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ORAL PRESENTATION
Session: 5 Non-equilibrium thermodynamics: Approaches and formalisms
(scheduled: Wednesday, 10:45 )
On a possible difference between the barycentric velocity and the velocity that gives translational momentum in fluids
D. Bedeaux1, S. Kjelstrup1, H.C. Öttinger2
1 Dept. of Chem, Norw. Univ. of Sc. and Techn, Trondheim, Norway
2 ETH Zürich, Dept. of Materials, Polymer Physics, Switzerland
This contribution explores the rather controversial proposal by Howard Brenner that the velocities that follow from the mass flux and from the translational momentum in a fluid are not equal. We show that standard non-equilibrium thermodynamics can be formulated such that it is in full agreement with this proposal. We argue that the merits of the proposal must be based on the physics of the problem. It cannot be dismissed as being in contradiction with non-equilibrium thermodynamics. We show that Brenner's proposal gives a separation in a binary mixture beyond that of the Soret equilibrium, due to a gradient in the pressure divided by the temperature. Experiments to verify this are proposed. © IWNET 2006
ORAL PRESENTATION
Session: 5 Non-equilibrium thermodynamics: Approaches and formalisms
(scheduled: Wednesday, 10:20 )
Nonequilibrium thermodynamics of elasto-viscoplastic deformation
M. Hütter, T.A. Tervoort, H.C. Öttinger
Department of Materials, ETH Zurich, Switzerland
Plasticity theories describe the transition from compressible elastic behavior at low stress to isochoric plastic deformation at high stress levels, and are often formulated by relating the elastic strain rate to an objective stress rate. In this contribution, the modeling of such behavior by way of nonequilibrium thermodynamics is examined, namely by using the GENERIC formalism. First, nonisothermal general elasticity is formulated in terms of the left Cauchy-Green strain tensor, the temperature, and the momentum density. In a second step, we study specific relaxation mechanisms of the strain tensor to describe elasto-viscoplastic behavior with emphasis on volume relaxation, and discuss the relation to common inelastic deformation models. For various equations of state, predictions of the model for specific mechanical tests are presented. © IWNET 2006
ORAL PRESENTATION
Session: 5 Non-equilibrium thermodynamics: Approaches and formalisms
(scheduled: Wednesday, 08:50 )
Non-Equilibrium Thermodynamics of Boundary Conditions
H.C. Öttinger
ETH Zürich, Department of Materials, Institute of Polymers, HCI H 543, CH-8093 Zürich, Switzerland
While the field equations for complex fluids are usually formulated such that they respect the principles of nonequilibrium thermodynamics, the choice of appropriate boundary conditions is often considered as a purely mathematical problem. We here emphasize that also the formulation of boundary conditions should be guided by thermodynamics. The GENERIC framework is generalized to systems consisting of coupled 3-d bulk and 2-d boundary variables. The ideas and concepts are illustrated for two examples: (i) bulk and surface diffusion phenomena for a dilute suspension of Brownian particles, and (ii) velocity slip of entangled polymer melts at solid walls. © IWNET 2006
POSTER PRESENTATION
Tuesday, 15:40, Panel No. 1
Towards experimental tests of the Brenner modification to the Navier-Stokes equations: Dynamic light scattering
A. Bardow, M. Kröger, H.C. Öttinger
Institute of Polymers, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland
A modification of the classical Navier-Stokes equations has recently been proposed by Brenner (Physica A 349 (2005) 11, 60). In the modified theory, a contribution for mass diffusion is included in the continuity equation. A formal model could then be derived using the GENERIC framework of nonequilibrium thermodynamics. The modified theory was based on experimental support from thermophoresis which however depends on the correct formulation of boundary conditions. The controversy therefore remained. Since such an additional mass diffusion transport mode should contribute to dynamic light scattering spectra, the consequences of the modified theory for light scattering spectra are discussed in this work. For liquids, the new theory is consistent with measured scattering data since the modification to the spectrum is usually negligible. The effect could, however, be observable in gases. The relationship to existing experimental data is discussed. © IWNET 2006
POSTER PRESENTATION
Tuesday, 15:40, Panel No. 2
Regularization of the Burnett Hydrodynamics
M. Colangeli1, I.V. Karlin2, H.C. Öttinger1
1 ETH Zürich, Dept. of Materials, Polymer Physics, Switzerland
2 Institute of Energy Technology, ETH Zurich, Zurich 8092, Switzerland
As it was first demonstrated by Bobylev [1], even in the simplest regime (one-dimensional linear deviations around the global equilibrium), the Burnett hydrodynamic equations violate the basic physics behind the Boltzmann equation. Namely, sufficient short acoustic waves are amplified with time instead decaying. This contradicts the H-theorem, since all near-equilibrium perturbations must decay. The lower order truncation of the Chapman-Enskog expansion also contradicts the dissipative properties of Grad moment equations [2]. The mathematical reason for the instability paradox is shown and a method to regularize the equations of hydrodynamics is proposed. © IWNET 2006
[1] Bobylev, A.V., Instabilities in the Chapman-Enskog Expansion and Hyperbolic Burnett Equations, Journal of Stat. Phys., DOI: 10.1007/s10955-005-8087-6 (2006).
[2] Gorban, A.N, Karlin, I.V., Hydrodynamics from Grad's equations: What can we learn from exact solutions? Ann. Phys. (Leipzig) 11 (2002).
POSTER PRESENTATION
Tuesday, 15:40, Panel No. 7
Nonequilibrium thermodynamics aspects of a disspative electromagnetism
A. Jelic, M. Hütter, H.C. Öttinger
ETH Zurich, Department of Materials, Switzerland
The standard macroscopic Maxwell equations are obtained from the microscopic ones by spatial and/or ensemble averaging. However, in both cases, only single time properties are considered, while temporal correlations and two-time ensemble averages are neglected. In this work we examine specifically dissipative effects in electromagnetism on macroscopic scales by coarse-graining the microscopic Maxwell equations with respect to time. Particular emphasis is put on the derivation of the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them, which give rise to dissipative processes such as Ohmic currents, the thermoelectric effect, and also to irreversible contributions to the electric and magnetic fields. In order to capture the interplay between the thermodynamic behavior of the medium and the electromagnetic field, and to discuss dissipative effects in electromagnetism in a consistent manner we have used the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework. The results are compared to the ones of Liu and coworkers, who previously incorporated dissipative effects into the Maxwell equations [1]. © IWNET 2006
[1] Phys. Rev. Lett. 70, 3580 (1993) and later papers.
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and Kleanthi for IWNET 2006