition from the viewpoints of structure, dynamics, kinetics, and equilibrium thermodynamics, (ii) technological applications of the volume transition, and (iii) the relation between the phase transition and biological interactions.

Volume phase transition and related phenomena of polymer gels

A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a numerical application of the theory, we consider the kinetics of coarsening for a binary fluid in two space dimensions.

Akira Onuki

Papers

Nonequilibrium steady state of critical fluids under shear flow: A renormalization group approach

Light scattering by critical fluids under shear flow

Dynamics and Patterns in Complex Fluids

Critical Phenomena of Classical Fluids under Flow. I : Mean Field Approximation

Fluctuations in Nonequilibrium Steady States with Laminar Shear Flow: Classical Fluids near the Critical Point