Showing papers on "Transport phenomena published in 2011"

Gravitational anomaly and transport phenomena.

Abstract: Quantum anomalies give rise to new transport phenomena. In particular, a magnetic field can induce an anomalous current via the chiral magnetic effect and a vortex in the relativistic fluid can also induce a current via the chiral vortical effect. The related transport coefficients can be calculated via Kubo formulas. We evaluate the Kubo formula for the anomalous vortical conductivity at weak coupling and show that it receives contributions proportional to the gravitational anomaly coefficient. The gravitational anomaly gives rise to an anomalous vortical effect even for an uncharged fluid.

Mass Transport through Carbon Nanotube Membranes in Three Different Regimes: Ionic Diffusion and Gas and Liquid Flow

Abstract: Transport phenomena through the hollow conduits of carbon nanotubes (CNTs) are subjects of intense theoretical and experimental research. We have studied molecular transport over the large spectrum of ionic diffusion to pressure-driven gaseous and liquid flow. Plasma oxidation during the fabrication of the membrane introduces carboxylic acid groups at the CNT entrance, which provides electrostatic “gatekeeper” effects on ionic transport. Diffusive transport of ions of different charge and size through the core of the CNT is close to bulk diffusion expectations and allows estimation of the number of open pores or porosity of the membrane. Flux of gases such as N2, CO2, Ar, H2, and CH4 scaled inversely with their molecular weight by an exponent of 0.4, close to expected kinetic theory velocity expectations. However, the magnitude of the fluxes was ∼15- to 30-fold higher than predicted from Knudsen diffusion kinetics and consistent with specular momentum reflection inside smooth pores. Polar liquids such as ...

Optimal protocols and optimal transport in stochastic thermodynamics

Abstract: Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow

Abstract: [1] Domains composed of a porous part and an adjacent free-flow region are of special interest in many fields of application. So far, the coupling of free flow with porous-media flow has been considered only for single-phase systems. Here we extend this classical concept to two-component nonisothermal flow with two phases inside the porous medium and one phase in the free-flow region. The mathematical modeling of flow and transport phenomena in porous media is often based on Darcy's law, whereas in free-flow regions the (Navier-) -Stokes equations are used. In this paper, we give a detailed description of the employed subdomain models. The main contribution is the developed coupling concept, which is able to deal with compositional (miscible) flow and a two-phase system in the porous medium. It is based on the continuity of fluxes and the assumption of thermodynamic equilibrium, and uses the Beavers-Joseph-Saffman condition. The phenomenological explanations leading to a simple, solvable model, which accounts for the physics at the interface, are laid out in detail. Our model can account for evaporation and condensation processes at the interface and is used to model evaporation from soil influenced by a wind field in a first numerical example.

Resonant electron transport in single-molecule junctions: Vibrational excitation, rectification, negative differential resistance, and local cooling

Abstract: Vibronic effects in resonant electron transport through single-molecule junctions are analyzed. The study is based on generic models for molecular junctions, which include electronic states on the molecular bridge that are vibrationally coupled and exhibit Coulomb interaction. The transport calculations employ a master equation approach. The results, obtained for a series of models with increasing complexity, show a multitude of interesting transport phenomena, including vibrational excitation, rectification, negative differential resistance, as well as local cooling. While some of these phenomena have been observed or proposed before, the present analysis extends previous studies and allows a more detailed understanding of the underlying transport mechanisms. In particular, it is shown that many of the observed phenomena can only be explained if electron-hole pair creation processes at the molecule-lead interface are taken into account. Furthermore, vibronic effects in systems with multiple electronic states and their role for the stability of molecular junctions are analyzed.

Porous Media Transport Phenomena

Abstract: Description: The book that makes transport in porous media accessible to students and researchers alike Porous Media Transport Phenomena covers the general theories behind flow and transport in porous media a solid permeated by a network of pores filled with fluid which encompasses rocks, biological tissues, ceramics, and much more. Designed for use in graduate courses in various disciplines involving fluids in porous materials, and as a reference for practitioners in the field, the text includes exercises and practical applications while avoiding the complex math found in other books, allowing the reader to focus on the central elements of the topic. Covering general porous media applications, including the effects of temperature and particle migration, and placing an emphasis on energy resource development, the book provides an overview of mass, momentum, and energy conservation equations, and their applications in engineered and natural porous media for general applications. Offering a multidisciplinary approach to transport in porous media, material is presented in a uniform format with consistent SI units. An indispensable resource on an extremely wide and varied topic drawn from numerous engineering fields, Porous Media Transport Phenomena includes a solutions manual for all exercises found in the book, additional questions for study purposes, and PowerPoint slides that follow the order of the text.

Fokker–Planck model for computational studies of monatomic rarefied gas flows

Abstract: In this study, we propose a non-linear continuous stochastic velocity process for simulations of monatomic gas flows. The model equation is derived from a Fokker–Planck approximation of the Boltzmann equation. By introducing a cubic non-linear drift term, the model leads to the correct Prandtl number of 2/3 for monatomic gas, which is crucial to study heat transport phenomena. Moreover, a highly accurate scheme to evolve the computational particles in velocity- and physical space is devised. An important property of this integration scheme is that it ensures energy conservation and honours the tortuosity of particle trajectories. Especially in situations with small to moderate Knudsen numbers, this allows to proceed with much larger time steps than with direct simulation Monte Carlo (DSMC), i.e. the mean collision time not necessarily has to be resolved, and thus leads to more efficient simulations. Another computational advantage is that no direct collisions have to be calculated in the proposed algorithm. For validation, different micro-channel flow test cases in the near continuum and transitional regimes were considered. Detailed comparisons with DSMC for Knudsen numbers between 0.07 and 2 reveal that the new solution algorithm based on the Fokker–Planck approximation for the collision operator can accurately predict molecular stresses and heat flux and thus also gas velocity and temperature profiles. Moreover, for the Knudsen Paradox, it is shown that good agreement with DSMC is achieved up to a Knudsen number of about 5.

Anomalous transport coefficients from Kubo formulas in Holography

Abstract: In the presence of dense matter quantum anomalies give rise to two new transport phenomena. An anomalous current is generated either by an external magnetic field or through vortices in the fluid carrying the anomalous charge. The associated transport coefficients are the anomalous magnetic and vortical conductivities. Whereas a Kubo formula for the anomalous magnetic conductivity is well known we develop a new Kubo type formula that allows the calculation of the vortical conductivity through a two point function of the anomalous current and the momentum density. We also point out that the anomalous vortical conductivity can be understood as a response to a gravitomagnetic field. We apply these Kubo formulas to a simple Holographic system, the R-charged black hole.

Magnetohydrodynamic biorheological transport phenomena in a porous medium: A simulation of magnetic blood flow control and filtration†

Abstract: Application of magnetic fields to medical science is growing rapidly, with the development of novel magnetic pumps, hydromagnetic separation devices, etc. In this paper, we study the dual control mechanisms of transverse magnetic field and porous media filtration on viscous convection heat transfer in a buoyancy-driven blood flow regime in a vertical pipe, as a model of a blood separation configuration. Non-Newtonian characteristics of the blood are modeled with the well-tested, thermodynamically rigorous micropolar model introduced by Eringen. Porous media effects are simulated with a Darcy–Forchheimer drag force model. The two-point boundary value problem is normalized and the resulting dimensionless linear momentum, angular momentum (Eringen micro-rotation) and energy conservation equations are solved by the Differential Transform M ethod (DTM). The convergence analysis elucidates that the DTM yields exceedingly accurate results, which are validated with a comparison with optimized fourth-order Runge–Kutta numerical quadrature. The influence of micropolar vortex viscosity parameter (Eringen parameter (Er), Hartmann magnetohydrodynamic number ( Ha), aspect ratio (A), Darcy number ( Da), heat generation/absorption parameter (α) and Grashof number on the flow variables are studied in detail. The present study has important applications in magnetic field control of biotechnological (hemodynamic) processes, biomagnetic device technology, etc. Copyright © 2010 John Wiley & Sons, Ltd.

Fluid Mechanics of Viscoelasticity: General Principles, Constitutive Modelling, Analytical and Numerical Techniques

Abstract: General Principles. 1. Kinematics of fluid flow. 2. Balance equations for smooth and non-smooth regions. Constitutive Modelling. 3. Formulation of constitutive equations - the simple fluid. 4. Constitutive equations derived from microstructures. Analytical and Numerical Techniques. 5. The shape and nature of general solutions. 6. Simple models and complex phenomena. 7. Computational viscoelastic fluid dynamics.

Transport phenomena in fluids: Finite-size scaling for critical behavior

Abstract: Results for transport properties, in conjunction with phase behavior and thermodynamics, are presented to understand the critical behavior of a binary Lennard-Jones fluid, on the basis of Monte Carlo and molecular dynamics simulations. Evidence for much stronger finite-size effects in dynamics compared to statics has been demonstrated. Results for bulk viscosity are the first in the literature where the critical divergence is quantified via a novel application of finite-size scaling. Our results are in accordance with the theoretical predictions of mode-coupling and dynamic renormalization group calculations.

The Role of Tortuosity in Upscaling

Abstract: The concept of tortuosity is an integral part of models that describe transport in multiscale systems. Traditionally, tortuosity is defined as the ratio of an effective path length to the shortest path length in the microstructure. While the shortest path length can be unambiguously specified, the same is not true for the effective path length, since it changes from one type of transport to another. Consequently, it is possible to have different values of tortuosity for different transport processes taking place in the same system. This is convenient since, under this approach, different transport processes can involve the same type of filters of the microscale information, but the nature of such information is what characterizes each type of transport process. In order to avoid running into unclear interpretations, a set of tortuosity rules are proposed, which relate this concept only to the microscale geometry. On the basis of these rules, we examine the pertinence of introducing the tortuosity concept in mass transport. In particular, we study mass diffusion with and without chemical reaction and convection in porous media. Of all these cases, our analysis indicates that the concept of tortuosity is only adequate for passive diffusion, since in the other cases there is an unavoidable coupling of the transport phenomena that determine the effective path of the solute.

Peristaltic Transport of a Rheological Fluid: Model for Movement of Food Bolus Through Esophagus

Abstract: Fluid mechanical peristaltic transport through esophagus has been of concern in the paper. A mathematical model has been developed with an aim to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths. The Ostwald-de Waele power law of viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid. The model is formulated and analyzed with the specific aim of exploring some important information concerning the movement of food bolus through the esophagus. The analysis has been carried out by using lubrication theory. The study is particularly suitable for cases where the Reynolds number is small. The esophagus is treated as a circular tube through which the transport of food bolus takes places by periodic contraction of the esophageal wall. Variation of different variables concerned with the transport phenomena such as pressure, flow velocity, particle trajectory and reflux are investigated for a single wave as well as for a train of periodic peristaltic waves. Locally variable pressure is seen to be highly sensitive to the flow index `n'. The study clearly shows that continuous fluid transport for Newtonian/rheological fluids by wave train propagation is much more effective than widely spaced single wave propagation in the case of peristaltic movement of food bolus in the esophagus.

Transport in Anisotropic Superfluids: A Holographic Description

Abstract: We study transport phenomena in p-wave superfluids in the context of gauge/gravity duality. Due to the spacetime anisotropy of this system, the tensorial structure of the transport coefficients is non-trivial in contrast to the isotropic case. In particular, there is an additional shear mode which leads to a non-universal value of the shear viscosity even in an Einstein gravity setup. In this paper, we present a complete study of the helicity two and helicity one fluctuation modes. In addition to the non-universal shear viscosity, we also investigate the thermoelectric effect, i.e. the mixing of electric and heat current. Moreover, we also find an additional effect due to the anisotropy, the so-called flexoelectric effect.

Multiscale Modeling of Transport Phenomena and Dendritic Growth in Laser Cladding Processes

Abstract: A multiscale model is developed in this article to investigate the transport phenomena and dendrite growth in the diode-laser-cladding process. A transient model with an improved level-set method is built to simulate the heat/mass transport and the dynamic evolution of the molten pool surface on the macroscale. A novel model integrating the cellular automata (CA) and phase field (PF) methods is used to simulate the dendritic growth of multicomponent alloys in the mushy zone. The multiscale model is validated against the experiments, and the predicted geometry of clad tracks and the predicted dendrite arm spacing of microstructure match reasonably well with the experimental results. The effects of the processing parameters on the track geometry and microstructure are also investigated.

Numerical Modeling of Transport Phenomena and Dendritic Growth in Laser Spot Conduction Welding of 304 Stainless Steel

Abstract: A multi-scale model is developed to investigate the heat/mass transport and dendrite growth in laser spot conduction welding. A macro-scale transient model of heat transport and fluid flow is built to study the evolution of temperature and velocity field of the molten pool. The molten pool geometry and other solidification parameters are calculated, and the predicted pool geometry matches well with experimental result. On the micro-scale level, the dendritic growth of 304 stainless steel is simulated by a novel model that has coupled the Cellular Automata (CA) and Phase Field (PF) methods. The epitaxial growth is accurately identified by defining both the grain density and dendrite arm density at the fusion line. By applying the macro-scale thermal history onto the micro-scale calculation domain, the microstructure evolution of the entire molten pool is simulated. The predicted microstructure achieves a good quantitative agreement with the experimental results.Copyright © 2011 by ASME

Multiscale thermodynamics and mechanics of heat

Abstract: Heat transfer is investigated on three levels of description: Fourier, Cattaneo, and Peierls. The microscopic nature of the heat that becomes important, in particular in nanoscale systems, is characterized by a vector field related to the heat flux on the Cattaneo level and by the phonon distribution function on the Peierls level. All dynamical theories discussed in the paper are fully nonlinear and all are proven to be compatible among themselves, with equilibrium thermodynamics, and with mechanics. An investigation of the first two compatibilities gives rise to potentials having the physical interpretation of nonequilibrium entropies. The compatibility with mechanics is manifested by the Hamiltonian structure of the time-reversible part of the time evolution.

The two‐dimensional pore and polarization transport model to describe mixtures separation by nanofiltration: Model validation

Abstract: Nanofiltration is a membrane process which is used to separate charged molecules such as ions. Even if this process is well known, there is no mean to predict the performances of a given separation. The aim of this paper is to present a two-dimensional model called “pore and polarization transport model” which includes all the steps of the ions transfer. The membrane transport modeling is based on the classical one-dimensional vision coupling the Donnan, steric, and dielectric exclusions with the extended Nernst-Planck transport equation. But the originality of this study comes from the modeling of the transport through the polarization layer. The model used in this study is an improvement of the previous version, which includes an electrical gradient within the polarization layer allowing the prediction of polarization layer establishment even for ionic mixtures. The purpose of this article is to describe the model accurately before validating it with various ionic solutions. © 2010 American Institute of Chemical Engineers AIChE J, 2011

Effective pressure interface law for transport phenomena between an unconfined fluid and a porous medium using homogenization

Abstract: We present modeling of the incompressible viscous flows in the domain containing an unconfined fluid and a porous medium. For such setting a rigorous derivation of the Beavers-Joseph-Saffman interface condition was undertaken by J\"ager and Mikeli\'c [SIAM J. Appl. Math. \rm 60 (2000), p. 1111-1127] using the homogenization method. So far the interface law for the pressure was conceived and confirmed only numerically. In this article we justify rigorously the pressure jump condition using the corresponding boundary layer.

Simultaneous analysis of ion and electron heat transport by power modulation in JET

Abstract: Heating power modulation experiments using ion cyclotron resonance heating (ICRH) in the (3)He minority scheme have been performed in the JET tokamak to investigate heat transport properties. This RF scheme provides a dominant localized ion heating, but also some electron heating, and therefore both ion and electron heat channels were modulated. This allows us to carry out a simultaneous transport analysis of ion and electron heat transport channels, including transient transport phenomena. This also provides an experimental assessment of the ICRH heat sources of the (3)He scheme. The modulation approach, so far widely used for electron transport studies, has been validated for ion heat transport in these experiments and yields results on stiffness and threshold of the ion temperature gradient (ITG)-driven ion heat transport. The results for the electron channel demonstrate the importance of the ITG-driven, off-diagonal, contribution to electron heat transport in plasmas with significant ion heating.