Mechano-Chemistry; Interdiffusion in Solid Solutions

In this work we show that the volume velocity, ρυ , rather than the local centre of mass velocity should be used in continua. We use the volume continuity equation to define the volume frame of reference in the multicomponent, compressible continua. The volume velocity (material velocity) is a unique frame of reference for all internal forces and processes, e.g., the mass diffusion. No basic changes are required in the foundations of linear irreversible thermodynamics except recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in every continuum. The volume fixed frame of reference allows the translation of the Newton’s discrete mass-point molecular mechanics into continuum mechanics and the use of the Cauchy linear momentum equation of fluid mechanics and Navier-Lamé equation of mechanics of solids. Our proposed modifications of Navier-Lamé and energy conservation equations are selfconsistent with the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffusive volume transport. We do show that the local diffusion processes do not change the centre of mass of the system and that the internal stress depends on the gradient of the local volume velocity only.

Download Full-text

Simulation of Flow and Heat Transfer in a Moving Bed Reactor With Cross Flow

Volume 10: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B, and C ◽

10.1115/imece2008-67639 ◽

2008 ◽

Author(s):

Marcelo J. S. de Lemos

Keyword(s):

Heat Transfer ◽

Relative Velocity ◽

Solid Phase ◽

Cross Flow ◽

Vertical Direction ◽

Momentum Equation ◽

Solid Matrix ◽

Flow And Heat Transfer ◽

Temperature Distributions ◽

Solid Phases

Heat transfer in a porous reactor under cross flow is investigated. The reactor is modeled as a porous bed in which the solid phase is moving horizontally and the flow is forced into the bed in a vertical direction. Equations are time-and-volume averaged and the solid phase is considered to have a constant imposed velocity. Additional drag terms appearing the momentum equation are a function of the relative velocity between the fluid and solid phases. Turbulence equations are also affected by the speed of the solid matrix. Results show temperature distributions for several ratios of the solid to fluid speed.

Download Full-text

Membrane potentials I. The theory of the e. m. f. of cells containing ion-exchange membranes

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1961.0116 ◽

1961 ◽

Vol 262 (1309) ◽

pp. 246-256 ◽

Cited By ~ 34

Keyword(s):

Membrane Potential ◽

Ion Exchange ◽

Irreversible Thermodynamics ◽

Membrane Potentials ◽

Ion Exchange Membranes ◽

Centre Of Mass ◽

Solvent Molecules

The principal theories of membrane potential are rigorously reformulated and compared. The limitations of the theory of Teorell-Meyers-Sievers are discussed, as are those of the pseudo-thermostatic treatment of Scatchard. The theory of irreversible thermodynamics is applied in a form in which the velocities of ion and solvent molecules are both referred to that of the centre of mass of the system. The conditions under which these theories may be tested are also considered.

Download Full-text

On the application of kinematic models to simulate the diffusive processes of debris flows

Natural Hazards and Earth System Science ◽

10.5194/nhess-10-1689-2010 ◽

2010 ◽

Vol 10 (8) ◽

pp. 1689-1695 ◽

Cited By ~ 1

Author(s):

M. Arattano ◽

L. Franzi

Keyword(s):

Debris Flow ◽

Debris Flows ◽

Diffusion Processes ◽

Kinematic Model ◽

Wave Model ◽

Momentum Equation ◽

Case Scenario ◽

Kinematic Approximation ◽

Kinematic Models ◽

Frictional Forces

Abstract. Debris flows generally propagate along steep mountain torrents with dynamics primarily governed by gravitational and frictional forces. Thus, debris flows modelling can be successfully performed through the application of kinematic models, which consider only the effects of slope and friction and neglect the remaining terms of the momentum equation. However, the diffusion processes that can be observed in the field, such as the spreading of the debris flow wave as it flows downstream, can not be theoretically predicted by kinematic models, since diffusion is a second-order process neglected in the kinematic approximation. In this paper, this issue is discussed and an application for both a generalized diffusion wave model and a kinematic model is proposed of a debris flow which occurred in an Italian instrumented torrent to identify, in a real case scenario, the effective value of the neglected terms in the kinematic approximation.

Download Full-text

External Aerodynamics Simulations in a Rotating Frame of Reference

International Journal of Aerospace Engineering ◽

10.1155/2014/654037 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14

Author(s):

Filomena Cariglino ◽

Nicola Ceresola ◽

Renzo Arina

Keyword(s):

Source Term ◽

Computational Cost ◽

Momentum Equation ◽

Frame Of Reference ◽

Navier Stokes ◽

Rotating Frame ◽

Stability Derivatives ◽

Rotating Reference Frame ◽

Naca 0012 ◽

Derivatives Of

This paper presents the development of a tool integrated in the UNS3D code, proprietary of Alenia Aermacchi, for the simulation of external aerodynamic flow in a rotating reference frame, with the main objective of predicting propeller-aircraft integration effects. The equations in a rotating frame of reference have been formulated in terms of the absolute velocity components; in this way, the artificial dissipation needed for convergence is lessened, as the Coriolis source term is only introduced in the momentum equation. An Explicit Algebraic Reynolds Stress turbulence model is used. The first assessment of effectiveness of this method is made computing stability derivatives of a NACA 0012 airfoil. Finally, steady Navier-Stokes and Euler simulations of a four-blade single-rotating propeller are presented, demonstrating the efficiency of the chosen approach in terms of computational cost.

Download Full-text

On the processes of migration and diffusion in the systems with solid-state reagents

Journal of Electrochemical Science and Engineering ◽

10.5599/jese.753 ◽

2020 ◽

Vol 10 (2) ◽

pp. 219-227

Author(s):

Viacheslav Barsukov ◽

Volodymyr Khomenko ◽

Oksana Chernysh

Keyword(s):

Charge Transfer ◽

Solid State ◽

Diffusion Model ◽

Diffusion Processes ◽

Solid Phase ◽

Electrode Processes ◽

Bulk Solid ◽

Efficient Diffusion ◽

The Difference ◽

And Migration

This paper deals with peculiarities of diffusion and migration in electrochemical systems with solid-state reagents (ESSSR). Contradictions of the diffusion model are analyzed. It is the difference of applied potentials and the corresponding electric field strength in the bulk solid phase and at the interfaces which is the primary driving force of charge transfer in ESSSR. The time characteristic of diffusion processes is not comparable to the duration of electrode processes at charging/discharging of batteries and especially electrochemical capacitors. In many real systems involving ESSSR, the process of diffusion in solid phase is absent. Examples of charge transfer processes in ESSSR (nickel hydroxide electrode, sparingly soluble quinoid compounds, Li+ intercalation in graphite, etc.) are considered, and the processes are explained using the Grothuss, tunnel and other migration mechanisms. It is shown in this paper that the linear relationship between peak currents in voltammetric curves and the square root of potential scan rate cannot be presented as an ultimate support of the diffusion model, but as а more universal property of ESSSR. In this aspect, the efficient diffusion coefficient, Deff, could be at best discussed, not to distort the ideas of charge-transfer migration mechanisms in the ESSSR.

Download Full-text

Numerical model of heat transfer in three phases of the poroelastic medium

Studia Geotechnica et Mechanica ◽

10.1515/sgem-2016-0019 ◽

2016 ◽

Vol 38 (2) ◽

pp. 53-59

Author(s):

Anna Uciechowska-Grakowicz ◽

Tomasz Strzelecki

Keyword(s):

Heat Transfer ◽

Mathematical Model ◽

Solid Phase ◽

Irreversible Thermodynamics ◽

Pore Fluid ◽

Gas Filtration ◽

Two Phase ◽

Phase Medium ◽

Thermal Consolidation ◽

The Mathematical Model

Abstract In this paper, the results of numerical analysis of the thermal consolidation of a two phase medium, under the assumption of independent heat transfer in fluid and the solid phase of the medium, are presented. Three cases of pore fluid were considered: liquid, represented by water, and gas, represented by air and carbon dioxide. The mathematical model was derived from irreversible thermodynamics, with the assumption of a constant heat transfer between the phases. In the case of the accepted geometry of the classical dimensions of the soil sample and boundary conditions, the process leads to equalization of temperatures of the skeleton on the pore fluid. Heat transfer is associated with the fluid flow in the pores of the medium. In the case of gas as the pore fluid, a non-linear mathematical model of gas filtration through the pores of the medium was accepted. For the computing process, relationships between viscosity or density and temperature proposed by other authors were taken into account. Despite accepting mechanical constants of the solid phase that do not depend on temperature, the obtained model is nonlinear and develops the classical Biot–Darcy model.

Download Full-text

Solid-Phase Diffusion Interaction in Multilayer Thin-Film System Cr/Cu/Ni at Pulse Laser Heating

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.272.31 ◽

2008 ◽

Vol 272 ◽

pp. 31-40 ◽

Cited By ~ 1

Author(s):

M. Vasylyev ◽

M.M. Nishenko ◽

Sergey I. Sidorenko ◽

S.M. Voloshko

Keyword(s):

Thin Film ◽

Laser Pulse ◽

Pulse Energy ◽

Laser Heating ◽

Laser Pulse Energy ◽

Diffusion Processes ◽

Solid Phase ◽

Exponential Dependence ◽

Film Substrate ◽

Pulse Laser Heating

The laser-induced mass transfer in thin-film substrate /Cr/Cu/Ni system is studied by means of Auger Electron Spectroscopy (AES). For the laser-pulse energy values, E = 100-170mJ, the diffusion of Cu atoms into Ni layer and their accumulation within this layer are observed, whereas at E > 170mJ the same is true for Cr atoms. The observed phenomena are explained on the basis of calculated temperature distribution in the system at issue during lased action. Enhanced transfer of Cr atoms towards external surface is observed under the irradiation regimes leading to the melting of intermediate copper layer. Diffusion coefficients of copper and chromium calculated from their surface accumulation show an exponential dependence on the laser-pulse energy. Under laser heating, the diffusion processes are more manifested as compared with those under conventional thermal annealing. This is bound up with higher concentration of nonequilibrium defects generated within the irradiation zone.

Download Full-text

Bi-Velocity Method and Linear Nonreversible Thermodynamics, Interdiffusion in R2

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.297-301.1461 ◽

2010 ◽

Vol 297-301 ◽

pp. 1461-1468 ◽

Cited By ~ 2

Author(s):

Marek Danielewski ◽

Bartek Wierzba

Keyword(s):

Phenomenological Models ◽

Drift Velocity ◽

Irreversible Thermodynamics ◽

Mechanics Of Solids ◽

Two Dimensional ◽

Perfect Agreement ◽

Diffusion Multiple ◽

Dimensional Diffusion ◽

Self Consistent ◽

Linear Irreversible Thermodynamics

Kirkendall and Darken findings of the drift velocity since 1948 have stimulated progress in transport phenomenological models. The convection velocity (the Darken drift in solids), , and velocity of diffusion, , require definition and the method how the diffusion displacement is defined, computed and measured. The equation of volume continuity allowed the extension of the Darken method and avoids the rigid assumption of the constant molar concentration. In this work, we use the bi-velocity approach, i.e., the generalized Darken method, to model interdiffusion in two-dimensional diffusion multiple. We show the convergence of one- and two-dimensional models in the case of the process at the constant volume and perfect agreement between R1 and R2 simulations. We impose modifications in the foundations of mechanics of solids namely, the Navier-Lamé-Fourier equations. We show that the method can be used in the mechano-chemistry of solids and is self-consistent with linear irreversible thermodynamics.

Download Full-text