THE DETACHMENT OF BUBBLES UNDER A POROUS RIGID SURFACE DURING ALUMINUM ELECTROLYSIS

2002 ◽  
Vol 12 (11) ◽  
pp. 1617-1652 ◽  
Author(s):  
PETR KLOUČEK ◽  
MICHEL V. ROMERIO
Keyword(s):  
Free Energy ◽  
Liquid Layer ◽  
Minimization Problem ◽  
Critical Pressure ◽  
Mass Density ◽  
Aluminum Electrolysis ◽  
Liquid Interfaces ◽  
Rigid Surface ◽  
Constrained Minimization Problem ◽  
Solid Liquid

We determine the critical pressure and width of a liquid layer at which the sudden detachment of bubbles at solid–liquid interfaces occurs. We obtain these values by solving numerically a constrained minimization problem corresponding to the conservation of mass density of gas contained in the bubble attached to a rigid surface, and to the conservation of its free energy.

Quantitative Evaluation of the Interfacial Free Energies at A Solid-Liquid Lamellar Eutectic Interface

1981 ◽  
Vol 12 ◽  
Author(s):  
W. F. Kaukler ◽  
J. W. Rutter
Keyword(s):  
Free Energy ◽  
Solid Phase ◽  
Interfacial Free Energy ◽  
Eutectic System ◽  
Liquid Interfaces ◽  
Free Energies ◽  
Two Phases ◽  
Interfacial Free Energies ◽  
The Individual ◽  
Solid Liquid

The solid-liquid interfacial free energies of each of the individual phases comprising the eutectic system, Carbon Tetrabromide-Hexachloroethane, were measured as a function of composition using a “grain boundary groove” technique. Thermodynamic data were combined with groove shape measurements made from high resolution optical photomicrographs of the solid-liquid interfaces to give the interfacial free energy data. An interfacial free energy balance at the eutectic trijunction was performed to obtain all the forces acting on that point. The three interphase interfacial free energies at the eutectic trijunctions as well as a solid-solid phase boundary torque were evaluated.It was found that the solid-liquid interfacial free energies of the two phases of the eutectic could be evaluated from photomicrographs of growing or stationary eutectic interfaces. In addition, it was found that for a substantial range of freezing conditions the eutectic interface shape can be predicted from a knowledge of the interfacial free energies alone.

Influence of solvent structure and hydrogen bonding on catalysis at solid–liquid interfaces

2021 ◽  
Author(s):  
David S. Potts ◽  
Daniel T. Bregante ◽  
Jason S. Adams ◽  
Chris Torres ◽  
David W. Flaherty
Keyword(s):  
Free Energy ◽  
Hydrogen Bonding ◽  
Excess Free Energy ◽  
Catalytic Reactions ◽  
Liquid Interfaces ◽  
Solvent Structure ◽  
Solid Liquid ◽  
Influence Of Solvent

A pedagogical review that deconvolutes the excess free energy effects of several solvent phenomena and connects findings across a variety of catalytic reactions and materials.

The equilibrium shapes of small liquid droplets in solid–liquid phase mixtures: metallic h.c.p. and metalloid systems

1969 ◽  
Vol 312 (1509) ◽  
pp. 257-276 ◽  
Keyword(s):  
Free Energy ◽  
Interfacial Free Energy ◽  
Interfacial Structure ◽  
Liquid Droplets ◽  
Liquid Interfaces ◽  
Spherical Droplet ◽  
Factors Affecting ◽  
Interfacial Energies ◽  
Equilibrium Shapes ◽  
Solid Liquid

Solid–liquid interfacial free energy is shown to be highly anisotropic in alloys of some h. c. p. metals and of two metalloids. This anisotropy is evaluated from a study of the equilibrium shapes of small droplets of alloy liquid entrained within solid grains. Factors affecting the attainment of equilibrium in such droplets are considered, and γ -plots are obtained for solid–liquid interfaces in the h. c. p. metals zinc and cadmium. In the magnesium alloys studied, spherical droplet shapes were observed, indicative of essentially isotropic interfacial energies. Droplet shapes were also analysed in some alloys of bismuth and of antimony. The results are related to current ideas of solid–liquid interfacial structure.

scholarly journals Solvation free energies for periodic surfaces: comparison of implicit and explicit solvation models

2016 ◽  
Vol 18 (46) ◽  
pp. 31850-31861 ◽  
Author(s):  
Stephan N. Steinmann ◽  
Philippe Sautet ◽  
Carine Michel
Keyword(s):  
Free Energy ◽  
Liquid Interfaces ◽  
Free Energies ◽  
Periodic Surfaces ◽  
Solvation Energies ◽  
Solvation Models ◽  
Implicit And Explicit ◽  
Solvation Free Energies ◽  
Solid Liquid ◽  
Explicit Solvation

A strategy based on molecular mechanics free energy of perturbation, seeded by quantum mechanics, is presented to take solvation energies into account in the context of periodic, solid–liquid interfaces.

scholarly journals Polar effects at solid/liquid interfaces

1970 ◽  
Vol 48 (5) ◽  
pp. 865-866 ◽  
Author(s):  
A. C. Lowe ◽  
A. C. Riddiford
Keyword(s):  
Contact Angle ◽  
Free Energy ◽  
Unit Area ◽  
Liquid Interface ◽  
Liquid Interfaces ◽  
Advancing Contact Angle ◽  
Solid Liquid Interface ◽  
Glass Surfaces ◽  
Solid Liquid

Studies of the advancing contact angle of water upon several alkylchlorosilaned glass surfaces at 22 °C lead to the view that, at zero or very low interfacial velocities, the free energy per unit area of the solid/liquid interface is governed by both dispersive and polar forces. At higher velocities, the polar forces may be neglected.

scholarly journals A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 890
Author(s):  
Suthep Suantai ◽  
Kunrada Kankam ◽  
Prasit Cholamjiak
Keyword(s):  
Image Processing ◽  
Minimization Problem ◽  
Convex Functions ◽  
Lower Semicontinuous ◽  
Image Inpainting ◽  
Constrained Minimization ◽  
Convex Minimization Problem ◽  
Mild Conditions ◽  
Constrained Minimization Problem ◽  
Weak Convergence Theorem

In this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild conditions. It is known that image processing such as inpainting problems can be modeled as the constrained minimization problem of the sum of convex functions. In this connection, we aim to apply the suggested method for solving image inpainting. We also give some comparisons to other methods in the literature. It is shown that the proposed algorithm outperforms others in terms of iterations. Finally, we give an analysis on parameters that are assumed in our hypothesis.

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