On the notion of a ξ –vector and a stress tensor for a general class of anisotropic diffuse interface models

1997 ◽  
Vol 453 (1963) ◽  
pp. 1611-1630 ◽  
Author(s):  
A. A. Wheeler ◽  
G. B. McFadden
Keyword(s):  
Stress Tensor ◽  
General Class ◽  
Diffuse Interface ◽  
Interface Models

scholarly journals THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES

2012 ◽  
Vol 22 (03) ◽  
pp. 1150013 ◽  
Author(s):  
HELMUT ABELS ◽  
HARALD GARCKE ◽  
GÜNTHER GRÜN
Keyword(s):  
Surface Diffusion ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Momentum Balance ◽  
Two Phase ◽  
Interface Models ◽  
Natural Energy ◽  
Soluble Species ◽  
Sharp Interface Models ◽  
Dissipation Inequalities

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is frame indifferent. Moreover, it is generalized to situations with a soluble species. Using the method of matched asymptotic expansions we derive various sharp interface models in the limit when the interfacial thickness tends to zero. Depending on the scaling of the mobility in the diffusion equation, we either derive classical sharp interface models or models where bulk or surface diffusion is possible in the limit. In the latter case a new term resulting from surface diffusion appears in the momentum balance at the interface. Finally, we show that all sharp interface models fulfill natural energy inequalities.

scholarly journals The contact line behaviour of solid-liquid-gas diffuse-interface models

2013 ◽  
Vol 25 (9) ◽  
pp. 092111 ◽  
Author(s):  
David N. Sibley ◽  
Andreas Nold ◽  
Nikos Savva ◽  
Serafim Kalliadasis
Keyword(s):  
Contact Line ◽  
Diffuse Interface ◽  
Interface Models ◽  
Solid Liquid

General Derivations for Conjugate Strains of Eshelby-Like Stress Tensors

Volume 1 ◽  
2004 ◽  
Author(s):  
K. Behfar ◽  
A. Sheshmani ◽  
R. Naghdabadi
Keyword(s):  
Stress Tensor ◽  
General Class ◽  
General Type ◽  
Principal Axis ◽  
Stretch Tensor ◽  
Stress Tensors ◽  
Definition Of ◽  
General Relations ◽  
The Right ◽  
Conjugate Stress

In this paper, a general type of Eshelby-like stress tensor is defined which is based on the right stretch tensor and is equal to the product of a general class of strain and the corresponding conjugate stress tensor. The Eshelby-like stress tensor depending on the fact that from which side the stress tensor is multiplied by, is categorized into the right-weighted and left-weighted ones. General relations for conjugate strains of Eshelby-like stress tensors are investigated using the method, based on the definition of energy conjugacy and Hill’s principal axis method.

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