Revisiting the Lattice Boltzmann Method Through a Nonequilibrium Thermodynamics Perspective

In this paper, we incorporate a nonequilibrium thermodynamics perspective that is consistent with the Onsager reciprocity principle into the lattice Boltzmann framework to propose a novel regularized lattice Boltzmann formulation for modeling the Navier–Stokes–Fourier equations. The new method is applied to one-dimensional (1D) isothermal situations wherein the advantages of incorporating such a nonequilibrium perspective can be explicitly appreciated. In such situations, the nonequilibrium contribution of the lattice populations obtained by the new method completely vanishes, and the lattice update is entirely reduced to evaluating the equilibrium distribution function. Such a counterintuitive 1D mesoscopic description is not obtained in any other existing lattice Boltzmann scheme. We therefore numerically test the proposed formulation on two complex problems, namely, shockwave and nonlinear wave propagation, and compare results with analytical results along with six existing lattice Boltzmann schemes; it is found that the new method indeed yields results that are more stable and accurate. These results highlight the potency of the nonequilibrium thermodynamics-based approach for obtaining accurate and stable lattice Boltzmann computations, and provide new insights into established lattice Boltzmann simulation methods.

Analytical Transport Network Theory for Onsager, Coupled Flows: Part 1—Channel-Scale Modeling of Linear, Electrokinetic Flow

The analytical transport network (ATN) model for flow through microstructural networks is extended to linearly coupled flows subject to Onsager reciprocity. Electrokinetic flow is used as an example system. Through the extension, we gain an improved understanding of if, and how, morphology and topology influence coupled flow systems differently than un-coupled flows. In Part 1, a channel-scale model is developed to describe electrokinetic flow through a channel of arbitrary morphology. The analytical model agrees well with finite element analysis (FEA), but is significantly less expensive in terms of computational resources, and, furthermore, offers general insight into morphology's additional influence on coupled flows relative to uncoupled flows. In Part 2, we exploit these savings to develop a computationally economical, network-scale model and associated algorithm for its implementation to voxel-based three-dimensional images. Included in the algorithm is a means for rapidly calculating a structure's tortuosity factor. This modeling effort represents an important initial step in extending the ATN approach to coupled flow phenomena relevant to emerging technologies that rely on heterogeneous, hierarchical materials.

Electro-Osmotic Behavior of Polymeric Cation-Exchange Membranes in Ethanol-Water Solutions

The aim of this work is to apply linear non-equilibrium thermodynamics to study the electrokinetic properties of three cation-exchange membranes of different structures in ethanol-water electrolyte solutions. To this end, liquid uptake and electro-osmotic permeability were estimated with potassium chloride ethanol-water solutions with different ethanol proportions as solvent. Current–voltage curves were also measured for each membrane system to estimate the energy dissipation due to the Joule effect. Considering the Onsager reciprocity relations, the streaming potential coefficient was discussed in terms of ethanol content of the solutions and the membrane structure. The results showed that more porous heterogeneous membrane presented lower values of liquid uptake and streaming potential coefficient with increasing ethanol content. Denser homogeneous membrane showed higher values for both, solvent uptake and streaming coefficient for intermediate content of ethanol.

The fourth law of thermodynamics: steepest entropy ascent

When thermodynamics is understood as the science (or art) of constructing effective models of natural phenomena by choosing a minimal level of description capable of capturing the essential features of the physical reality of interest, the scientific community has identified a set of general rules that the model must incorporate if it aspires to be consistent with the body of known experimental evidence. Some of these rules are believed to be so general that we think of them as laws of Nature, such as the great conservation principles, whose ‘greatness’ derives from their generality, as masterfully explained by Feynman in one of his legendary lectures. The second law of thermodynamics is universally contemplated among the great laws of Nature. In this paper, we show that in the past four decades, an enormous body of scientific research devoted to modelling the essential features of non-equilibrium natural phenomena has converged from many different directions and frameworks towards the general recognition (albeit still expressed in different but equivalent forms and language) that another rule is also indispensable and reveals another great law of Nature that we propose to call the ‘fourth law of thermodynamics’. We state it as follows: every non-equilibrium state of a system or local subsystem for which entropy is well defined must be equipped with a metric in state space with respect to which the irreversible component of its time evolution is in the direction of steepest entropy ascent compatible with the conservation constraints. To illustrate the power of the fourth law, we derive (nonlinear) extensions of Onsager reciprocity and fluctuation–dissipation relations to the far-non-equilibrium realm within the framework of the rate-controlled constrained-equilibrium approximation (also known as the quasi-equilibrium approximation). This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

Three-Scale Multiphysics Modeling of Transport Phenomena within Cortical Bone

Bone tissue can adapt its properties and geometry to its physical environment. This ability is a key point in the osteointegration of bone implants since it controls the tissue remodeling in the vicinity of the treated site. Since interstitial fluid and ionic transport taking place in the fluid compartments of bone plays a major role in the mechanotransduction of bone remodeling, this theoretical study presents a three-scale model of the multiphysical transport phenomena taking place within the vasculature porosity and the lacunocanalicular network of cortical bone. These two porosity levels exchange mass and ions through the permeable outer wall of the Haversian-Volkmann canals. Thus, coupled equations of electrochemohydraulic transport are derived from the nanoscale of the canaliculi toward the cortical tissue, considering the intermediate scale of the intraosteonal tissue. In particular, the Onsager reciprocity relations that govern the coupled transport are checked.