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A linear weakly nonlocal and finite-speed theory of heat conduction in rigid solids was presented by Lebon and Grmela in Phys. Lett. A 214 (1996) 184. In the present paper, this work is extended to a fully nonlinear theory. The extension is based on the requirement that the Hamiltonian structure already present in the linear approach is kept in the nonlinear theory. From the physical point of view, this requirement guarantees that solutions to the governing equations agree with certain fundamental experimental observations. During the time evolution, the total energy is shown to remain constant and the total entropy is shown to grow.

A nonlocal heal conduction model, based on nonequilibrium thermodynamics, is proposed. This is achieved by introducing a supplementary stale variable, besides the internal energy. Compatibility with the second law of thermodynamics is examined. The analysis is limited to a linear and weakly nonlocal description.

The setting of classical configuration space kinetic theory of polymeric fluids is extended by adopting the field of internal momentum into the set of independent state variables. The internal momentum predicted by the extended theory compares well with the internal momentum seen in molecular simulations. The extended theory is also shown to provide an intrinsically consistent formulation of the time evolution of macromolecules with internal friction.

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.

A novel nonequilibrium molecular dynamics, originating in mesoscopic theory of suspensions, is introduced to investigate the behavior of model polymeric fluids consisting of several hundred ellipsoids of revolution (spheroids) that interact via the Gay-Berne potential. This dynamics is used to generate new microstructural, thermodynamic and rheological data. The microcanonical equtions of motion for the translational and angular momenta as well as for mass-centers and orientational unit vectors are derived from a Hamiltonian. These expresssions are then augmented by SLLOD-like and Gaussian thermostat terms added consistently to equations for both the rotational and translational degrees of freedom; the role of Gaussian thermostat is to maintain constant kinetic temperature of the assembly of spheroids. The thermodynamic results are calculated along one isotherm (nondimensional temperature T maintained at unity). Rheology is investigated for two state points (namely for particle number density p equal to 0.25, 0.4 and T set to 1), that lie well inside the isotropic phase if no external flow is applied. A state point is defined by the fluid's temperature T,. and the concentration of particles per unit volume p. As indicated by snapshots of molecular configurations, at the intermediate shear rates (nondimensional shear rate approximately 1–2), ellipsoids become aligned to the direction of flow and the stress tensor begins to be nonsymmetric. At even higher shear rates, this configuration breaks down leading to the formation of a transitory isotropic-type fluid, and then to the build-up of a highly ordered structure exhibiting global orientation of particles in the direction of the vorticity axis. For ϱ = 0.4, the first (N1) and the second (N2) normal stress differences are positive and negative respectively, but at low densities (ϱ = 0.25), n1 becomes slightly negative. In addition to the stress tensor, we compute the conformation tensor, the order parameter and the co

We report new macro-rheological results extracted from non-equilibrium molecular dynamics (NEMD) simulations of Couette flow. We investigate atomic liquids for new state points, and in addition two types of dumbbell liquids: (1) finitely extensible nonlinear elastic (FENE) and (2) newly defined generalized Lennard-Jones (GLJ), up to a nondimensional shear rate of 15. The dumbbell liquids exhibit shear thinning, non-zero first and second normal stress differences, and volumetric dilatancy. These effects are weakly sensitive to details in shape of the intra-molecular potentials, and to the dominant frequency associated with vibrations of dumbbells. However, the Newtonian viscosity of dumbbell liquids strongly depends on the size of dumbbells. The onset of shear thinning of FENE and GLJ dumbbells is delayed to higher shear rates in comparison with atomic liquids. In general, for the entire investigated region, we see that dumbbells are slightly more elastic than atomic liquids.

The microscopic and the mesoscopic results are presented for several finitely extensible non-linear elastic (FENE) dumbbell fluids investigated under imposed flow according to SLLOD dynamics. The contracted distribution functions are calculated in both position and velocity spaces, and the fluid structure is probed by two conformation tensors. It is observed that dumbbells form a variety of short and long range structures depending on the imposed shear rate and the size of a single dumbbell. The assumption of Maxwellian distributed bead velocities, which is often used in the elastic dumbbell theories, is shown not to be satisfied except at low shear rates. Under shear, the distribution of the end-to-end distances is similar to the Gibbs equilibrium distribution function in configuration space if intra-molecular interactions are much stronger than inter-molecular forces. On the average, the longest dumbbells are found at between 30° and 50° to the direction of flow, and the shortest at between -50° and -30°.