Volume 48, Issue 2

Boltzmann kinetic equation is put into the form of an abstract time evolution equation representing links connecting autonomous mesoscopic dynamical theories involving varying amount of details. In the chronological order we present results that led to the abstract time equation evolution in both state space and the space of vector fields. In the final section we list some open problems.

Dispersive diffusion and wave propagation seem to be unconnected and fundamentally different evolution equations. In the context of anomalous diffusion however modeling approaches based on fractional diffusion equations have been presented, which allow to build a continuous bridge between the two regimes. The transition from irreversible dispersive diffusion to reversible wave propagation shows an unexpected increase in entropy production. This seemingly paradoxical behavior of fractional diffusion is reviewed and compared to the behavior of a tree-based diffusion model.

Even for large nonequilibrium systems, local equilibrium subsystems in the presence of strong inhomogeneities may be very small. Such situations typically arise either in the presence of large gradients of temperature, velocity or pressure, or in transition zones between different phases. For small thermodynamic systems, the Euler equation of macroscopic thermodynamics does not hold. One less equation implies one additional degree of freedom, which is the hallmark of small thermodynamic systems. I would like to offer some remarks on the description and role of small local equilibrium subsystems in nonequilibrium thermodynamics.

The dynamics of blood carrying microscopic copper particles through overlapping stenotic arteries is an important research area needed for scrutinizing and exploring dynamics through blood vessels. Adipose tissue deposition and other elements of atherosclerosis generate the uncommon artery disease known as arterial stenosis. It limits blood flow and raises the risk of heart disease. Using the Casson model, it is feasible to shed light on the peristaltic blood flow of copper nanoparticles over an overlapping stenotic artery. Nothing is known about the study of heat sink/source, buoyancy and Lorent force, and volume fraction because the focus is on the dynamics of blood carrying minute copper particles through an overlapping stenotic artery. When the Lorentz force is significant, the transport mentioned above was evaluated utilizing stenosis approximations to examine the stream function, wall shear stress, Nusselt number, and flow resistance distribution. In addition, temperature solutions were identified analytically, whereas a perturbation approach acquired velocity solutions. Temperature distribution and velocity are greater in stenosed arteries than in unstenosed arteries. Furthermore, extreme velocity and temperature rise as it reaches the core of the artery and falls as one approaches the wall. When the heat source parameter values increase due to an improvement in the fluid’s thermal state, the temperature distribution increases.

Endoreversible chemical pump (ECP) is a theoretical model of electrochemical, photochemical, solid-state apparatus and mass exchangers. ECP can be classified as two-, three- and four-mass-reservoir devices. The usual performance indicators for ECPs are energy pumping rate (EPR) and coefficient of performance (COP). Energy-based ecological function objective (EFO) is introduced to performance optimization of three-reservoir ECP. Optimization relationships between EFO and COP with linear and diffusive mass transfer laws (MTLs) are deduced. Numerical examples are provided, and influences of cycle parameters and MTLs on optimal EFO performances are analyzed. For linear MTL, compared performances at maximum EFO point and point where dimensionless EPR is 0.016, COP increases 14.4% and entropy generation rate (EGR) drops 52% with only 30% loss of EPR. For diffusive MTL, compared performances at maximum dimensionless EFO point and point where dimensionless EPR is 0.01, COP increases 11.3% and EGR drops 46.9% with only 30% loss of EPR. It demonstrates that EFO is a trade-off between EPR and dissipation of EPR, which is beneficial to utilize energy effectively. With the same chemical potentials of three reservoirs, the maximum dimensionless EFO and the corresponding COP with linear MTL are bigger than those with diffusive MTL.

Among the chemical reactions having a pronounced thermodynamic driving force to the formation of products, a distinction has to be made between processes which attain a chemical equilibrium state very much shifted towards the products and those where the final equilibrium state corresponds to the truly complete consumption of reactant(s), i.e. where a true chemical equilibrium is actually not attained under the given conditions. Based on a few selected examples, two thermodynamic arguments are led which rationalise the above distinction from different points of view: a phase-rule point of view and a Gibbs energy minimization approach. “Conceptually complete” reactions involve pure phases and, as a consequence, establishing chemical equilibrium would imply a negative variance, what is avoided by the complete consumption of one or more phases. In the Gibbs energy approach, “conceptually complete” reactions and “practically complete” ones can be distinguished (at fixed temperature and pressure) by the different way to attain the minimum Gibbs energy condition, respectively with sharp (not differentiable) and flat (zero derivative) minimum points as a function of the extent of reaction ξ .

For isothermal liquid flows, the condition of incompressibility provides a useful simplification for describing their mechanical properties. Nevertheless, it overlooks acoustic effects, and it provides the unpleasant shortcoming of infinite propagation speed of velocity perturbations, no matter the type of constitutive equation for the shear stresses is adopted. In this paper, we provide a derivation of a new formulation of the Navier–Stokes equations for liquid flows that overcomes the above issues. The pressure looses its ancillary status of mere gauge variable (or equivalently Lagrange multiplier of the incompressibility condition) enforcing the solenoidal nature of the velocity field, and attains the proper physical meaning of hydrodynamic field variable characterized by its own spatiotemporal evolution. From the experimental evidence of sound attenuation, related to the occurrence of a non-vanishing bulk viscosity, the evolution equation for pressure in out-of-equilibrium conditions is derived without introducing any adjustable parameters. The connection between compressibility and memory effects in the propagation of internal stresses is established. Normal mode analysis and some preliminary simulations are also discussed.

The phenomenon of conservatively perturbed-equilibrium (CPE) in multi-route catalytic reactions was studied in the plug-flow reactor (PFR). The following multi-route mechanisms were chosen for studying, i.e., the two-route mechanism with the single common intermediate, the three-route mechanism with some common steps, and the two-route mechanism with the single common step and two common intermediates. All mentioned mechanisms exhibit the CPE-phenomenon. At given rate coefficients, the mechanism with the single common intermediate showed the greater CPE-effect than the mechanism with the common steps. A special computer experiment was performed in which the kinetic characteristics of non-catalytic and catalytic reactions have been compared. In this experiment, both non-catalytic and catalytic reactions have the same overall-reactions with the given equilibrium constant. It was shown that the absolute values of extreme concentrations at the CPE-point are almost the same. In this case, it is possible to estimate the concentrations at the CPE-values for complex reactions based on similar characteristics of the corresponding simple ones.