Book ChapterDOI
Fluid Dynamics of Two Miscible Liquids with Diffusion and Gradient Stresses
TLDR
In this paper, the mass per unit total volume of one of the liquids in a material volume is conserved in the absence of diffusion, and the diffusion equation for the mass fraction ψ is derived.Abstract:
This chapter is based on papers by Joseph [1990b], Galdi, Joseph, Preziosi and Rionero [1991], Joseph anu [1991] and Hu and Joseph [1992]. The density of incompressible fluids can vary with concentration and temperature, but not with pressure. The velocity field u of such incompressible fluids is not in general solenoidal: div u ≠ 0. We require that the mass per unit total volume of one of the liquids in a material volume is conserved in the absence of diffusion. This yields the diffusion equation for the mass fraction ψ. Alternatively, if we obtain an equation for the volume fraction φ, then the left hand side of the diffusion equation differs from the usual substantial derivative of φ by the addition of φ div u.read more
Citations
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Journal ArticleDOI
Diffuse-interface methods in fluid mechanics
TL;DR: 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 are addressed.
Journal ArticleDOI
Regular Article: Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling
TL;DR: In this article, the Navier-Stokes equations are modified by the addition of the continuum forcing [emailprotected]?->@f, where C is the composition variable and @f is C's chemical potential.
Journal ArticleDOI
Quasi–incompressible Cahn–Hilliard fluids and topological transitions
John Lowengrub,Lev Truskinovsky +1 more
TL;DR: In this article, a physically motivated regularization of the Euler equations is proposed to allow topological transitions to occur smoothly, where the sharp interface is replaced by a narrow transition layer across which the fluids may mix.
Journal ArticleDOI
The mixing transition in Rayleigh-Taylor instability
TL;DR: In this article, a large-eddy simulation technique is described for computing Rayleigh-Taylor instability, based on high-wavenumber-preserving subgrid-scale models, combined with high-resolution numerical methods.
Journal ArticleDOI
Miscible displacements in capillary tubes. Part 1. Experiments
TL;DR: In this article, a diagnostic measure of the amount of viscous fluid left behind on the tube wall has been found, for both vertical and horizontal tubes, as a function of the Peclet (Pe) and Atwood (At) numbers.
References
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Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
Book
The non-linear field theories of mechanics
TL;DR: A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys as mentioned in this paper, which is not the case in modern physics, since it concerns solely the small particles of matter.
Journal ArticleDOI
Viscous fingering in porous media
TL;DR: Mecanisme de digitation visqueuse. as discussed by the authors : Deplacements non miscibles en cellules de Hele Shaw. Butteau et al. describe a set of ecoulements in a cellule.
Journal ArticleDOI
Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell
TL;DR: In this paper, the mean amplitude of a wave at an unstable horizontal interface between two fluids moving vertically through a saturated porous medium is observed to grow rapidly to become fingers (i.e. the amplitude greatly exceeds the wavelength).