Interfacial Transport Phenomena

Slattery, John C.

doi:10.1007/978-1-4757-2090-7

Cited by 340 publications

(533 citation statements)

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“…where f is the bulk free energy density, g is the "excessive" [53,54] surface free energy density at a material interface Γ within domain V, defined by Φ(x, t) = 0, ρ s is the surface excessive mass density, c s is the surface excessive active liquid crystal concentration, p s and Q s are the polarity vector and nematic tensor on the surface, and ∇ s = I s · ∇ is the surface gradient operator, where I s = I − nn, n is the unit normal of the interfacial surface, given by n = ∇Φ ∇Φ . Here, we assume the excessive free energy density g on the free surface depends on the gradients of the order parameters as well.…”

Section: Models For Passive Liquid Crystalsmentioning

confidence: 99%

Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle

Yang

Forest

et al. 2016

Entropy

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Abstract:We articulate and apply the generalized Onsager principle to derive transport equations for active liquid crystals in a fixed domain as well as in a free surface domain adjacent to a passive fluid matrix. The Onsager principle ensures fundamental variational structure of the models as well as dissipative properties of the passive component in the models, irrespective of the choice of scale (kinetic to continuum) and of the physical potentials. Many popular models for passive and active liquid crystals in a fixed domain subject to consistent boundary conditions at solid walls, as well as active liquid crystals in a free surface domain with consistent transport equations along the free boundaries, can be systematically derived from the generalized Onsager principle. The dynamical boundary conditions are shown to reduce to the static boundary conditions for passive liquid crystals used previously.

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Section: Models For Passive Liquid Crystalsmentioning

confidence: 99%

Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle

Yang

Forest

et al. 2016

Entropy

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“…After using the surface divergence theorem together with the interface mass balance equation, details of derivation can be found in [28], the corresponding strong form of equations of linear momentum for the interface follows directly as…”

Section: Balance Of Linear Momentummentioning

confidence: 99%

Modeling of non-local interactions on a phase transformation interface

Dobovšek¹

2009

ESOMAT 2009 - 8th European Symposium on Martensitic Transformations

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Abstract.If an interaction between phases of different composition at an interface is significant, the classical model of an interface is no longer satisfactory. In such cases, the transition layer has to be modeled as a surface phase with intrinsic non-local properties. The boundary of separation, which defines the interface, must possess its own internal structure in order to allow accommodation of complex phenomena while balancing opposite tendencies on each side of the interface. Consequently, an extended model is needed that is capable of describing the intrinsic properties of the interface. To achieve this goal, we employ a special model of an interface with simple structure, where the mathematical notion of a simple structure corresponds to the material model without rotational degrees of freedom in each lattice point of the interface. By employing characteristic features of the model, we are in a position to describe quantitatively and qualitatively the structural and compositional non-local changes across the interface.

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“…In these theories, the interfacial region separating distinct material phases is idealized as a dividing surface (in the sense of Gibbs [5]) endowed with physical properties such as internal energy, entropy and stress [17]. A key decision in such continuum surface theories is postulating a constitutive relation for the surface stress tensor.…”

Section: Introductionmentioning

confidence: 99%

Plane-Strain Fracture with Curvature-Dependent Surface Tension: Mixed-Mode Loading

Walton

2013

J Elast

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There have been a number of recent papers by various authors addressing static fracture in the setting of the linearized theory of elasticity in the bulk augmented by a model for surface mechanics on fracture surfaces with the goal of developing a fracture theory in which stresses and strains remain bounded at crack-tips without recourse to the introduction of a crack-tip cohesive-zone or process-zone. In this context, surface mechanics refers to viewing interfaces separating distinct material phases as dividing surfaces, in the sense of Gibbs, endowed with excess physical properties such as internal energy, entropy and stress. One model for the mechanics of fracture surfaces that has received much recent attention is based upon the Gurtin-Murdoch surface elasticity model. However, it has been shown recently that while this model removes the strong (square-root) crack-tip stress/strain singularity, it replaces it with a weak (logarithmic) one. A simpler model for surface stress assumes that the surface stress tensor is Eulerian, consisting only of surface tension. If surface tension is assumed to be a material constant and the classical fracture boundary condition is replaced by the jump momentum balance relations on crack surfaces, it has been shown that the classical strong (square-root) crack-tip stress/strain singularity is removed and replaced by a weak, logarithmic singularity. If, in addition, surface tension is assumed to have a (linearized) dependence upon the crack-surface mean-curvature, it has been shown for pure mode I (opening mode), the logarithmic stress/strain singularity is removed leaving bounded crack-tip stresses and strains. However, it has been shown that curvature-dependent surface tension is insufficient for removing the logarithmic singularity for mixed mode (mode I, mode II) cracks. The purpose of this note is to demonstrate that a simple modification of the curvature-dependent surface tension model leads to bounded crack-tip stresses and strains under mixed mode I and mode II loading.

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Interfacial Transport Phenomena

Cited by 340 publications

References 0 publications

Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle

Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle

Modeling of non-local interactions on a phase transformation interface

Plane-Strain Fracture with Curvature-Dependent Surface Tension: Mixed-Mode Loading

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