Thermodynamic Resistance to Matter Flow at The Interface of a Porous Membrane.

Nanoporous materials are important in industrial separation, but their application is subject to strong interfacial barriers to the entry and transport of fluids. At certain conditions the fluid inside and outside the nanoporous material can be viewed as a two-phase system, with an interface between them, which poses an excess resistance to matter flow. We show that there exist two kinds of phenomena which influence the interfacial resistance: hydrodynamic effects and thermodynamic effects, which are independent of each other. Here, we investigate the role of the thermodynamic effects in carbon nanotubes (CNTs) and slit pores and compare the associated thermodynmic resistance with that due to hydrodynamic effects traditionally modeled by the established Sampson expression. Using CH4 and CO2 as model fluids, we show that the thermodynamic resistance is especially important for moderate to high pressures, at which the fluid within the CNT or slit pore is in the condensed state. Further, we show that at such pressures the thermodynamic resistance becomes comparable with the internal resistance to fluid transport at length scales typical of membranes used in fuel cells, and of importance in membrane-based separation, and nanofluidics in general.

Local equilibrium and the second law of thermodynamics for irreversible systems with thermodynamic inertia.

Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative values of the entropy production, which is in contradiction with the second law of thermodynamics. In this paper, we address this question by suggesting a variational formulation of irreversible evolution of a system with non-zero thermodynamic inertia. We introduce the Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" systems. We show that the standard evolution equations, in particular, the Maxwell-Cattaneo-Vernotte equation, can be derived from the variational procedure without going beyond the assumption of local equilibrium. We also argue that the second law of thermodynamics in non-equilibrium should be understood as a consequence of the variational procedure and the property of local equilibrium. For systems with instantaneous response this leads to the standard requirement of the local instantaneous entropy production being always positive. However, if a system is characterized by delayed response, the formulation of the second law of thermodynamics should be altered. In particular, the quantity, which is always positive, is not the instantaneous entropy production, but the entropy production averaged over a proper time interval.

Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics.

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an "integral of evolution" which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.

Compressibility, thermal expansion coefficient and heat capacity of CH4 and CO2 hydrate mixtures using molecular dynamics simulations.

Understanding the thermal and mechanical properties of CH4 and CO2 hydrates is essential for the replacement of CH4 with CO2 in natural hydrate deposits as well as for CO2 sequestration and storage. In this work, we present isothermal compressibility, isobaric thermal expansion coefficient and specific heat capacity of fully occupied single-crystal sI-CH4 hydrates, CO2 hydrates and hydrates of their mixture using molecular dynamics simulations. Eight rigid/nonpolarisable water interaction models and three CH4 and CO2 interaction potentials were selected to examine the atomic interactions in the sI hydrate structure. The TIP4P/2005 water model combined with the DACNIS united-atom CH4 potential and TraPPE CO2 rigid potential were found to be suitable molecular interaction models. Using these molecular models, the results indicate that both the lattice parameters and the compressibility of the sI hydrates agree with those from experimental measurements. The calculated bulk modulus for any mixture ratio of CH4 and CO2 hydrates varies between 8.5 GPa and 10.4 GPa at 271.15 K between 10 and 100 MPa. The calculated thermal expansion and specific heat capacities of CH4 hydrates are also comparable with experimental values above approximately 260 K. The compressibility and expansion coefficient of guest gas mixture hydrates increase with an increasing ratio of CO2-to-CH4, while the bulk modulus and specific heat capacity exhibit the opposite trend. The presented results for the specific heat capacities of 2220-2699.0 J kg(-1) K(-1) for any mixture ratio of CH4 and CO2 hydrates are the first reported so far. These computational results provide a useful database for practical natural gas recovery from CH4 hydrates in deep oceans where CO2 is considered to replace CH4, as well as for phase equilibrium and mechanical stability of gas hydrate-bearing sediments. The computational schemes also provide an appropriate balance between computational accuracy and cost for predicting mechanical and thermal properties of gas hydrates in the high temperature range (≥260 K), and the schemes may be useful for the study of other complex hydrate systems.

Curvature dependence of the interfacial heat and mass transfer coefficients.

Nucleation is often accompanied by heat transfer between the surroundings and a nucleus of a new phase. The interface between two phases gives an additional resistance to this transfer. For small nuclei the interfacial curvature is high, which affects not only equilibrium quantities such as surface tension, but also the transport properties. In particular, high curvature affects the interfacial resistance to heat and mass transfer. We develop a framework for determining the curvature dependence of the interfacial heat and mass transfer resistances. We determine the interfacial resistances as a function of a curvature. The analysis is performed for a bubble of a one-component fluid and may be extended to various nuclei of multicomponent systems. The curvature dependence of the interfacial resistances is important in modeling transport processes in multiphase systems.

Effect of compressibility in bubble formation in closed systems.

We analyze the stability of small bubbles in a closed system with fixed volume, temperature, and number of molecules. We show that there exists a minimum stable size of a bubble. Thus there exists a range of densities where no stable bubbles are allowed and the system has a homogeneous density which is lower than the coexistence density of the liquid. This becomes possible due to the finite liquid compressibility. Capillary analysis within the developed "modified bubble" model illustrates that the existence of the minimum bubble size is associated to the compressibility and it is not possible when the liquid is strictly incompressible. This finding is expected to have very important implications in cavitation and boiling.

Toward a possibility to exchange CO2 and CH4 in sI clathrate hydrates.

We study the thermodynamic conditions for exchange of CH(4) with CO(2) in sI clathrate hydrates using Grand Canonical Monte Carlo simulations. From the variations in the Helmholtz energy, we suggest a thermodynamic path for exchange of CH(4) by CO(2). The results can be understood from single-component occupancy isotherms. Simulations of pure component systems show that all methane sites are essentially equivalent, whereas carbon dioxide distinguishes between two types of sites, large or small. Mixture of CO(2) and CH(4) in the clathrate can be regarded as ideal, as long as only the large sites are occupied. A strong preference in selectivity is demonstrated for methane when the smaller sites become filled. The Helmholtz energies of the hydrate with a CO(2)-CH(4) gas mixture for temperatures between 278 and 328 K and pressures between 10(4) and 10(9) Pa indicate that there exists a region of stability of a mixed hydrate referred to single-component hydrates.

Resistances for heat and mass transfer through a liquid-vapor interface in a binary mixture.

In this paper we calculate the interfacial resistances to heat and mass transfer through a liquid-vapor interface in a binary mixture. We use two methods, the direct calculation from the actual nonequilibrium solution and integral relations, derived earlier. We verify, that integral relations, being a relatively faster and cheaper method, indeed gives the same results as the direct processing of a nonequilibrium solution. Furthermore we compare the absolute values of the interfacial resistances with the ones obtained from kinetic theory. Matching the diagonal resistances for the binary mixture we find that kinetic theory underestimates the cross coefficients. The heat of transfer is, as a consequence, correspondingly larger.

Transport of heat and mass in a two-phase mixture: From a continuous to a discontinuous description.

We present a theory that describes the transport properties of the interfacial region with respect to heat and mass transfer. Postulating the local Gibbs relation for a continuous description inside the interfacial region, we derive the description of the Gibbs surface in terms of excess densities and fluxes along the surface. We introduce overall interfacial resistances and conductances as the coefficients in the force-flux relations for the Gibbs surface. We derive relations between the local resistivities for the continuous description inside the interfacial region and the overall resistances of the surface for transport between the two phases for a mixture. It is shown that interfacial resistances depend among other things on the enthalpy profile across the interface. Since this variation is substantial, the coupling between heat and mass flow across the surface is also substantial. In particular, the surface puts up much more resistance to the heat and mass transfer than the homogeneous phases over a distance comparable to the thickness of the surface. This is the case not only for the pure heat conduction and diffusion but also for the cross effects such as thermal diffusion. For the excess fluxes along the surface and the corresponding thermodynamic forces, we derive expressions for excess conductances as integrals over the local conductivities along the surface. We also show that the curvature of the surface affects only the overall resistances for transport across the surface and not the excess conductivities along the surface.

Numerical solution of the nonequilibrium square-gradient model and verification of local equilibrium for the Gibbs surface in a two-phase binary mixture.

In this paper we apply the general analysis described in our first paper to a binary mixture of cyclohexane and n -hexane. We use the square gradient model for the continuous description of a nonequilibrium surface and obtain numerical profiles of various thermodynamic quantities in various stationary state conditions. Details of the numerical procedure are given and discussed. In the second part of this paper we focus on the verification of local equilibrium of the surface as described with excess densities. We give a definition of the temperature and chemical potentials of the surface and verify that these quantities are independent of the choice of the dividing surface. We verify numerically that the surface in a stationary state of the mixture can be described in terms of Gibbs excess densities, which are found to be in good approximation equal to their equilibrium values at the stationary state temperature and chemical potentials of the surface.

Nonequilibrium properties of a two-dimensionally isotropic interface in a two-phase mixture as described by the square gradient model.

In earlier work a systematic extension of the van der Waals square gradient model to nonequilibrium one-component systems was given. In this work the focus was on heat and mass transfer through the liquid-vapor interface as caused by a temperature difference or an over- or underpressure. We will give an extension of this approach to multicomponent nonequilibrium systems in the systematic context of nonequilibrium thermodynamics. An explicit expression for the pressure tensor is derived valid also for curved surfaces. It is shown how the Gibbs relation should be modified in the interfacial region, in both equilibrium and nonequilibrium. The two-dimensional isotropy of a curved interface is discussed. Furthermore, we give numerically obtained profiles of the concentration, the mole fraction, and the temperature, which illustrate the solution for some special cases.