Density profiles at liquid–vapor and liquid–liquid interfaces: An integral equation study

1997 ◽  
Vol 107 (17) ◽  
pp. 6925-6935 ◽  
Author(s):  
Stanislav Iatsevitch ◽  
Frank Forstmann
Keyword(s):  
Integral Equation ◽  
Liquid Interfaces ◽  
Density Profiles ◽  
Liquid Vapor

Liquid-vapor and liquid-liquid interfaces in Ising fluids: An integral equation approach

2007 ◽  
Vol 126 (12) ◽  
pp. 124702 ◽  
Author(s):  
I. P. Omelyan ◽  
R. Folk ◽  
I. M. Mryglod ◽  
W. Fenz
Keyword(s):  
Integral Equation ◽  
Equation Approach ◽  
Liquid Interfaces ◽  
Integral Equation Approach ◽  
Liquid Vapor

Density Profiles for a Model of Localized Site Adsorption of a Dimerizing Fluid on Crystalline Surfaces. Integral Equation Study

1996 ◽  
Vol 100 (14) ◽  
pp. 5941-5948 ◽  
Author(s):  
Andrij Trokhymchuk ◽  
Orest Pizio ◽  
Douglas Henderson ◽  
Stefan Sokołowski
Keyword(s):  
Integral Equation ◽  
Density Profiles ◽  
Crystalline Surfaces

scholarly journals A Critical Assessment of Methods for the Intrinsic Analysis of Liquid Interfaces: 2. Density Profiles

2010 ◽  
Vol 114 (43) ◽  
pp. 18656-18663 ◽  
Author(s):  
Miguel Jorge ◽  
György Hantal ◽  
Pál Jedlovszky ◽  
M. Natália D. S. Cordeiro
Keyword(s):  
Critical Assessment ◽  
Liquid Interfaces ◽  
Density Profiles

The boundary integral equation for curved solid/liquid interfaces propagating into a binary liquid with convection

2021 ◽  
Author(s):  
Ekaterina Titova ◽  
Dmitri Alexandrov
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Curvilinear Coordinates ◽  
Forced Flow ◽  
Function Technique ◽  
Liquid Interfaces ◽  
Convective Boundary ◽  
Solid Liquid

Abstract The boundary integral method is developed for unsteady solid/liquid interfaces propagating into undercooled binary liquids with convection. A single integrodifferential equation for the interface function is derived using the Green function technique. In the limiting cases, the obtained unsteady convective boundary integral equation (CBIE) transforms into a previously developed theory. This integral is simplified for the steady-state growth in arbitrary curvilinear coordinates when the solid/liquid interface is isothermal (isoconcentration). Finally, we evaluate the boundary integral for a binary melt with a forced flow and analyze how the melt undercooling depends on P\'eclet and Reynolds numbers.

Liquid-vapor interfaces inXY-spin fluids: An inhomogeneous anisotropic integral-equation approach

2009 ◽  
Vol 79 (1) ◽  
Author(s):  
I. P. Omelyan ◽  
R. Folk ◽  
A. Kovalenko ◽  
W. Fenz ◽  
I. M. Mryglod
Keyword(s):  
Integral Equation ◽  
Equation Approach ◽  
Integral Equation Approach ◽  
Liquid Vapor

A Mean-Field Pressure Formulation for Liquid-Vapor Flows

2006 ◽  
Vol 129 (7) ◽  
pp. 894-901 ◽  
Author(s):  
Shi-Ming Li ◽  
Danesh K. Tafti
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Capillary Waves ◽  
Wave Number ◽  
Density Profiles ◽  
Pressure Formulation ◽  
Boltzmann Method ◽  
Relationship Of ◽  
The Relationship ◽  
Liquid Vapor

A nonlocal pressure equation is derived from mean-field free energy theory for calculating liquid-vapor systems. The proposed equation is validated analytically by showing that it reduces to van der Waals’ square-gradient approximation under the assumption of slow density variations. The proposed nonlocal pressure is implemented in the mean-field free energy lattice Boltzmann method (LBM). The LBM is applied to simulate equilibrium liquid-vapor interface properties and interface dynamics of capillary waves and oscillating droplets in vapor. Computed results are validated with Maxwell constructions of liquid-vapor coexistence densities, theoretical relationship of variation of surface tension with temperature, theoretical planar interface density profiles, Laplace’s law of capillarity, dispersion relationship between frequency and wave number of capillary waves, and the relationship between radius and the oscillating frequency of droplets in vapor. It is shown that the nonlocal pressure formulation gives excellent agreement with theory.

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