Yu. A. Buevich

Motion resistance of a particle suspended in a turbulent medium

The equation of motion of a particle in a turbulent fluid was considered by Tchen [1], who started from the known Basset-BoussinesqOseen equation for the accelerated motion of a particle in a stationary fluid, and then on the basis of intuitive considerations supplemented it by a term associated with the action of the pressure forces which arise with unsteady motion of the fluid, Tchens result was criticized and developed further in the study of Corrsin and Lumley [2] who, using the same method, suggested the equation

Approximate statistical theory of a fluidized bed

Under the conditions of developed fluidization there are intensive fluctuations both in the fluidizing medium and in the dispersed solid phase. These motions have a decisive effect on the rheologlcal properties of the fluidized bed, and on the chemical reactions and transport processes taking place in it [1], Thus, for example, in the experiments of Wicke and Fetting [2], who investigated the heat transfer between a fluidized bed and the walls of a heated container, the effective heat transfer coefficient was found to be higher by an order of magnitude than the corresponding result for a fluidized bed held down by a wire grid so that the random motion of the solid phase was reduced. It is clear that the initial stage of any study of the structure of the fluidized bed as a whole, and of the subsequent development of any model, must involve an investigation of local structural properties, including the above fluctuations.The time variation of the individual particle velocities is due to two different causes. First, there is the interaction between the particles both through direct collisions and through the medium of the liquid phase, and, secondly, there is the interaction with the viscous fluid. These two factors are not independent, so that the set of fluidized particles has certain features characteristic for both a dense gas, with a potential intramolecular interaction, and a set of particles executing Brownian motion in a continuous medium.Any detailed statistical theory of a system of fluidized particles must be based on a representation of the random particle motions in the medium by a stochastic process with some definite properties (see, for example, [3–4]). Ideally, this theory should lead to the formulation of a transport equation which, in view of the above properties of the system, should have some of the features of both the usual Boltzman transport equation and the Fokker-Planck equation. The solution of this final equation is, of course, more difficult than the solution of the Boltzman or Fokker-Planck equations. Moreover, there is also the problem of applying this equation to different special cases. An alternative approach is to develop an approximate, but still sufficiently effective, theory of the local properties of the fluidized bed, which would combine relative simplicity in application with sufficient rigor and generality. This kind of theory is put forward in the present paper. The conclusions to which it leads are in good qualitative agreement with experiment.

Diffusion separation of hydrogen from gas mixtures

Experiments are described and a model is evaluated for the process of production of superpure hydrogen from mixtures with ammonia and nitrogen by selective diffusion through thin metallic membranes.

Fluctuation in the number of particles in dense disperse systems

A statistical theory is formulated to describe the number of particles in an arbitrarily designated volume of a dense disperse system as a random function of time. This theory is a natural extension to concentrated systems of the Smolukhovskii-Einstein statistic, which they proposed for the Brownian motion of indistinguishable noninteracting particles.

Internal pulsations in flows of finely dispersed suspensions

The results are given of calculations for the flow of a finely dispersed suspension when momentum and energy are exchanged between individual particles exclusively through the ambient fluid, i.e., the role of direct collisions between particles is negligible. Using the results, one can not only calculate the rms characteristics of the pseudoturbulence and, in particular, find the stresses in the dispersed phase but also to give a natural explanation of the phenomena observed in experiments on sedimentation and hydrodynamic self-diffusion of particles in monodisperse suspensions.

Hydrodynamic thermal burst in radial bearing

The work involves the investigation of the conditions of occurrence of a thermal burst in an unloaded bearing with a pseudoplastic liquid. It is shown that in a loaded bearing a local thermal burst is possible.

Nonstationary heating of a fixed granular mass

The reduction of the system of heat-transfer equations in phases of a disperse medium to a single equation is considered. The problem of heating a layer of granular material by a stream of hot fluid is investigated as an illustration.

Transport of heat or mass in a dispersed flow

A rigorous derivation of the equations of heat transport is carried out by averaging over an ensemble for a system consisting of a continuous medium with particles imbedded in it, and the closure problem for these equations is discussed.

Structure of filtration pseudoturbulence

The problem of large-scale (“pseudoturbulent”) motion of a fluid in a nonuniform porous medium was formulated in [1]. Since in practice the local porosity ε(x) is unknown, it may be considered a continuous random point function. The difference of the local values of the porosity ε(x) from the mean value ε∘ for the medium as a whole leads to the occurrence of random pseudoturbulent motions of the filtering fluid, which are superposed on the mean filtration flow. The characteristics of the large-scale filtration motion in a medium with this sort of random porosity were considered in detail in [1], where the formal solution is presented for the resulting equations for two-point correlations, based on the use of considerations of spatial invariance. Also presented is a qualitative discussion of the effect of pseudoturbulence of the filtering medium on the transport processes in the medium.We note that the considered problem of pseudoturbulence of a filtering fluid in a nonuniform porous medium does not have anything in common with the statistical problem of the motion of small fluid elements in a broken porous space. The latter problem is interesting in connection with the analysis of the convective diffusion processes in a porous body (both uniform and nonuniform) and, beginning with [3], has been considered in several studies, including [2].In the present study we have used a method for solving the problem which is significantly different in comparison with that of [1], based on the representation of the variation of the local porosity from point to point as a random process with independent increments. This method has the advantage that it permits expressing the required correlation functions in the form of quadratures with arbitrary values of the characteristic parameters. In the following, for simplicity we consider the axisymmetric problem under the assumption that the two-point correlation of the deviations of the local values of the porosity from the mean are representable in the form of an isotropie Gaussian function of the distance between the points. The explicit expressions for the correlations are also written in some approximation and the physical consequences resulting from these assumptions are discussed.

The hydromechanics of suspensions

Thermodynamic forces are introduced into the momentum conservation equations for the phases of a monodisperse suspension of fine particles in order to permit effective description of the presence of diffusion processes in flows, thus circumventing the main difficulty encountered in the hydromechanics of suspensions.