Effect of the Ion, Solvent, and Thermal Interaction Coefficients on Battery Voltage.

In order to increase the adoption of batteries for sustainable transport and energy storage, improved charging and discharging capabilities of lithium-ion batteries are necessary. To achieve this, accurate data that describe the internal state of the cells are essential. Several models have been derived, and transport coefficients have been reported for use in these models. We report for the first time a complete set of transport coefficients to model the concentration and temperature polarization in a lithium-ion battery ternary electrolyte, allowing us to test common assumptions. We include effects due to gradients in chemical potentials and in temperature. We find that the voltage contributions due to salt and solvent polarization are of the same order of magnitude as the ohmic loss and must be taken into account for more accurate modeling and understanding of battery performance. We report new Soret and Seebeck coefficients and find thermal polarization to be significant in cases relevant to battery research. The analysis is suitable for electrochemical systems, in general.

Structure-function relationships in the nasal cavity of Arctic and subtropical seals.

The heating and moistening of inhaled air, and the cooling and moisture removal from exhaled air, are crucial for the survival of animals under severe environmental conditions. Arctic mammals have evolved specific adaptive mechanisms to retain warmth and water and restrict heat loss during breathing. Here, the role of the porous turbinates of the nasal cavities of Arctic and subtropical seals is studied with this in mind. Mass and energy balance equations are used to compute the time-dependent temperature and water vapor profiles along the nasal passage. A quasi-1D model based on computed tomography images of seal nasal cavities is used in numerical simulations. Measured cross-sectional areas of the air channel and the perimeters of the computed tomography slices along the nasal cavities of the two seal species are used. The model includes coupled heat and vapor transfer at the air-mucus interface and heat transfer at the interfaces between the tissues and blood vessels. The model, which assumes constant blood flow to the nose, can be used to predict the temperature of the exhaled air as a function of ambient temperature. The energy dissipation (entropy production) in the nasal passages was used to measure the relative importance of structural parameters for heat and water recovery. We found that an increase in perimeter led to significant decreases in the total energy dissipation. This is explained by improved conditions for heat and water transfer with a larger complexity of turbinates. Owing to differences in their nasal cavity morphology, the Arctic seal is expected to be advantaged in these respects relative to the subtropical seal.

Nanoparticle Dynamics in Composite Hydrogels Exposed to Low-Frequency Focused Ultrasound.

Pulsed focused ultrasound (FUS) in combination with microbubbles has been shown to improve delivery and penetration of nanoparticles in tumors. To understand the mechanisms behind this treatment, it is important to evaluate the contribution of FUS without microbubbles on increased nanoparticle penetration and transport in the tumor extracellular matrix (ECM). A composite agarose hydrogel was made to model the porous structure, the acoustic attenuation and the hydraulic conductivity of the tumor ECM. Single-particle tracking was used as a novel method to monitor nanoparticle dynamics in the hydrogel during FUS exposure. FUS exposure at 1 MHz and 1 MPa was performed to detect any increase in nanoparticle diffusion or particle streaming at acoustic parameters relevant for FUS in combination with microbubbles. Results were compared to a model of acoustic streaming. The nanoparticles displayed anomalous diffusion in the hydrogel, and FUS with a duty cycle of 20% increased the nanoparticle diffusion coefficient by 23%. No increase in diffusion was found for lower duty cycles. FUS displaced the hydrogel itself at duty cycles above 10%; however, acoustic streaming was found to be negligible. In conclusion, pulsed FUS alone cannot explain the enhanced penetration of nanoparticles seen when using FUS and microbubbles for nanoparticle delivery, but it could be used as a tool to enhance diffusion of particles in the tumor ECM.

Transport coefficients for ion and solvent coupling. The case of the lithium-ion battery electrolyte.

Transport properties are essential for the understanding and modeling of electrochemical cells, in particular complex systems like lithium-ion batteries. In this study, we demonstrate how a certain degree of freedom in the choice of variables allows us to efficiently determine a complete set of transport properties. We apply the entropy production invariance condition to different sets of electrolyte variables and obtain a general set of formulas. We demonstrate the application of these formulas to an electrolyte typical for lithium-ion batteries, 1M lithium hexafluoro-phosphate in a 1:1 wt. % mixture of ethylene and diethyl carbonates. While simplifications can be introduced, they provide inadequate predictions of conductivity and transport numbers, and we argue that a full matrix of Onsager coefficients is needed for adequate property predictions. Our findings highlight the importance of a complete set of transport coefficients for accurate modeling of complex electrochemical systems and the need for careful consideration of the choice of variables used to determine these properties.

Local equilibrium in liquid phase shock waves.

We have assessed the assumption of local thermodynamic equilibrium in a shock wave by comparing local thermodynamic data generated with nonequilibrium molecular dynamics (NEMD) simulations with results from corresponding equilibrium simulations. The shock had a Mach number approximately equal to 2 in a Lennard-Jones spline liquid. We found that the local equilibrium assumption holds perfectly well behind the wave front, and is a very good approximation in the front itself. This was supported by calculations of the excess entropy production in the shock front with four different methods that use the local equilibrium assumption in different ways. Two of the methods assume local equilibrium between excess thermodynamic variables by treating the shock as an interface in Gibbs's sense. The other two methods are based on the local equilibrium assumption in a continuous description of the shock front. We show for the shock studied in this work that all four methods give excess entropy productions that are in excellent agreement, with an average variance of 3.5% for the nonequilibrium molecular dynamics (NEMD) simulations. In addition, we solved the Navier-Stokes (N-S) equations numerically for the same shock wave using an equilibrium equation of state (EoS) based on a recently developed perturbation theory. The results for the density, pressure, and temperature profiles agree well with the profiles from the NEMD simulations. For instance, the shock waves generated in the two simulations travel with almost the same speed; the average absolute Mach-number deviation of the N-S simulations relative to NEMD is 2.6% in the investigated time interval.

Thermal modeling of the respiratory turbinates in arctic and subtropical seals.

Mammals possess complex structures in their nasal cavities known as respiratory turbinate bones, which help the animal to conserve body heat and water during respiratory gas exchange. We considered the function of the maxilloturbinates of two species of seals, one arctic (Erignathus barbatus), one subtropical (Monachus monachus). By means of a thermo-hydrodynamic model that describes the heat and water exchange in the turbinate region we are able to reproduce the measured values of expired air temperatures in grey seals (Halichoerus grypus), a species for which experimental data are available. At the lowest environmental temperatures, however, this is only possible in the arctic seal, and only if we allow for the possibility of ice forming on the outermost turbinate region. At the same time the model predicts that for the arctic seals, the inhaled air is brought to deep body temperature and humidity conditions in passing the maxilloturbinates. The modeling shows that heat and water conservation go together in the sense that one effect implies the other, and that the conservation is most efficient and most flexible in the typical environment of both species. By controlling the blood flow through the turbinates the arctic seal is able to vary the heat and water conservation substantially at its average habitat temperatures, but not at temperatures around -40 °C. The subtropical species has simpler maxilloturbinates, and our model predicts that it is unable to bring inhaled air to deep body conditions, even in its natural environment, without some congestion of the vascular mucosa covering the maxilloturbinates. Physiological control of both blood flow rate and mucosal congestion is expected to have profound effects on the heat exchange function of the maxilloturbinates in seals.

Seebeck, Peltier, and Soret effects: On different formalisms for transport equations in thermogalvanic cells.

Thermogalvanic cells convert waste heat directly to electric work. There is an abundance of waste heat in the world and thermogalvanic cells may be underused. We discuss theoretical tools that can help us understand and therefore improve on cell performance. One theory is able to describe all aspects of the energy conversion: nonequilibrium thermodynamics. We recommend to use the theory with operationally defined, independent variables, as others have done before. These describe well-defined experiments. Three invariance criteria serve as a basis for any description: of local electroneutrality, entropy production invariance, and emf's independence of the frame of reference. Alternative formalisms, using different sets of variables, start with ionic or neutral components. We show that the heat flux is not the same in the two formalisms and derive a new relationship between the heat fluxes. The heat flux enters the definition of the Peltier coefficient and is essential for the understanding of the Peltier heat at the electrode interfaces and of the Seebeck coefficient of the cell. The Soret effect can occur independently of any Seebeck effect, but the Seebeck effect will be affected by the presence of a Soret effect. Common misunderstandings are pointed out. Peltier coefficients are needed for the interpretation and design of experiments.

Legendre-Fenchel transforms capture layering transitions in porous media.

We have investigated the state of a nanoconfined fluid in a slit pore in the canonical and isobaric ensembles. The systems were simulated with molecular dynamics simulations. The fluid has a transition to a close-packed structure when the height of the slit approaches the particle diameter. The Helmholtz energy is a non-convex function of the slit height if the number of particles does not exceed that of one monolayer. As a consequence, the Legendre transform cannot be applied to obtain the Gibbs energy. The Gibbs energy of a non-deformable slit pore can be transformed into the Helmholtz energy of a deformable slit pore using the Legendre-Fenchel transform. The Legendre-Fenchel transform corresponds to the Maxwell construction of equal areas.

Soret separation and thermo-osmosis in porous media.

When a temperature difference is applied over a porous medium soaked with a fluid mixture, two effects may be observed, a component separation (the Ludwig-Soret effect, thermodiffusion) and a pressure difference due to thermo-osmosis. In this work, we have studied both effects using non-equilibrium thermodynamics and molecular dynamics. We have derived expressions for the two characteristic parameters, the Soret coefficient and the thermo-osmotic coefficient in terms of phenomenological transport coefficients, and we show how they are related. Numerical values for these coefficients were obtained for a two-component fluid in a solid matrix where both fluid and solid are Lennard-Jones/spline particles. We found that both effects depend strongly on the porosity of the medium and weakly on the interactions between the fluid components and the matrix. The Soret coefficient depends strongly on whether the fluid is sampled from inside the porous medium or from bulk phases outside, which must be considered in experimental measurements using packed columns. If we use a methane/decane mixture in bulk as an example, our results for the Soret coefficient give that a temperature difference of 10 K will separate the mixture to about 49.5/50.5 and give no pressure difference. In a reservoir with 30% porosity, the separation will be 49.8/50.2, whereas the pressure difference will be about 15 bar. Thermo-osmotic pressures with this order or magnitude have been observed in frost-heave experiments.

Cassie-Baxter and Wenzel States and the Effect of Interfaces on Transport Properties across Membranes.

Mass transfer across a liquid-repelling gas permeable membrane is influenced by the state(s) of the liquid-vapor interface(s) on the surface of the membrane, the pore geometry, and the solid-fluid interactions inside the membrane. By tuning the different local contributions, it is possible to enhance the temperature difference-driven mass flux across the membrane for a constant driving force. Non-equilibrium molecular dynamics simulations were used to simulate a temperature difference-driven mass flux through a gas permeable membrane with the evaporating liquid on one side and the condensing liquid on the other. Both sides were simulated for Wenzel- and Cassie-Baxter-like states. The interaction between the fluid and the solid inside the gas permeable membrane varied between the wetting angles of θ = 125° and θ = 103°. For a constant driving force, the Cassie-Baxter state led to an increased mass flux of almost 40% in comparison to the Wenzel state (given a small pore resistance). This difference was caused by an insufficient supply of vapor particles at the pore entrance in the Wenzel state. The difference between the Wenzel and Cassie-Baxter states decreased with increasing resistance of the pore. The condensing liquid-vapor interface area contributed in the same manner to the overall transport resistance as the evaporating liquid-vapor interface area. A higher repulsion between the fluid and the solid inside the membrane decreased the overall resistance.

Enhancing carrier flux for efficient drug delivery in cancer tissues.

Ultrasound focused toward tumors in the presence of circulating microbubbles improves the delivery of drug-loaded nanoparticles and therapeutic outcomes; however, the efficacy varies among the different properties and conditions of the tumors. Therefore, there is a need to optimize the ultrasound parameters and determine the properties of the tumor tissue important for the successful delivery of nanoparticles. Here, we propose a mesoscopic model considering the presence of entropic forces to explain the ultrasound-enhanced transport of nanoparticles across the capillary wall and through the interstitium of tumors. The nanoparticles move through channels of variable shape whose irregularities can be assimilated to barriers of entropic nature that the nanoparticles must overcome to reach their targets. The model assumes that focused ultrasound and circulating microbubbles cause the capillary wall to oscillate, thereby changing the width of transcapillary and interstitial channels. Our analysis provides values for the penetration distances of nanoparticles into the interstitium that are in agreement with experimental results. We found that the penetration increased significantly with increasing acoustic intensity as well as tissue elasticity, which means softer and more deformable tissue (Young modulus lower than 50 kPa), whereas porosity of the tissue and pulse repetition frequency of the ultrasound had less impact on the penetration length. We also considered that nanoparticles can be absorbed into cells and to extracellular matrix constituents, finding that the penetration length is increased when there is a low absorbance coefficient of the nanoparticles compared with their diffusion coefficient (close to 0.2). The model can be used to predict which tumor types, in terms of elasticity, will successfully deliver nanoparticles into the interstitium. It can also be used to predict the penetration distance into the interstitium of nanoparticles with various sizes and the ultrasound intensity needed for the efficient distribution of the nanoparticles.

Theory and simulation of shock waves: Entropy production and energy conversion.

We have considered a shock wave as a surface of discontinuity and computed the entropy production using nonequilibrium thermodynamics for surfaces. The results from this method, which we call the "Gibbs excess method" (GEM), were compared with results from three alternative methods, all based on the entropy balance in the shock-front region, but with different assumptions about local equilibrium. Nonequilibrium molecular dynamics (NEMD) simulations were used to simulate a thermal blast in a one-component gas consisting of particles interacting with the Lennard-Jones/spline potential. This provided data for the theoretical analysis. Two cases were studied, a weak shock with Mach number M≈2 and a strong shock with M≈6 and with a Prandtl number of the gas Pr≈1.4 in both cases. The four theoretical methods gave consistent results for the time-dependent surface excess entropy production for both Mach numbers. The internal energy was found to deviate only slightly from equilibrium values in the shock front. The pressure profile was found to be consistent with the Navier-Stokes equations. The entropy production in the weak and strong shocks were approximately proportional to the square of the Mach number and decayed with time at approximately the same relative rate. In both cases, some 97% of the total entropy production in the gas occurred in the shock wave. The GEM showed that most of the shock's kinetic energy was converted reversibly into enthalpy and entropy, and a small amount was dissipated as produced entropy. The shock waves traveled at almost constant speed, and we found that the overpressure determined from NEMD simulations agreed well with the Rankine-Hugoniot conditions for steady-state shocks.

Thermo-osmotic pressure and resistance to mass transport in a vapor-gap membrane.

We have investigated the transport of fluid through a vapor-gap membrane. The transport due to a membrane temperature difference was investigated under isobaric as well as non-isobaric conditions. Such a concept is relevant for water cleaning and power production purposes. A coarse-grained water model was used for modelling transport through pores of different diameters and lengths. The wall-fluid interactions were set so as to mimic hydrophobic interactions between water and membrane. The mass transport through the membrane scaled linearly with the applied temperature difference. Soret equilibria were obtained when the thermo-osmotic pressure was 18 bar K-1. The state of the Soret equilibrium did not depend on the pore size or pore length as expected. We show that the Soret equilibrium cannot be sustained by a gradient in vapor pressure. The fluxes of heat and mass were used to compute the total resistances to the transport of heat and mass.

Peltier effects in lithium-ion battery modeling.

A high battery temperature has been shown to be critical for lithium-ion batteries in terms of performance, degradation, and safety. Therefore, a precise knowledge of heat sources and sinks in the battery is essential. We have developed a thermal model for lithium-ion batteries, a model that includes terms not included before, namely, Peltier and Dufour heat effects. The model is derived using non-equilibrium thermodynamics for heterogeneous systems, the only theory which is able to describe in a systematic manner the coupling of heat, mass, and charge transport. The idea of this theory is to deal with surfaces as two-dimensional layers. All electrochemical processes in these layers are defined using excess variables, implying, for instance, that the surface has its own temperature. We show how the Peltier and Dufour heats affect a single cell and may produce an internal temperature rise of 8.5 K in a battery stack with 80 modules. The heat fluxes leaving the cell are also functions of these reversible heat effects. Most of the energy that is dissipated as heat occurs in the electrode surfaces and the electrolyte-filled separator. The analysis shows that better knowledge of experimental data on surface resistances, transport coefficients, and Dufour and Peltier heats is essential for further progress in thermal modeling of this important class of systems.

Special Issue on Nanoscale Thermodynamics.

This Special Issue concerns recent developments of a theory for energy conversion on the nanoscale, namely nanothermodynamics [...].

Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore.

We have described for the first time the thermodynamic state of a highly confined single-phase and single-component fluid in a slit pore using Hill's thermodynamics of small systems. Hill's theory has been named nanothermodynamics. We started by constructing an ensemble of slit pores for controlled temperature, volume, surface area, and chemical potential. We have presented the integral and differential properties according to Hill, and used them to define the disjoining pressure on the new basis. We identified all thermodynamic pressures by their mechanical counterparts in a consistent manner, and have given evidence that the identification holds true using molecular simulations. We computed the entropy and energy densities, and found in agreement with the literature, that the structures at the wall are of an energetic, not entropic nature. We have shown that the subdivision potential is unequal to zero for small wall surface areas. We have showed how Hill's method can be used to find new Maxwell relations of a confined fluid, in addition to a scaling relation, which applies when the walls are far enough apart. By this expansion of nanothermodynamics, we have set the stage for further developments of the thermodynamics of confined fluids, a field that is central in nanotechnology.

Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media.

A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill's thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed.

Fractal-Like Flow-Fields with Minimum Entropy Production for Polymer Electrolyte Membrane Fuel Cells.

The fractal-type flow-fields for fuel cell (FC) applications are promising, due to their ability to deliver uniformly, with a Peclet number Pe~1, the reactant gases to the catalytic layer. We review fractal designs that have been developed and studied in experimental prototypes and with CFD computations on 1D and 3D flow models for planar, circular, cylindrical and conical FCs. It is shown, that the FC efficiency could be increased by design optimization of the fractal system. The total entropy production (TEP) due to viscous flow was the objective function, and a constant total volume (TV) of the channels was used as constraint in the design optimization. Analytical solutions were used for the TEP, for rectangular channels and a simplified 1D circular tube. Case studies were done varying the equivalent hydraulic diameter (Dh), cross-sectional area (DΣ) and hydraulic resistance (DZ). The analytical expressions allowed us to obtain exact solutions to the optimization problem (TEP→min, TV=const). It was shown that the optimal design corresponds to a non-uniform width and length scaling of consecutive channels that classifies the flow field as a quasi-fractal. The depths of the channels were set equal for manufacturing reasons. Recursive formulae for optimal non-uniform width scaling were obtained for 1D circular Dh -, DΣ -, and DZ -based tubes (Cases 1-3). Appropriate scaling of the fractal system providing uniform entropy production along all the channels have also been computed for Dh -, DΣ -, and DZ -based 1D models (Cases 4-6). As a reference case, Murray's law was used for circular (Case 7) and rectangular (Case 8) channels. It was shown, that Dh-based models always resulted in smaller cross-sectional areas and, thus, overestimated the hydraulic resistance and TEP. The DΣ -based models gave smaller resistances compared to the original rectangular channels and, therefore, underestimated the TEP. The DZ -based models fitted best to the 3D CFD data. All optimal geometries exhibited larger TEP, but smaller TV than those from Murray's scaling (reference Cases 7,8). Higher TV with Murray's scaling leads to lower contact area between the flow-field plate with other FC layers and, therefore, to larger electric resistivity or ohmic losses. We conclude that the most appropriate design can be found from multi-criteria optimization, resulting in a Pareto-frontier on the dependencies of TEP vs TV computed for all studied geometries. The proposed approach helps us to determine a restricted number of geometries for more detailed 3D computations and further experimental validations on prototypes.

A Legendre-Fenchel Transform for Molecular Stretching Energies.

Single-molecular polymers can be used to analyze to what extent thermodynamics applies when the size of the system is drastically reduced. We have recently verified using molecular-dynamics simulations that isometric and isotensional stretching of a small polymer result in Helmholtz and Gibbs stretching energies, which are not related to a Legendre transform, as they are for sufficiently long polymers. This disparity has also been observed experimentally. Using molecular dynamics simulations of polyethylene-oxide, we document for the first time that the Helmholtz and Gibbs stretching energies can be related by a Legendre-Fenchel transform. This opens up a possibility to apply this transform to other systems which are small in Hill's sense.