Publications

Dinariyev, O. Yu. A hydrodynamic description of a multicomponent multiphase mixture in narrow pores and thin layers // J. Appl. Mechs, Vol. 59
No.5, pp. 745752, 1995.
A hydrodynamic model of the isothermal processes in a multicomponent viscous mixture which interacts with fixed surfaces is constructed. In the steady case, the model reduces to a description using the Landaude Gennes functional. Typical solutions of the equations for a mixture close to a surface or when there are phase transitions are analysed. Classical surface and capillary phenomena are matched with these solutions. Hence, the proposed model enables timedependent viscous flows of a liquid and a gas in narrow pores and wellknown static surface effects to be described simultaneously, namely, the anomalous properties of thin films and surface layers, and capillary condensation and wettability, which is one of the problems in the modern theory of capillary phenomena.

O. Yu. Dinariev, Flow through a capillary with surfaceactive walls. Density functional method // Fluid dynamics ISSN 00154628 1997, vol. 32, no2, pp. 270276
Isothermal singlecomponent fluid flow between plane parallel walls or in a circular capillary is considered with allowance for surface effects. The hydrodynamic description in which the free energy of the system is a functional of the density field is used. A system of nonlinear differential equations for the density and velocity is obtained in the limit of a section flow region small cross. The solution is found for the first two orders of perturbation theory in the weaklycompressible fluid approximation

O. Yu. Dinariev, Description of capillarygravity waves within the framework of density functional theory // Fluid dynamics ISSN 00154628 1999, vol. 34, no5, pp. 729734
Wave motions in the neighborhood of a phase interface in a multicomponent fluid mixture are considered within the framework of density functional theory. In the incompressibility approximation and in the absence of dissipative processes it is shown that the massaverage displacement dynamics can be described by a Schrodingertype equation. A procedure for finding a solution by the perturbation theory method in the form of an expansion in the ratio of the interphase zone thickness to the wavelength is proposed. The first three approximations are calculated. For capillarygravity waves a dispersion relation which extends the classical formula to the case of an interphase zone of finite thickness is obtained

Dinariyev, O. Yu. The description of a multicomponent mixture by the density functional method when there are surface phases present // J. Appl. Mechs, Vol. 65 No.3, pp. 471478, 2001.
The description of multicomponent mixtures, with an expression for the free energy or the entropy in the form of a density functional [1, 2], is extended to the case when the system contains surface phases, when the finite number of particles of the mixture can be linked with certain geometrical surfaces. Equations are obtained which define the static state and hydrodynamic flows for a mixture with an arbitrary number of volume and surface phases.

Dinariyev, O. Yu. Thermal effects in the description of a multicomponent mixture using the density functional method // J. Appl. Mechs, Vol. 62
No.3, pp. 397405, 1998.
The use of a model, based on an expression for the total entropy in the form of a functional with the temperature and density gradients of the components, is proposed to describe a multicomponent, multiphase system using continuous hydrodynamics (that is, within the framework of the approach of the continuum mechanics without discontinuities in the hydrodynamic quantities). It is proved that this model is consistent with the zeroth law of thermodynamics. Expressions for the stress tensor, the diffusion fluxes and the heat flux are found from the condition that the entropy production is nonnegative. Compared with the classical Newton, Fick and Fourier laws, these expressions contain thirdorder spatial derivatives. The problem of a mixture between two parallel and impermeable walls at different temperatures is analysed. In this case, the system of dynamic equations reduces to a system of ordinary differential equations. It is shown that the number of free parameters, on which the solution depends, corresponds to the number of boundary and general integral conditions.

O. Yu. Dinariev, Substantiation of the Method of Density Functional in Classical and Quantum Statistical Mechanics // Russian Physics Journal Volume 43, Number 9 / September, 2000
The relationship between a description of a multicomponent mixture based on the entropy functional with the terms quadratic in the density gradients of components and in the temperature on the one hand, and a description within the framework of classical and quantum statistical mechanics on the other hand, is investigated. Explicit expressions for the entropy functional are written in the context of classical and quantum theories. A quadratic approximation is then calculated for the case of small perturbations of a uniform state. The terms quadratic in the gradients are separated in this approximation. This allows ab initio calculations of the corresponding phenomenological coefficients to be done.

Dinariyev, O. Yu. Multicomponent Mixture Flow in an Axisymmetric Capillary in the Presence of a Mobile Surface Phase // Fluid Dynamics, Volume 37, Issue 5, September  October 2002, Pages 753  761
Within the framework of the densityfunctional method, the hydrodynamics of a multicomponent mixture in the presence of a mobile surface phase is investigated. A system of interrelated three and twodimensional hydrodynamic equations for isothermal volume and surface flows is formulated. For flow in a thin axisymmetric capillary, the principal term of the asymptotic expansion of the solution in powers of the characteristic capillary radius to length ratio is obtained. For slow motion, the solution is found in quadratures.

A. Yu. Dem'yanov and O. Yu. Dinariyev, Application of the densityfunctional method for numerical simulation of flows of multispecies multiphase mixtures // Journal of Applied Mechanics and Technical Physics, Volume 45, Issue 5, 2004, Pages 670678
Numerical examples of application of the density functional used to describe isothermal flows of twophase twospecies mixtures are given. The following flows are calculated in a twodimensional formulation: impact of a drop on a liquid layer, breakdown of a drop in the velocity field of the Couette flow, formation of the wetting angle of a drop on a solid surface, and development of the Rayleigh–Taylor and Kelvin–Helmholtz instabilities at the gas–liquid interface.

A.Yu.Demyanov, O.Yu.Dinariev, Modeling of multicomponent multiphase mixture flows on the basis of the densityfunctional method // Fluid Dynamics, Vol.39, Issue 6, 2004, pp. 933944.
Examples of numerical calculations of isothermal flows of twophase twocomponent mixtures based on the densityfunctional method are presented. Using this method, the following problems are calculated in the twodimensional formulation: drop impact on a liquid layer, drop rupture in a Couette flowfield, wettingangle formation for a drop on a solid surface, development of RayleighTaylor and KelvinHelmholz instability on a gasliquid surface.

O. Yu. Dinariev, N. V. Evseev, Description of the Flows of TwoPhase Mixtures with Phase Transitions in Capillaries by the DensityFunctional Method // Journal of Engineering Physics and Thermophysics, Volume 78, Number 3 / May, 2005, Pages 474481
The problem of mathematical modeling of flows of multicomponent mixtures with phase transitions has been considered. The free energy of a mixture is given as a functional containing squared density gradients of the components. This permits continuous description of multiphase mixtures without discontinuities at the interfaces. Numerical solutions for the flows of twophase mixtures in capillaries with different wall wettability conditions have been obtained

O. Yu. Dinariev, N. V. Evseev, Description of ViscousFluid Flows with Moving Solid Phase in the DensityFunctional Theory // Journal of Engineering Physics and Thermophysics Volume 80, Number 5 / SeptemberOctober, 2007

O. Yu. Dinariev, N. V. Evseev, Application of densityfunctional theory to calculation of flows of threephase mixtures with phase transitions // Journal of Engineering Physics and Thermophysics Volume 80, Number 6 / November, 2007
The problem of mathematical modeling of flows of threephase threecomponent mixtures with phase transitions has been investigated using densityfunctional theory. The analytical and numerical results demonstrating the efficient application of this approach to description of twophase flows were obtained earlier. In the present work, methods extending the densityfunctional technique to the case of threephase mixtures have been proposed. Numerical solutions for flows of threephase mixtures, including those with phase transitions, have been given.

O. Yu. Dinariev, Application of density functional theory to relativistic hydrodynamics // Russian Physics Journal Volume 50, Number 3 / March, 2007
The density functional method is used in nonrelativistic hydrodynamics for a description of multicomponent multiphase mixtures. The method is based on an expression for the entropy in the form of a functional with terms quadratic in gradients of component densities. In the present work, the density functional theory is generalized to the relativistic case. This generalization involves a solution of a number of problems: relativistically covariant formulation of the theory equations, derivation of basic relationships with allowance for the generalized relativistic principle of entropy production, and check of the relativistic causality of the theory. It is demonstrated that higherorder derivatives in the theory appear to be compatible with the causality in the basic relationships nonlocal in space and time.

O.Yu. Dinariev, N.V. Evseev, Modeling of Surface Phenomena in the Presence of SurfaceActive Agents on the Basis of the DensityFunctional Theory. // Fluid Dynamics, 2010, Vol. 45, No. 1, pp. 8595.
Within the framework of the densityfunctionalmethod in multiphase multicomponent mixture hydrodynamics, the possibility of modeling surfaceactive agents on a"fluidfluid" phase interface is shown. The method is based on the continuum description of multiphase mixtures with introducing terms quadratic in component density gradients to entropy or free energy. The determining equations are derived. Hydrodynamic model problems which demonstrate certain typical phenomena (the accumulation of surfaceactive agents on the phase interface, the corresponding decrease in surface tension, and the Gibbs and Marangoni effects) are solved numerically.
 Demianov A.Yu., Dinariev O.Yu. and Evseev N.V. Basics of the density functional theory in hydrodynamics. Nauka, Moscow, 2009. [In Russian]

A. Demianov, O. Dinariev, N. Evseev, Density functional modeling in multiphase compositional hydrodynamics // Can. J. Chem. Eng., V.89, April 2011, pp.206226.
This work is essentially a review of a density functional approach in multiphase hydrodynamics developed by the authors during the last 15 years [Dinariev, J Appl Math Mech 1995;59(5):745–752; Dinariev, J Appl Math Mech 1998;62(3):397–405; Demyanov and Dinariev, Fluid Dynam 2004;39(6):933–944; Demianov et al., “Basics of the Density Functional Theory in Hydrodynamics,” Fizmatlit, Moscow; 2009 (in Russian); Dinariev and Evseev, Fluid Dynam 2010;45(1):85–95]. The basic assumption is a representation of the entropy or the Helmholtz energy of the mixture as a functional that is dependent upon chemical component densities. The hydrodynamic system of equations (local conservation laws for chemical components, momentum, and energy) is used to describe multiphase processes, and the constitutive relations (expressions for stresses, diffusion, and heat fluxes) are derived from entropy growth requirement. The authors present the results of numerical simulations describing static and dynamic multiphase systems.
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