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Density Functional Theory in Hydrodynamics

Posted By: DFT
Date:Wed, 7 Jul 2004, 8:20 a.m.

In modeling of multicomponent multiphase flow with phase transitions the spatial distribution of phases and their properties (composition, pressure, velocity) a re usually unknown from the beginning: this information must be extracted from the full solution of the hydrodynamic problem. This makes difficult the application of the classical Navier-Stokes model. Indeed, if the geometry of phases is unknown, then it is also unknown, what viscosity coefficient must be put in Navier-Stokes equation in the given point of space. Also, there is a difficulty in formulation of the conditions at the interfacial surface: the Laplace condition presupposes the smoothness of the surface, and this absolutely excludes the well known phenomena of division or coalescence of fluid droplets or gas bubbles. These problems are solved solved in the density functional theory, which describes the multicomponent multiphase mixture continuously without density jumps and interfacial surfaces. This is achieved by the introduction into the Helmholz energy or into the entropy the square component density gradient terms. As a result the hydrodynamics of multiphase mixture is described in a unified way meaning the governing system of equations is the same at any space point. The density functional approach possesses the following advantages: it takes account of the structure of the interfacial region and of the surface layers; the surface tension coefficients are calculated from other parameters of the model; the model describes phase transitions and the flow simultaneously including the formation and the decay of phases, the condensation and the evaporation near solid surfaces; the model is indifferent to the complexity of the spatial geometry of the considered phases.

Density functional theory in hydrodynamics


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