A. A. Belkin

On the thermal conductivity of nanofluids

The dependence of the effective thermal conductivity λ of nanofluids on the properties of dispersed nanoparticles has been studied by the molecular dynamics method. It is established that the thermal conductivity of a nanofluid always exceeds that of the carrier medium, the excess depending on the volume fraction of nanoparticles, their masses, and sizes. An increase in the nanoparticle mass at a constant size leads to a more pronounced increase in λ than does the growth in size at a constant mass, which implies that the density of dispersed nanoparticles is an important factor that determines the thermal conductivity of nanofluids.

On the Effective Viscosity of Nanosuspensions

The effective viscosity of nanosuspensions is simulated using the molecular dynamics method. It is found that viscosity is controlled not only by the volume concentration of nanoparticles, by also by their mass and diameter. The viscosity of even strongly rarefied nanosuspensions (with a low concentration of nanoparticles) cannot be described by the Einstein relation. This means that the mechanism responsible for the increase in the viscosity of the medium is not of hydrodynamic origin. It is shown that the formation of viscosity of nanosuspensions is associated to a considerable extent with nonequilibrium microfluctuations of density and velocity of the carrier medium, which are induced by the motion of nanoparticles.

Diffusion of Nanoparticles and Macromolecules in Dense Gases and Liquids

The method of molecular dynamics is used to study the diffusion of large molecules or nanoparticles in a dense molecular medium (liquid or gas) in a wide range of densities. Particles and molecules are simulated by hard, absolutely elastic spheres. The ratio of the particle and molecule diameters of the medium varies from unity to four, and the mass ratio, from unity to 300. The density of the carrier medium is characterized by the parameter V/V0(V0is the volume of close-packed structure of molecules, and Vis the volume of the calculation cell), which is varied from 2 to 75.3. The dependences of the diffusion coefficient of a particle on its mass and on the density of carrier gas are investigated. It is found that the relaxation of the autocorrelation function of the velocity of a particle is described well by the superposition of two exponential functions with different relaxation times. The obtained data are compared with known theoretical models.

Nanoparticle velocity relaxation in a condensed carrying medium

The interaction of a nanoparticle occurring in a carrying condensed medium with fluctuations of the medium momentum caused by the particle motion have been studied. The space-time velocity correlation functions of the nanoparticle and surrounding molecules were determined by the molecular dynamics method. These functions exhibit one or two maxima, depending on the system parameters. The first maximum is related to an acoustic wave propagating in the medium, and the second, to multiple collisions between the nanoparticle and nearest neighbor molecules. It is established that collective effects significantly influence both the velocity autocorrelation function and the diffusion coefficient of the nanoparticle.

About Fluids Structure in Microchannels

The paper deals with molecular dynamics simulation of fluid flow characteristics in nanochannels. A new MD algorithm is developed to simulate plane flow with a pressure drop along the channel. Fluids of hard spheres and Lennard-Jones molecules are considered. Emphasis is on the study of the dependence of the hydraulic flow resistance on the fluid structure. An analysis was made of (i) the density distribution across and along the channel; (ii) radial distribution function of the fluid near the channel wall and in bulk; (iii) influence of the interaction law of the molecules with the wall; (iv) the dependence of the flow resistance coefficient on the Reynolds and Knudsen numbers.

Nanoparticle Friction Force and Effective Viscosity of Nanosuspensions

The transport properties of nanofluids are investigated by the molecular dynamics method. It is shown that the force acting on a nanoparticle is nonstationary, in contrast to the Stokes force. In the initial stage of relaxation, the friction force is greater than the Stokes value. Subsequently, this force decreases and reaches an asymptotic value. This value is comparable to the Stokes force only for a massive particle. A correlation for determining the friction coefficient is constructed. It is established that the effective viscosity coefficient of nanofluids depends not only on the volume concentration of nanoparticles but also on the nanoparticle mass and radius.

Force acting on a nanoparticle in a fluid

A force acting on a nanoparticle occurring in a fluid has been studied by the molecular dynamics method. It is shown that this force is nonstationary and exhibits a relaxation character. At the initial instant, it is two to three times the Stokes force, but then decreases and, outside the first relaxation region, becomes smaller than the Stokes force. A stationary force acting on a nanoparticle is determined by the particle mass and size. Correlation expressions for determining the drag coefficient are constructed. It is established that the drag force is anisotropic.

The velocity autocorrelation function of nanoparticles in a hard-sphere molecular system

The diffusion of nanoparticles in a dense molecular medium representing a fluid (liquid or gas) composed of hard absolutely elastic spheres was studied by the molecular dynamics method in a broad range of the medium density. It was established that relaxation of the velocity autocorrelation function of the particles is well described by a superposition of two exponents with different characteristic relaxation times. Dependence of the velocity autocorrelation function on the particle and radius and on the carrying fluid density was studied.

Nonclassical Properties of Molecular Diffusion in Liquids and Dense Gases

The diffusion of molecules in liquids and dense gases is demonstrated to be nonclassical for long time intervals. This means that the time dependence of the mean-square displacement of molecules is nonlinear. This result was obtained by molecular dynamics simulations over a wide range of density of the medium. The problem of plateau values of the diffusion coefficient is discussed. Nonclassical diffusion equations are derived and discussed.

Fluid viscosity under confined conditions

Closed equations of fluid transfer in confined conditions are constructed in this study using ab initio methods of nonequilibrium statistical mechanics. It is shown that the fluid viscosity is not determined by the fluid properties alone, but becomes a property of the “fluid-nanochannel walls” system as a whole. Relations for the tensor of stresses and the interphase force, which specifies the exchange by momentum of fluid molecules with the channel-wall molecules, are derived. It is shown that the coefficient of viscosity is now determined by the sum of three contributions. The first contribution coincides with the expression for the coefficient of the viscosity of fluid in the bulk being specified by the interaction of fluid molecules with each other. The second contribution has the same structure as the first one but is determined by the interaction of fluid molecules with the channel-wall molecules. Finally, the third contribution has no analog in the usual statistical mechanics of transport processes of a simple fluid. It is associated with the correlation of intermolecular forces of the fluid and the channel walls. Thus, it is established that the coefficient of viscosity of fluid in sufficiently small channels will substantially differ from its bulk value.