Open AccessKAHN-HILLIARD MODEL FOR MIXTURES OF BINARY LIQUIDS
Author(s) -
Dauren Zhakebayev,
D. Agadayeva
Publication year - 2020
Publication title -
vestnik nacionalʹnoj inženernoj akademii respubliki kazahstan
Language(s) - English
Resource type - Journals
eISSN - 2709-4707
pISSN - 2709-4693
DOI - 10.47533/2020.1606-146x.15
Subject(s) - cahn–hilliard equation , binary number , flow (mathematics) , boundary value problem , scalar (mathematics) , grid , representation (politics) , two phase flow , mathematics , statistical physics , mechanics , mathematical analysis , physics , partial differential equation , geometry , arithmetic , politics , political science , law
This article presents a model that is suitable for modeling changes in the chemical potential and the rate of attraction of phases, taking into account thermal effects, by solving the Kahn-Hilliard equation under various initial conditions. Thermal radiation is solved in the framework of the Kahn-Hilliard equation, which has been applied to many physical applications, such as two - and three-phase fluid flow, phase separation, flow visualization, and quantum dot formation. In this article, the numerical solution of the Kahn-Hilliard equation is made on a spaced grid, where the scalar values (pressure, phase function, density, viscosity) are determined in the center of the cell, and the velocity components are at a distance of half a step. Numerical research has shown that the use of a spaced grid avoids the appearance of a so-called staggered oscillating pattern for pressure. An additional advantage of using a spaced grid is that the discrete pressure field automatically satisfies the discrete representation of the integral boundary condition.