Heat and mass transfer across phase boundaries: Estimates of coupling coefficients

Heat and mass transport across phase boundaries are central in many engineering problems. The systematic description offered by classical non-equilibrium thermodynamics theory, when extended to surfaces, gives the interaction between the two fluxes in terms of coupling coefficients. It is shown in this paper that these coupling coefficients are large. The few experimental and computational results that are available confirm this. Neglect of coupling coefficients, which is common in most models for surface transport, may lead to errors in the heat flux. We present values for the coupling coefficient in a one-component system in terms of the heat of transfer, as obtained from non-equilibrium molecular dynamics simulations, kinetic theory and the integrated non-equilibrium van der Waals' square gradient model

Heat and mass transfer across phase boundaries: Estimates of coupling coefficients

Heat and mass transport across phase boundaries are central in many engineering problems. The systematic description offered by classical non-equilibrium thermodynamics theory, when extended to surfaces, gives the interaction between the two fluxes in terms of coupling coefficients. It is shown in this paper that these coupling coefficients are large. The few experimental and computational results that are available confirm this. Neglect of coupling coefficients, which is common in most models for surface transport, may lead to errors in the heat flux. We present values for the coupling coefficient in a one-component system in terms of the heat of transfer, as obtained from non-equilibrium molecular dynamics simulations, kinetic theory and the integrated non-equilibrium van der Waals' square gradient mode

Stable and efficient time integration of a dynamic pore network model for two-phase flow in porous media

We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method developed herein. The explicit methods are known to suffer from numerical instabilities at low capillary numbers. A new time-step criterion is suggested in order to stabilize them. Numerical experiments, including a Haines jump case, are performed and these demonstrate that stabilization is achieved. Further, the results from the Haines jump case are consistent with experimental observations. A performance analysis reveals that the semi-implicit method is able to perform stable simulations with much less computational effort than the explicit methods at low capillary numbers. The relative benefit of using the semi-implicit method increases with decreasing capillary number $\mathrm{Ca}$, and at $\mathrm{Ca} \sim 10^{-8}$ the computational time needed is reduced by three orders of magnitude. This increased efficiency enables simulations in the low-capillary number regime that are unfeasible with explicit methods and the range of capillary numbers for which the pore network model is a tractable modeling alternative is thus greatly extended by the semi-implicit method.Comment: 33 pages, 12 figure

Non-isothermal transport of multi-phase fluids in porous media. The entropy production

We derive the entropy production for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in pressure, temperature, and chemical potentials. Thermodynamic extensive variables on the macro-scale are obtained by integrating over a representative elementary volume (REV). Using Euler homogeneity of the first order, we obtain the Gibbs equation for the REV. From this we define the intensive variables, the temperature, pressure and chemical potentials and, using the balance equations, derive the entropy production for the REV. The entropy production defines sets of independent conjugate thermodynamic fluxes and forces in the standard way. The transport of two-phase flow of immiscible components is used to illustrate the equations.Comment: 25 pages, 7 figures, Talk at Interpore, New Orleans, 201

Non-isothermal transport of multi-phase fluids in porous media. Constitutive equations

We develop constitutive equations for multi-component, multi-phase, macro-scale flow in a porous medium exposed to temperature-, composition-, and pressure -gradients. The porous medium is non-deformable. We define the pressure and the composition of the representative elementary volume (REV) in terms of the volume and surface averaged pressure and the saturation, and the respective driving forces from these variables. New contributions due to varying porosity or surface tension offer explanations for non-Darcy behavior. The interaction of a thermal and mechanical driving forces give thermal osmosis. An experimental program is suggested to verify Onsager symmetry in the transport coefficients.Comment: 22 pages, 2 figure

Nanothermodynamic description and molecular simulation of a single-phase fluid in a slit pore

We describe the thermodynamic state of a highly confined single-phase and single-component fluid in a slit pore using Hill's thermodynamics of small systems. This theory was more recently named nanothermodynamics. We start by constructing an ensemble of slit pores for controlled temperature, volume, surface area, and chemical potential. We present the integral and differential properties according to Hill, and use them to define the disjoining pressure. We identify all thermodynamic pressures by their mechanical counterparts in a consistent manner, and investigate the identification by molecular dynamics simulations. We define and compute the disjoining pressure, and show that it contains the standard definition. We compute the entropy and energy densities, and find in agreement with the literature, that the forces at the wall are of an energetic, not entropic nature. The subdivision potential is zero for this slit pore with large walls, but unequal to zero for related sets of control variables. We show 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 separated far enough. By this expansion of nanothermodynamics, we set the stage for further developments of the thermodynamics of confined fluids, a field that is central in nanotechnology.Comment: 10 figures, 26 page