M. Criado-Sancho

Thermodynamics of fluids under flow

From the contents: Non-equilibrium Thermodynamics and Rheology.- Ideal Gases.- Non-ideal Fluids.- Polymeric Solutions.- Non-equilibrium Chemical Potential and Shear-Induced Effects.- Comparison Between Thermodynamical and Dynamical Approaches.- Thermodynamic Couplings Between Flow and Diffusion.- Chemical Reactions Under Flow.- Concluding Remarks and Perspectives.- Appendices: A. Survey of Experimental Information.- B. Liquid Crystals.- C. Summary of Vector and Tensor Notation.- D. Useful Integrals in the Kinetic Theory of Gases.- E. Some Physical Constants.- Subject Index.

Thermodynamic stability and temperature overshooting in dual-phase-lag heat transfer

Abstract The dual-phase-lag model in heat transfer includes relaxation times for the heat flux and for the temperature gradient. Here we show that a thermodynamic stability analysis suggests that the initial value for the temperature gradient cannot be arbitrarily high but it is bounded by 1.42( T τ T ) , with T the initial value of the local temperature and tT the relaxation time of the temperature gradient. This could restrict the possibility of observing the temperature overshooting predicted by the dynamical equations.

Nonequilibrium chemical potential and shear-induced migration of polymers in dilute solutions

We consider the contribution of a nonequilibrium chemical potential depending on the shear rate on shear-induced polymer migration. It is seen that this nonequilibrium contribution strongly enhances, above a threshold of polymer concentration and of shear rate, the migration of the polymer towards the regions with lower stress. This enhancement may explain why the migration rate experimentally observed is much higher than that predicted by constitutive laws where the nonequilibrium effects on the chemical potential are ignored.

Shear induced polymer migration: analysis of the evolution of concentration profiles

In order to analyze the evolution of the concentration profile experimentally observed by MacDonald and Muller under shear-induced polymer migration in a rotating cone-and-plate device, we use a constitutive equation for the diffusion flux, where the gradient of a generalized non-equilibrium chemical potential appears instead of the concentration gradient. From this model of coupling between diffusion and viscous pressure, together with the mass balance equation, we derive some general features of the concentration profile, the temporal behavior of the polymer concentration near the apex of the cone and some relevant trends of the dynamical process of polymer migration.

Hydrodynamic interactions and the shear-induced shift of the critical point in polymer solutions

Abstract The shift of the critical point of dilute polymer under shear was studied explicity, by starting from the Rouse—Zimm model and from a thermodynamic model based on a non-equilibrium Gibbs free energy which includes non-equilibrium corrections. The thermodynamic criterion for the spinodal line is compatible with the dynamic analyses when the normal pressure effects along the velocity gradient may be neglected and when the fluctuations vary only along the velocity gradient direction. Our main result is that the hydrodynamic interactions between macromolecules reduce the shift in the spinodal line.

Heat fluctuations and phonon hydrodynamics in nanowires

We evaluate the second moments of the fluctuations of the total longitudinal heat flux in cylindrical nanowires described by phonon hydrodynamics with boundary conditions accounting for phonon boundary collisions. It is found that the second moments exhibit an explicit dependence on the boundary conditions and, therefore, may provide a suitable tool for analyzing phonon boundary collisions. Furthermore, an analogous dependence is also manifested in the relative probability of forward and backward fluctuations of the heat flux in a nonequilibrium steady state, thus providing a complementary tool of research for phonon boundary collisions.

Non-equilibrium chemical potential and stress-induced migration of polymers in tubes

Abstract A non-equilibrium chemical potential depending on the viscous pressure tensor is used to describe shear-induced diffusion in polymer solutions flowing along cylindrical tubes. Our results generalize previous ones in three main aspects: a Flory–Huggins expression for the equilibrium contribution to the chemical potential is used instead of the ideal-gas like expression, the full expression for the steady-state compliance of the solution is taken into account instead of only the polymer contribution, and the influence of the solute molecular mass is explicitly considered. As a qualitatively new result of considerable practical interest, it stands the prediction that in some circumstances, a dynamical instability may appear, which accelerates and enhances the separation process.

A thermodynamic model for shear-induced concentration banding and macromolecular separation

We present a simple thermodynamic model for shear-induced concentration banding in polymer solutions, based on a nonequilibrium chemical potential depending on the shear rate. This dependence provides a coupling between diffusion and shear, besides the more classical coupling provided by the divergence of the viscous pressure tensor. When both couplings are taken into account, shear-induced concentration banding appears in a natural way. If the initial homogeneous concentration is higher than a threshold value, shear banding appears for sufficiently high value of the shear rate γ; if the initial concentration is lower, the steady-state concentration profile under shear is smooth. The banding profile depends on the polymer molecular mass and therefore it provides a basis for the chromatographic separation of polymers of different molecular mass.

Thermal rectification in inhomogeneous nanoporous Si devices

We analyze the thermal rectification coefficient of a graded inhomogeneous porous Si device, as a function of the spatial porosity distribution, taking into account ballistic phonon-pore collisions when phonon mean-free path is much longer than the radius of the pores. We compare the results for the thermal rectifying coefficient with that for a discontinuous bulk-porous device having the same average porosity.

Thermodynamics of ideal gases under shear: a maximum-entropy approach

The maximum-entropy formalism is used here as a basis of a thermodynamic description of ideal gases under shear. We have obtained expressions for the entropy and the equations of state in nonequilibrium steady states characterized by a given shear viscous pressure and have identified in physical terms the Lagrange multiplier conjugated to the viscous pressure. Our results for those thermodynamic quantities generalize previous expressions which were limited to second order in the shear viscous pressure. These results show a reduction of the shear viscosity at high shear rates and also show how previous results of nonequilibrium molecular dynamics could be compatible with our thermodynamic analysis.