Growth of a new phase in a substance in a metastable state

A model of kinetics of phase transitions in a substance in a metastable state is proposed, where the probability of extensive nucleation owing to homogeneous mechanisms is rather large; the model is an alternative to Kolmogorov’s model. The use of this model is demonstrated to offer analytical solutions that describe both the crystallization processes with similar densities of the liquid and solid phases and, for instance, the kinetics of nucleation and growth of bubbles in surface boiling. Solutions obtained by Kolmogorov’s model and by the present model coincide at the initial stage of the process where the volume fraction of the new phase is small. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 75–80, March–April, 2007.     

Lateral migration of a capsule in a plane Poiseuille flow in a channel

Three-dimensional numerical simulation is presented on the motion of a deformable capsule undergoing large deformation in a plane Poiseuille flow in a channel at small inertia. The capsule is modeled as a liquid drop surrounded by an elastic membrane which follows neo-Hookean law. The numerical methodology is based on a mixed finite-difference/Fourier transform method for the flow solver and a front-tracking method for the deformable interface. The methodology can address large deformation of a capsule over a wide range of capsule-to-medium viscosity ratio. An extensive validation of the methodology is presented on capsule deformation in linear shear flow and compared with the boundary-element/integral simulations. Motion of a capsule in wall-bounded parabolic flow is simulated over an extended period of time to consider both transient and steady-state motion. Lateral migration of the capsule towards the centerline of the channel is observed. Results are presented over a range of capillary number, viscosity ratio, capsule-to-channel size ratio, and lateral location. After an initial transient phase during which the capsule deforms very quickly, the flow of the capsule is observed to be a quasi-steady process irrespective of capillary number (Ca)$(\mathit{Ca})$, capsule-to-channel size ratio (a/H)$(a/H)$, and viscosity ratio (λ)$(\lambda )$. Migration velocity and capsule deformation are observed to increase with increasing Ca$\mathit{Ca}$ and a/H$a/H$, but decrease with increasing λ$\lambda$, and increasing distance from the wall. Numerical results on the capsule migration are compared with the analytical results for liquid drops, and capsules with Hookean membrane which are valid in the limit of small deformation. Unlike the prediction for liquid drops, capsules are observed to migrate toward the centerline for 0.2?λ?5$0.2?\lambda ?5$ range considered here. The migration velocity is observed to depend linearly on (a/H)³$(a/H{)}^3$, in agreement with the small-deformation theory, but non-linearly on Ca$\mathit{Ca}$ and the distance from the wall, in violation of the theory. Using the present numerical results and the analytical results, we present a correlation that can reasonably predict migration velocity of a capsule for moderate values of a/H$a/H$ and Ca$\mathit{Ca}$.     

On the dispersion of a solute in oscillating flow of a non-Newtonian fluid in a channel

The paper presents an exact analysis of the dispersion of an immiscible solute in a non-Newtonian fluid (known as an incompressible second-order fluid which shows viscoelastic behaviour) flowing slowly in a parallel plate channel in the presence of a periodic pressure gradient. Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficients K _i (τ)(i=1,2,3,…) are obtained as functions of time τ in the case when the initial solute distribution is in the form of a slug of finite extent. The analysis leads to the novel result that K ₂(τ) (which is a measure of the longitudinal dispersion coefficient of the solute) has a steady part S in addition to a fluctuating part D ₂(τ) due to the pulsatility of the flow. It is found that S decreases with increase in the viscoelastic parameter M for given values of the amplitude λ and frequency ω of the pressure pulsation. On the other hand, it is found that at a fixed instant τ, the amplitude of D ₂(τ) increases with increase in M for given values of λ and ω. Further it is shown that at a given instant τ, the amplitude of D ₂(τ) decreases with increase in ω for given λ and M and the profile for D ₂(τ) becomes progressively flatter with increase in ω. Finally the axial distribution of the average concentration θ _m of the solute over the channel cross-section is determined at different instants after the solute injection for several values of M, λ and ω. The present study is likely to have important bearing on the problem of dispersion of tracers in blood flow through arteries.     

Interaction of a surface wave with a crack in a concave half space

The interaction of a Rayleigh wave with a stationary crack in a rectilinear surface was treated in [1, 2]. It was shown that under certain conditions a surface wave can generate dynamic stresses large enough to extend a crack. However, there have been no studies of the interaction of a surface wave with a crack in a curvilinear half space, although this case is encountered more frequently in practice. We use the method of dynamic photoelasticity to observe the interaction of a surface wave with an edge crack along and normal to a concave half space. The research was performed on 350×400×15-mm samples of polymethyl methacrylate. A surface wave of duration up to 50sec was excited by a point micro explosion on the linear portion of the sample joined with the curvilinear part. The interaction of the surface wave with a crack was recorded in circularly polarized light by an SFR-1 high-speed motion-picture camera at 1.5 · 10⁶ frames/sec.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 137–143, May–June, 1979.     

Propagation of a stress pulse in a viscoelastic rod

Experimental work is reported on the propagation of a stress pulse in a viscoelastic waveguide. The data obtained are compared with results of analysis using one-dimensional wave-propagation theory. The waveguide used in this work is a low-density polyethylene rod 1/2 in. in diameter and 30-in. long. Stress input to the waveguide and the resulting particle velocity at three stations are measured using a crystal stress transducer, two Faraday-principle velocity transducers and a capacitor transducer. The experiment is described mathematically as a boundary-value problem formulated in terms of the one-dimensional equation of motion, the strain-displacement relationship, a hereditary constitutive equation and the stress-boundary condition. Fourier transform and inversion yield an integral expression for velocity which is evaluated numerically at three stations using measured values for the stress-boundary condition, material attenuation and phase velocity. The analytical results compare favorably with the experimental data. The one-dimensional theory appears adequate to describe pulse propagation of this type. The attenuation and phase velocity used here are found to be a linear function and a logarithmic increasing function of frequency respectively.     

Natural convection from a cylinder in a narrow gap and in a porous medium

The problem of natural convection from a horizontal cylinder in a narrow gap and in a porous medium is solved both theoretically and experimentally. An integral method for calculating heat transfer from the cylinder for constant flux on its surface was suggested. Numerical analysis clarified the role of regime and geometrical factors. It is shown that natural convection from a cylinder in a porous medium can be modeled by a Hele Shaw cell. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 140–150. January–February, 1999.     

Aerodynamic characteristics of a square cylinder with a rod in a staggered arrangement

The aerodynamic characteristics of a square cylinder with an upstream rod in a staggered arrangement were examined. The pressure measurement was conducted in a wind tunnel at a Reynolds number of Re_D=82,000 (based on the width of the square cylinder) and the flow visualization was carried out in a water tunnel with the hydrogen bubble technique at Re_D=5,200. When the rod and the square cylinder were in tandem, the reduction of drag was mainly caused by the increase of the rear suction pressure. When the staggered angle was introduced, the shield and disturbance effect of the rod on the square cylinder diminished, which results in the increase of the cylinder drag. The side force induced by the staggered angle is small (the maximum value is 20% of the drag of the isolate square cylinder). There were six different flow modes with various staggered angles and spacing ratios, and the corresponding flow patterns are presented in present paper.     

Entrance flow of a bingham fluid in a tube

The numerical solution of the entrance flow in a tube has been obtained for a Bingham fluid. The numerical procedure used is that of Patankar and Spalding [1]. The accuracy of the numerical results is demonstrated by comparing the fully-developed velocity profiles with analytical exact solutions. The results of the entrance flow in a tube for the case of a zero yield stress are compared with the entrance flow solution for a Newtonian fluid. Detailed results are presented for a wide range of yield numbers (=τ _y D/ūμ).     

Flow in a spherical cavity due to a stokeslet

The earth is considered as a rigid spherical cavity of radius a filled with a highly viscous incompressible fluid of viscosity η. The non-axisymmetric problem of flow due to a stokeslet of strength F/8πη located at (0, 0, c), c < a with its axis along OX, O being the centre of the sphere, is discussed for small Reynolds numbers. The expressions for velocity and pressure are obtained in terms of A(r, θ, φ) and B(r, θ, φ), biharmonic and harmonic functions respectively, using a sphere theorem for non-axisymmetric flow inside a sphere. The drag on the sphere exerted by the fluid is found to be independent of the location of the stokeslet.     

Hydrodynamics of a sphere in a stratified fluid

The flow pattern around a sphere moving at constant velocity in a fluid with an exponential density distribution is investigated by optical methods. The thin density boundary layer forming the high-gradient envelope of the wake is distinguished as one of the elements of the structure. The symmetry properties of the flow are investigated. The limits of applicability of the traditional approximation of weak stratification in the problem of excitation of attached internal waves are noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–9, January–February, 1989.     

Diffusion baroeffect in a capillary in a broad range of knudsen numbers

The magnitude of the diffusion baroeffect in a capillary is calculated in the entire range of Knudsen numbers based on a solution of BGK equations for a binary gas equation. The theoretical magnitudes of the baroeffect agree well with the experimental results obtained in a broad range of Knudsen numbers. The thermodynamic coefficients are calculated, and the Onsager reciprocal relation is demonstrated, from which in the limit of a viscous system it follows that the barodiffusion constant is equal to the coefficient of diffusion slippage.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 74–79, March–April, 1973.     

Drag of a cylinder in a two-phase flow

The paper reports an experimenta! investigation of the drag of a circular cylinder in the transverse flow of a gas suspension. The drag of a cylinder in an airflow has been fairly well studied [1, 2], It has been shown experimentally [3] that the presence of small numbers of solid particles in a gas flow can significantly change the aerodynamic properties of the body. A cylinder was chosen for the present study because it is a classical body, and the results obtained in investigations of it can, in a certain sense, be extrapolated to other bodies, for example, airfoils.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 123–129, January–February, 1992.     

Aeolian tones of a plate in a channel

The conditions of the onset of aeroacoustic resonance phenomena near a plate in a gas flow in a rectangular channel are studied theoretically and experimentally in a two-dimensional formulation. The eigenfrequency as a function of the plate's chord and its position in the channel, the shape of the eigenfunctions, and the effect of the Mach number of the basic gas flow versus the eigenfrequencies and eigenfunctions and the mechanism of self-excited oscillations are determined. A mathematical model by means of which the dependence of the resonance phenomena on the geometrical parameters of the structure were performed is proposed and substantiated. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 69–77, March–April, 1998.     

Microcavitation in the slow motion of a solid spherical particle along a wall in a fluid

In the slow motion of a spherical particle along a wall, a cavity in the form of a non-spherical bubble is detected visually in the narrow particle-wall clearance. The nondimensional parameters associated with cavity formation are formulated and the effect of these parameters on the particle motion is investigated.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 110–118. Original Russian Text Copyright © 2004 by Prokunin.     

On a nonlocal stationary free-boundary problem arising in the confinement of a plasma in a Stellarator geometry

We prove the existence and some qualitative properties of the solution to a two-dimensional free-boundary problem modeling the magnetic confinement of a plasma in a Stellarator configuration. The nonlinear elliptic partial differential equation on the plasma region was obtained from the three-dimensional magnetohydrodynamic system by Hender & Carreras in 1984 by using averaging arguments and a suitable system of coordinates (Boozer's vacuum coordinates). The free boundary represents the separation between the plasma and vacuum regions, and the model is described by an inverse-type problem (some nonlinear terms of the equation are unknown). Using the zero net current condition for the Stellarator configurations, we reformulate the problem with the help of the notion of relative rearrangement, leading to a new problem involving nonlocal terms in the equation. We use an iterative algorithm and establish some new properties on the relative rearrangement in order to prove the convergence of the algorithm and then the existence of a solution.     

Peristaltic flow of a nanofluid in a non-uniform tube

The present analysis discusses the peristaltic flow of a nanofluid in a diverging tube. This is the first article on the peristaltic flow in nanofluids. The governing equations for nanofluid are modelled in cylindrical coordinates system. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Temperature and nanoparticle equations are coupled so Homotopy perturbation method is used to calculate the solutions of temperature and nanoparticle equations, while exact solutions have been calculated for velocity profile and pressure gradient. The solution depends on Brownian motion number N _b , thermophoresis number N _t , local temperature Grashof number B _r and local nanoparticle Grashof number G _r . The effects of various emerging parameters are investigated for five different peristaltic waves. It is observed that the pressure rise decreases with the increase in thermophoresis number N _t . Increase in the Brownian motion parameter N _b and the thermophoresis parameter N _t temperature profile increases. Streamlines have been plotted at the end of the article.     

Natural convection in a vertical strip immersed in a porous medium

In this work, the conjugated heat transfer characteristics of a thin vertical strip of finite length, placed in a porous medium has been studied using numerical and asymptotic techniques. The nondimensional temperature distribution in the strip and the reduced Nusselt number at the top of the strip are obtained as a function of the thermal penetration parameter s, which measures the thermal region where the temperature of the strip decays to the ambient temperature of the surrounding fluid. The numerical values of this nondimensional parameter permits to classify the different physical regimes, showing different solutions: a thermally long behaviour, an intermediate transition and a short strip limit.     

Motion of a flexible finite-length filament in a flow of a viscous fluid

The two-dimensional problem of the configuration of a flexible filament of finite length in a deformable viscous fluid is solved. The flexuural stresses in the filament and the inertial and gravitational forces are not taken into account. The equilibrium equations are obtained. The friction force that acts on the filament surface from the side of the viscous fluid is proportional to the flow rate. The specific features of the evolution of a bent filament under the conditions of pure and simple shear of a fluid are studied numerically. Analytical solutions are obtained for the evolution of a rectilinear filament; in particular, the stretching force in the filament is found. For the indicated types of flow, the stability of a rectilinear filament against small perturbations is investigated. Volzhskii Polytechnical Institute at the Volgograd State Technical University, Volgograd 404121. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 144–153, March–April, 2000.     

Propagation of a shear crack in a randomly heterogeneous body

Propagation of a crack in a randomly heterogeneous body exposed to longitudinal shear is considered (in a Born approximation). It is proved that the stress means at the crack tip have singularities on the order of (r)^–1/2. The effective coefficient of stress intensity is introduced. It is known that the propagation of a crack in a homogeneous body is of a local nature, i.e., energy consumption in the growth of the crack is completely determined by the coefficient of stress intensity, which is a local characteristic. The equivalence of the force and energy approaches is mathematically expressed by the Irwin equation [1]. An analog of the Irwin equation is obtained for the case of a randomly heterogeneous body.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 145–148, January–February, 1976.     

Secondary flows in a layer with a free surface

The loss of stability of a plane-parallel incompressible viscous heat-conducting fluid flow in a horizontal layer subject to a longitudinal temperature gradient is considered. The lower surface of the layer is assumed to be rigid, while the upper one is free with a surface tension coefficient depending linearly on temperature. Both boundaries are assumed to be thermally-insulated. The critical value of the temperature gradient as a function of other relevant parameters is determined by analyzing the spectrum of the linearized problem. Secondary flows arising after the onset of instability are determined from an analysis of the full nonlinear problem using the expansion of the solution in a power series in terms of a supercritical state parameter in the vicinity of the bifurcation point. Three types of secondary flows are studied: plane two-dimensional waves propagating along the temperature gradient; plane waves travelling at a certain angle to the gradient; and three-dimensional waves propagating along the gradient. A numerical method of problem solution, based on the polynomial approximation, is described.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 85–98, September–October, 1994.