Volume Crystallization of a Nickel Droplet Containing Refractory Nanoparticles upon Its Impact onto a Substrate

A mathematical model is developed for nonequilibrium volume crystallization of a metallic droplet modified by mechanically activated refractory nanoparticles upon its impact onto a solid substrate. The model takes into account the kinetics of heterogeneous and homogeneous nucleation during melt cooling. Specific features of crystallization of a liquid metal (nickel) depending on the concentration and size of modifying particles are examined numerically. A typical feature of the process considered is the maximum supercooling of the melt, whose magnitude depends on the particle size and cooling intensity. Homogeneous nucleation is almost absent. The calculated radii of droplets solidified on the substrate are in good agreement with available experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 29–34, January–February, 2006.     

Seismic efficiency of a contact explosion and a high-velocity impact

The seismic energy transferred to an elastic half-space as a result of a contact explosion and a meteorite impact on a planet’s surface is estimated. The seismic efficiency of the explosion and impact are evaluated as the ratio of the energy of the generated seismic waves to the energy of explosion or the kinetic energy of the meteorite. In the case of contact explosions, this ratio is in the range of 10⁻⁴–10⁻³. In the case of wide-scale impact effects, where the crater in the planet’s crust is produced in the gravitational regime, a formula is derived that relates the seismic efficiency of an impact to its determining parameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 3–12, March–April, 2007.     

Flow of electrolytes in a porous medium

A two-scale model of ion transfer in a porous medium is obtained for one-dimensional horizontal flows under the action of a pressure gradient and an external electric field by the method of homogenization. Steady equations of electroosmotic flows in flat horizontal nano-sized slits separated by thin dielectric partitions are averaged over a small-scale variable. The resultant macroequations include Poisson’s equation for the vertical component of the electric field and Onsager’s relations between flows and forces. The total horizontal flow rate of the fluid is found to depend linearly on the pressure gradient and external electric field, and the coefficients in this linear relation are calculated with the use of microequations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 162–173, July–August, 2008.     

Derivation of Micro/Macro Lithium Battery Models from Homogenization

In this article, we develop a micro–macroscopic coupled model aimed at studying the interplay between electrokinetics and transport in lithium ion batteries. The system studied consists of a solid (electrode material) and a liquid phase (electrolyte) with periodic microscopic features. In this work, homogenization of generalized Poisson–Nernst–Planck (PNP) equation set leads to a micro/macro formulation similar in nature to the one developed in Newman’s model for lithium batteries. Underlying conservation equations are derived for each phase using asymptotic expansions and mathematical tools from homogenization theory, starting from a PNP micromodel, and in particular Newman’s model is obtained as a corollary of the micro/macro approach developed here. The advantage of homogenization lies in the fact that effective parameters can be derived directly from the analysis of the periodic microstructure and from the application of the theory developed in this article. In addition, the advantages of using homogenization in Lithium ion battery modeling are outlined. Lastly, this work is a necessary step toward more general homogenized models and toward mathematical proofs, and it is also needed preliminary analysis for multiscale computational schemes.     

Approximation of poisson integrals by repeated de la Vallée Poussin sums

We obtain asymptotic equalities for upper bounds of deviations of the repeated de la Vallée Poussin sums on classes of Poisson integrals. Under certain conditions, these equalities guarantee the solvability of the Kolmogorov–Nikol’skii problem for the repeated de la Vallée Poussin sums and classes of Poisson integrals. We indicate conditions under which the repeated de la Vallée Poussin sums guarantee a better order of approximation than ordinary de la Vallée Poussin sums.     

Numerical Simulation of Two-Phase Inertial Flow in Heterogeneous Porous Media

In this study, non-Darcy inertial two-phase incompressible and non-stationary flow in heterogeneous porous media is analyzed using numerical simulations. For the purpose, a 3D numerical tool was fully developed using a finite volume formulation, although for clarity, results are presented in 1D and 2D configurations only. Since a formalized theoretical model confirmed by experimental data is still lacking, our study is based on the widely used generalized Darcy–Forchheimer model. First, a validation is performed by comparing numerical results of the saturation front kinetics with a semi-analytical solution inspired from the Buckley–Leverett model extended to take into account inertia. Second, we highlight the importance of inertial terms on the evolution of saturation fronts as a function of a suitable Reynolds number. Saturation fields are shown to have a structure markedly different from the classical case without inertia, especially for heterogeneous media, thereby, emphasizing the necessity of a more complete model than the classical generalized Darcy’s one when inertial effects are not negligible.     

Numerical simulation of blood flow and interstitial fluid pressure in solid tumor microcirculation based on tumor-induced angiogenesis

A coupled intravascular–transvascular–interstitial fluid flow model is developed to study the distributions of blood flow and interstitial fluid pressure in solid tumor microcirculation based on a tumor-induced microvascular network. This is generated from a 2D nine-point discrete mathematical model of tumor angiogenesis and contains two parent vessels. Blood flow through the microvascular network and interstitial fluid flow in tumor tissues are performed by the extended Poiseuille’s law and Darcy’s law, respectively, transvascular flow is described by Starling’s law; effects of the vascular permeability and the interstitial hydraulic conductivity are also considered. The simulation results predict the heterogeneous blood supply, interstitial hypertension and low convection on the inside of the tumor, which are consistent with physiological observed facts. These results may provide beneficial information for anti-angiogenesis treatment of tumor and further clinical research. The project supported by the National Natural Science Foundation of China (10372026).     

Parameter Determination for Reductive Dechlorination of Chlorinated Solvents

The contamination of subsurface due to the chlorinated solvents such as tetrachlorethylene (PCE) and trichlorethylene (TCE) is one of the most difficult environmental problems to treat. Bioremediation has been shown by many researchers to be a remedial alternative for this type of contamination. Chlorinated solvents are not directly mineralized but rather are transformed by microorganisms into one or more intermediate compounds before converting into a final compound. These sequential reactions, termed “reductive dehalogenation”, consist of replacing a chlorine atom by a hydrogen atom. The pathway of degradation of PCE can be expressed by the following scheme PCE → TCE → DCE → VC → ETH, where dichloroethene (DCE), vinyl chloride (VC) and finally ETH is ethylene. Since the biotransformation rate coefficients of each intermediate compound are different, they have to be determined very precisely to establish an effective treatment operation. The sequential decay can be described by Michaelis–Menten’s kinetics, which constitutes a highly nonlinear system of ordinary differential equations (ODEs). This is very sensitive to the changes of biotransformation rate coefficients. In this study we introduce a methodology how to numerically estimate the rate coefficients for Michaelis–Menten’s equations from the knowledge of the concentrations of PCE, TCE, DCE, VC and ETH. The efficiency of the proposed method is demonstrated on some examples. Estimated biotransformation coefficients are employed to predict the concentrations of chlorinated solvents. Computations and measurements show a very good agreement.     

Henry’ Law and Gas Phase Disappearance

In a two-phase (liquid–gas) two-component (water–hydrogen) system we discuss the formulation of the possible dissolution of hydrogen in the liquid phase. We show how Henry’s law fits in a phase diagram and the problem is formulated as a set of nonlinear partial differential equations with complementarity constraints.     

Gas-dynamic signs of explosive eruptions of volcanoes. 2. Model of homogeneous-heterogeneous nucleation. Specific features of destruction of the cavitating magma

The dynamics of state of the crystallite-containing magma is studied within the framework of the gas-dynamic model of bubble cavitation. The effect of crystallites on flow evolution is considered for two cases: where the crystallites are cavitation nuclei (homogeneous-heterogeneous nucleation model) and where large clusters of crystallites are formed in the magma in the period between eruptions. In the first case, decompression jumps are demonstrated to arise as early as in the wave precursor; the intensity of these jumps turns out to be sufficient to form a series of discrete zones of nucleation ahead of the front of the main decompression wave. Results of experimental modeling of an explosive eruption with ejection of crystallite clusters (magmatic “bombs”) suggest that a cocurrent flow of the cavitating magma with dynamically varying properties (mean density and viscosity) transforms to an independent unsteady flow whose velocity is greater than the magma flow velocity. Experimental results on modeling the flow structure during the eruption show that coalescence of bubbles in the flow leads to the formation of spatial “slugs” consisting of the gas and particles. This process is analyzed within a combined nucleation model including the two-phase Iordansky-Kogarko-van Wijngaarden model and the model of the “frozen” field of mass velocities in the cavitation zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 167–177, March–April, 2009.     

Nucleation of cracks in a perforated fuel cell

A mathematical model is constructed for crack nucleation in an isotropic fuel cell (heat-releasing solid material) attenuated by a biperiodic system of cooling cylindrical channels with a circular cross section. Cracks are assumed to appear with increasing heat-release intensity in the bulk of the material. The solution of the problem on equilibrium of an isotropic perforated fuel cell with crack nuclei reduces to the solution of a nonlinear singular integral equation with a Cauchy-type kernel. The solution of the latter equation yields the forces in the band of crack nucleation. The condition of crack nucleation is formulated with allowance for the criterion of ultimate extension of bonds in the material. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 121–133, September–October, 2007.     

Dynamics of Phase Transitions and Hysteresis in a Viscoelastic Ericksen's Bar on an Elastic Foundation

This work is a follow-up on the study [32] of interface dynamics and hysteresis in materials undergoing solid-solid phase transitions. We consider the dynamics of a viscoelastic bar with a nonmonotone stress-strain relation and viscous stress linearly proportional to the strain rate. The bar is placed on an elastic foundation with stiffness β mimicking the interaction of phases in higher dimensions. Time-dependent displacement-controlled loading of the bar results in a tilted and serrated hysteresis loop, in qualitative agreement with some experimental observations in shape-memory alloys. The model exhibits three phase transition processes: phase nucleation, interface slip and phase annihilation. Between these dynamic processes the system gets stuck in local minimizers of the potential energy. As β increases from zero, a slip-dominated solution behavior transforms to the one where slip and annihilation events are preceded by a step-by-step nucleation process. We show that this transition is caused by an interplay between the slip-favoring inertia term and the nucleation-favoring elastic foundation terms. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nonideal effects behind reflected shock waves in a high-pressure shock tube

Abstract. Shock tubes often experience temperature and pressure nonuniformities behind the reflected shock wave that cannot be neglected in chemical kinetics experiments. Because of increased viscous effects, smaller tube diameters, and nonideal shock formation, the reflected-shock nonidealities tend to be greater in higher-pressure shock tubes. Since the increase in test temperature () is the most significant parameter for chemical kinetics, experiments were performed to characterize in the Stanford High Pressure Shock Tube using infrared emission from a known amount of CO in argon. From the measured change in vibrationally equilibrated CO emission with time, the corresponding ddt (or for a known time interval) of the mixture was inferred assuming an isentropic relationship between post-shock temperature and pressure changes. For a range of representative conditions in argon (24–530 atm, 1275–1900 K), the test temperature 2 cm from the endwall increased 3–8 K after 100 s and 15–40 K after 500 s, depending on the initial conditions. Separate pressure measurements using a shielded piezoelectric transducer confirmed the isentropic assumption. An analytical model of the reflected-shock gas dynamics was also developed, and the calculated 's agree well with those obtained from experiment. The analytical model was used to estimate the effects of temperature and pressure nonuniformities on typical chemical kinetics measurements. When the kinetics are fast (s), the temperature increase is typically negligible, although some correction is suggested for kinetics experiments lasting longer than 500 s. The temperature increase, however, has a negligible impact on the measured laser absorption profiles of OH (306 nm) and CH (216 nm), validating the use of a constant absorption coefficient. Infrared emission experiments are more sensitive to temperature and density changes, so nonuniformities should be taken into account when interpreting ir-emission data. Received 25 April 2000 / Accepted 8 September 2000     

A Two-Scale Model for Coupled Electro-Chemo-Mechanical Phenomena and Onsager’s Reciprocity Relations in Expansive Clays: II Computational Validation

In Part I Moyne and Murad [Transport in Porous Media 62, (2006), 333–380] a two-scale model of coupled electro-chemo-mechanical phenomena in swelling porous media was derived by a formal asymptotic homogenization analysis. The microscopic portrait of the model consists of a two-phase system composed of an electrolyte solution and colloidal clay particles. The movement of the liquid at the microscale is ruled by the modified Stokes problem; the advection, diffusion and electro-migration of monovalent ions Na⁺ and Cl⁻ are governed by the Nernst–Planck equations and the local electric potential distribution is dictated by the Poisson problem. The microscopic governing equations in the fluid domain are coupled with the elasticity problem for the clay particles through boundary conditions on the solid–fluid interface. The up-scaling procedure led to a macroscopic model based on Onsager’s reciprocity relations coupled with a modified form of Terzaghi’s effective stress principle including an additional swelling stress component. A notable consequence of the two-scale framework are the new closure problems derived for the macroscopic electro-chemo-mechanical parameters. Such local representation bridge the gap between the macroscopic Thermodynamics of Irreversible Processes and microscopic Electro-Hydrodynamics by establishing a direct correlation between the magnitude of the effective properties and the electrical double layer potential, whose local distribution is governed by a microscale Poisson–Boltzmann equation. The purpose of this paper is to validate computationally the two-scale model and to introduce new concepts inherent to the problem considering a particular form of microstructure wherein the clay fabric is composed of parallel particles of face-to-face contact. By discretizing the local Poisson–Boltzmann equation and solving numerically the closure problems, the constitutive behavior of the diffusion coefficients of cations and anions, chemico-osmotic and electro-osmotic conductivities in Darcy’s law, Onsager’s parameters, swelling pressure, electro-chemical compressibility, surface tension, primary/secondary electroviscous effects and the reflection coefficient are computed for a range particle distances and sat concentrations.     

Flow near the permeable boundary of a porous medium: An experimental investigation using LDA

 Fluid flow at the interface of a porous medium and an open channel is the governing phenomenon in a number of processes of industrial importance. Traditionally, this has been modeled by applying the Brinkman’s modification of Darcy’s law to obtain the velocity profile in terms of an additional parameter known as the “apparent viscosity” or the “slip coefficient”. To test this ad hoc approach, a detailed experimental investigation of the flow was conducted using Laser Doppler Anemometry (LDA) in the close vicinity of the permeable boundary of a porous medium. The porous medium used in the experiments consisted of a network of continuous glass strands woven together in a random fashion. A Hele–Shaw cell was partially filled with a fibrous preform such that an open channel flow is coupled with the Darcy flow inside the preform through the permeable interface of the preform. The open channel portion of the Hele–Shaw cell also acts as an ideal porous medium of known in-plane permeability which is much higher than the permeability of the fibrous porous medium. A viscous fluid is injected at a constant flow rate through the above arrangement and a saturated and steady flow is established through the cell. Using LDA, steady state velocity profiles are accurately measured by traversing across the cell in the direction perpendicular to the flow. A series of experiments were conducted in which fluid viscosity, flow rate, solid volume fraction of the porous medium and depth of the Hele–Shaw cell were varied. For each and every case in which the conditions for Hele–Shaw approximation were valid, the depth of the boundary layer zone or the screening length inside the fibrous preform was found to be of the order of the channel depth. This is much larger as compared to the Brinkman’s prediction of the screening length which is of the order of √K, where K is the permeability of the fibrous porous medium. Based on this finding, we modified the boundary condition in the Brinkman’s solution and found that the velocity profile results compared well with the experimental data for the planar geometry and the fibrous preforms for volume fractions of 7%, 14% and 21% for Hele–Shaw cell depths of 1.6 and 3.175 mm. For a cell depth of 4.8 cm, in which the Hele–Shaw approximation was not valid, the boundary layer thickness or the screening length was found to be less than the mold or channel depth but was still much larger than the Brinkman’s prediction. Received: 10 May 1996 / Accepted: 26 August 1996     

Subcritical crack growth in an aging plate with variable elastic modulus

The paper addresses subcritical growth of a crack in a thin isotropic plate made of an aging viscoelastic material with time-dependent elastic modulus. The behavior of the material is described by Arutyunyan’s creep theory. To simulate fracture, a modified Leonov–Panasyuk–Dugdale model and a critical crack opening displacement criterion are used. An equation describing the subcritical growth of the crack is derived assuming that Poisson’s ratio is constant. As an example, the critical loads are determined, and curves of subcritical crack growth are plotted for a specific material. The results are compared with the case of constant elastic modulus     

Simulation of void fraction profile evolution in subcooled nucleate boiling flow in a vertical annulus using a bubble-tracking approach

A three-dimensional bubble-tracking model of subcooled nucleate boiling flow in a vertical channel at low-pressure conditions is proposed with specific application to the case of boiling in an annulus with a central heating rod. Vapour is distributed in the liquid in the form of individually tracked bubbles. The overall behaviour of the liquid–vapour system results from motion, interaction, coalescence and boiling mechanisms prescribed mostly at the level of bubbles. Bubbles are nucleated at nucleation sites randomly distributed over the heated surface. After nucleation, bubbles slide on the heated wall, detach and then migrate into the lower-temperature region away from the heated surface, where they condense. The proposed model was applied to experiments on subcooled boiling from Purdue University (USA). Experimental and calculated void fraction radial profiles at different axial locations are compared.     

Effect of the boundary layer on the base pressure in a two-dimensional flow with a Mach number M = 5

New data on the base pressure in a two-dimensional ow with a Mach number M = 5 are obtained for a wide range of variation of the normalized boundary-layer thickness in the flow-separation cross section. The test results are compared with Tanner’s theory, and a conclusion is made that this numerical model has to be corrected. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 23–28, May–June, 2005.     

Natural vibration of a sandwich beam on an elastic foundation

The natural vibration of an elastic sandwich beam on an elastic foundation is studied. Bernoulli’s hypotheses are used to describe the kinematics of the face layers. The core layer is assumed to be stiff and compressible. The foundation reaction is described by Winkler’s model. The system of equilibrium equations is derived, and its exact solution for displacements is found. Numerical results are presented for a sandwich beam on an elastic foundation of low, medium, or high stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 57–63, May 2006.     

Numerical and experimental investigation of variable phase transformation number effect in porous media during freezing process

A model is proposed to investigate heat and moisture transfer in porous media during freezing process based on Luikov’s model by considering the effect of variation of phase transformation number, ε. This parameter has been mostly used as a constant by researchers. Three-dimensional Luikov’s equations are considered and solved numerically. The model is compared with obtained experimental data. It is shown that the effect of variable phase transformation number is noticeable in heat and moisture transfer process.