The Steady State for Dendritic Growth with Nonzero Surface Tension

2017 ◽  
pp. 109-128
Author(s):  
Jian-Jun Xu
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Dendritic Growth

Dendritic growth from a binary system in an external flow: Steady state solution with zero surface tension

2008 ◽  
Vol 310 (3) ◽  
pp. 655-664 ◽  
Author(s):  
Ming-Wen Chen ◽  
Xin-Feng Wang ◽  
Zi-Dong Wang ◽  
Jian-Xin Xie
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Binary System ◽  
Dendritic Growth ◽  
Steady State Solution ◽  
External Flow ◽  
State Solution

Dendritic growth from a melt in an external flow: uniformly valid asymptotic solution for the steady state

1994 ◽  
Vol 263 ◽  
pp. 227-244 ◽  
Author(s):  
Jian-Jun Xu
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Prandtl Number ◽  
Asymptotic Solution ◽  
Dendritic Growth ◽  
External Flow ◽  
Growth Region ◽  
Steady Growth

This work is part of an investigation dealing with the effect of external flow in a melt on dendritic growth. In this paper, we will consider steady growth with zero surface tension. Assuming that the Prandtl number Pr is large, we are able to obtain a uniformly valid asymptotic solution for the steady state in the whole growth region.

Theory of dendritic growth—II. Instabilities in the limit of vanishing surface tension

1978 ◽  
Vol 26 (11) ◽  
pp. 1689-1695 ◽  
Author(s):  
J.S. Langer ◽  
H. Müller-Krumbhaar
Keyword(s):  
Surface Tension ◽  
Dendritic Growth

Theory of dendritic growth—III. Effects of surface tension

1978 ◽  
Vol 26 (11) ◽  
pp. 1697-1708 ◽  
Author(s):  
H. Müller-Krumbhaar ◽  
J.S. Langer
Keyword(s):  
Surface Tension ◽  
Dendritic Growth

Exploration of interactions between decyl-β-d-glucopyranoside and bovine serum albumin in aqueous solution

RSC Advances ◽  
2016 ◽  
Vol 6 (24) ◽  
pp. 19700-19706 ◽  
Author(s):  
Gongke Wang ◽  
Huimin Hou ◽  
Ye Chen ◽  
Changling Yan ◽  
Guangyue Bai ◽  
...  
Keyword(s):  
Aqueous Solution ◽  
Surface Tension ◽  
Steady State ◽  
Bovine Serum Albumin ◽  
Serum Albumin ◽  
Absorption Spectroscopy ◽  
Bovine Serum ◽  
Aqueous Media ◽  
Steady State Fluorescence

The interactions between decyl-β-d-glucopyranoside (DG) and bovine serum albumin (BSA), in aqueous media, were investigated through the use of surface tension, steady-state fluorescence, and UV-vis absorption spectroscopy measurements.

On Three-Dimensional Nonlinear Subharmonic Resonant Surface Waves in a Fluid: Part I—Theory

1988 ◽  
Vol 55 (1) ◽  
pp. 213-219 ◽  
Author(s):  
X. M. Gu ◽  
P. R. Sethna ◽  
A. Narain
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Energy Dissipation ◽  
Surface Waves ◽  
Three Dimensional ◽  
Critical Depth ◽  
Transient Phenomena ◽  
Vertical Excitation ◽  
Rectangular Container ◽  
Dimensional Surface

Three-dimensional surface waves in a rectangular container subjected to vertical excitation are studied. The analysis includes the effects of surface tension, energy dissipation, and critical depth. Both steady state and transient phenomena are discussed.

Singular effects of surface tension in evolving Hele-Shaw flows

1996 ◽  
Vol 323 ◽  
pp. 201-236 ◽  
Author(s):  
Michael Siegel ◽  
Saleh Tanveer ◽  
Wei-Shen Dai
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Singularly Perturbed ◽  
Present Evidence ◽  
Finger Motion ◽  
The Impact

In this paper, we present evidence to show that a smoothly evolving zero-surface tension solution of the Hele-Shaw equations can be singularly perturbed by the presence of arbitrarily small non-zero surface tension in order-one time. These effects are explained by the impact of ‘daughter singularities’ on the physical interface, whose formation was suggested in a prior paper (Tanveer 1993). For the case of finger motion in a channel, it is seen that the daughter singularity effect is strong enough to produce the transition from a finger of arbitrary width to one with the selected steady-state width in O(1) time.

Long-wavelength surface-tension-driven Bénard convection: experiment and theory

1997 ◽  
Vol 345 ◽  
pp. 45-78 ◽  
Author(s):  
STEPHEN J. VANHOOK ◽  
MICHAEL F. SCHATZ ◽  
J. B. SWIFT ◽  
W. D. MCCORMICK ◽  
HARRY L. SWINNEY
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Temperature Difference ◽  
Silicone Oil ◽  
Interface Temperature ◽  
Layer Model ◽  
Long Wavelength ◽  
Two Layer Model ◽  
Gas Layer ◽  
Dry Spot

Surface-tension-driven Bénard (Marangoni) convection in liquid layers heated from below can exhibit a long-wavelength primary instability that differs from the more familiar hexagonal instability associated with Bénard. This long-wavelength instability is predicted to be significant in microgravity and for thin liquid layers. The instability is studied experimentally in terrestrial gravity for silicone oil layers 0.007 to 0.027 cm thick on a conducting plate. For shallow liquid depths (<.017 cm for 0.102 cm2 s−1 viscosity liquid), the system evolves to a strongly deformed long-wavelength state which can take the form of a localized depression (‘dry spot’) or a localized elevation (‘high spot’), depending on the thickness and thermal conductivity of the gas layer above the liquid. For slightly thicker liquid depths (0.017–0.024 cm), the formation of a dry spot induces the formation of hexagons. For even thicker liquid depths (>0.024 cm), the system forms only the hexagonal convection cells. A two-layer nonlinear theory is developed to account properly for the effect of deformation on the interface temperature profile. Experimental results for the long-wavelength instability are compared to our two-layer theory and to a one-layer theory that accounts for the upper gas layer solely with a heat transfer coefficient. The two-layer model better describes the onset of instability and also predicts the formation of localized elevations, which the one-layer model does not predict. A weakly nonlinear analysis shows that the bifurcation is subcritical. Solving for steady states of the system shows that the subcritical pitchfork bifurcation curve never turns over to a stable branch. Numerical simulations also predict a subcritical instability and yield long-wavelength states that qualitatively agree with the experiments. The observations agree with the onset prediction of the two-layer model, except for very thin liquid layers; this deviation from theory may arise from small non-uniformities in the experiment. Theoretical analysis shows that a small non-uniformity in heating produces a large steady-state deformation (seen in the experiment) that becomes more pronounced with increasing temperature difference across the liquid. This steady-state deformation becomes unstable to the long-wavelength instability at a smaller temperature difference than that at which the undeformed state becomes unstable in the absence of non-uniformity.

CRYSTAL GROWTH AND THE THERMODYNAMICS OF IRREVERSIBLE PROCESSES

1959 ◽  
Vol 37 (6) ◽  
pp. 739-754 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Entropy Production ◽  
Dendritic Growth ◽  
Transport Processes ◽  
Irreversible Processes ◽  
Interface Morphology ◽  
Crystal Face ◽  
Thermodynamics Of Irreversible Processes ◽  
Alloy Crystal

The principle of minimum rate of entropy production is applied to steady-state transport processes in the neighborhood of an alloy crystal face growing into its melt. The procedure gives a satisfactory rationale of observed interface morphology. It is noted that segregation, which occurs in cellular or dendritic growth of alloys, is a direct manifestation of the system's attempt to minimize entropy production by conserving free energy. The general problems of growth of pure and impure single crystals from the melt and vapor are discussed.

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