There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The phase-field method has become an important and extremely versatile technique for simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface approach, it allows us to study the evolution of arbitrary complex grain morphologies without any presumption on their shape or mutual distribution. It is also straightforward to account for different thermodynamic driving forces for microstructure evolution, such as bulk and interfacial energy, elastic energy and electric or magnetic energy, and the effect of different transport processes, such as mass diffusion, heat conduction and convection. The purpose of the paper is to give an introduction to the phase-field modeling technique. The concept of diffuse interfaces, the phase-field variables, the thermodynamic driving force for microstructure evolution and the kinetic phase-field equations are introduced. Furthermore, common techniques for parameter determination and numerical solution of the equations are discussed. To show the variety in phase-field models, different model formulations are exploited, depending on which is most common or most illustrative.

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An introduction to phase-field modeling of microstructure evolution

The term superhydrophilicity is only 11–12 years old and was introduced just after the explosion of research on superhydrophobic surfaces, in response to the demand for surfaces and coatings with exceptionally strong affinity to water. The definition of superhydrophilic substrates has not been clarified yet, and unrestricted use of this term to hydrophilic surfaces has stirred controversy in the last few years in the surface chemistry community. In this review, we take a close look into major definitions of hydrophilic surfaces used in the past, before we review the physics behind the superhydrophilic phenomenon and make recommendation on defining superhydrophilic surfaces and coatings. We also review chemical and physical methods used in the fabrication of substrates on surfaces of which water spreads completely. Several applications of superhydrophilic surfaces, including examples from the authors' own research, conclude this review.

Hydrophilic and superhydrophilic surfaces and materials

This paper provides a review of superhydrophobicity and related phenomena (superoleophobicity, omniphobicity, self-cleaning) induced by surface micro- and nanostructuring. The classical approaches to superhydrophobicity using the Young, Wenzel, and Cassie–Baxter models for the contact angle (CA) are presented. After that, the issues that are beyond the Wenzel and Cassie–Baxter theories are discussed, such as multiscale effects, 1D vs. 2D interactions, the effects of contact line, size of roughness details, curvature, and CA hysteresis dependence on roughness. New potential applications of superhydrophobicity are reviewed, such as new ways of energy transition, antifouling, and environment-friendly manufacturing.

Superhydrophobic surfaces and emerging applications: Non-adhesion, energy, green engineering

Contact angle hysteresis is an important physical phenomenon. It is omnipresent in nature and also plays a crucial role in various industrial processes. Despite its relevance, there is a lack of consensus on how to incorporate a description of contact angle hysteresis into physical models. To clarify this, starting from the basic definition of contact angle hysteresis, we introduce the formalism and models for implementing contact angle hysteresis into relevant physical phenomena. Furthermore, we explain the influence of the contact angle hysteresis in physical phenomena relevant for industrial applications such as sliding drops, coffee stain phenomenon (in general evaporative self-assembly), and curtain and wire coating techniques

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Contact angle hysteresis: a review of fundamentals and applications

A compliant woven tubular seal is provided in an arcuate cavity opening through an axial face of a plurality of shroud segments in opposition to a nozzle retaining ring. The annular composite tubular woven compliant seal includes a stainless steel inner metal core surrounded by an annular layer of silica fiber. Surrounding the silica fiber is a metal foil which prevents flow past the supplemental seal. An outer wear-resistant braiding serves as a protective covering and wear surface.

Composite tubular woven seal for gas turbine nozzle and shroud interface

Compression after high-velocity impact behavior of pseudo-elastic shape memory alloy embedded glass/epoxy composite laminates

There are numerous problems in which an interface propagates through a body as it is loaded, where, when a material particle crosses this moving interface, it transforms from a metastable state to a more stable state. Examples of this include twin boundary and phase boundary motion in solids. Typically, such an interface propagates in a direction normal to itself at a speed, which in continuum theory, is determined by a kinetic law. The kinetic law is viewed as providing a continuum-scale description of the micromechanical processes underlying the front motion. In this paper we use a simple mechanical analog to illustrate how the kinetic law can be calculated by modeling the microscale mechanisms.

Propagation of a Front by Kink Motion

In this paper we study the isothermal stress–elongation rate response of a bar capable of undergoing austenite–martensite phase transformations. Our approach is based on a thermodynamically consistent three-dimensional phase field theory of Fried and Gurtin (1994 Physica D 72 287–308) capable of very general kinetics. We propose specific constitutive equations and develop an algorithm for analysing displacement controlled uniaxial extension. A finite difference solution of the governing equations is carried out using material parameters for Ni–Ti. Most of the significant features of the isothermal behaviour for this alloy are quantitatively predicted very well when compared with experimental data from the literature. The proposed constitutive equations model the dependence of hysteresis on the elongation rate particularly well.

Srikanth Vedantam

Papers

Composite tubular woven seal for gas turbine nozzle and shroud interface

Compression after high-velocity impact behavior of pseudo-elastic shape memory alloy embedded glass/epoxy composite laminates

Propagation of a Front by Kink Motion

Constitutive equations for rate-dependent pseudoelastic behaviour of shape memory alloys

Phase field modelling of annealing twin formation, evolution and interactions during grain growth