On the necessity of including vapor kinetics to model the specific surface area evolution in snow

Vapor fluxes in snow are often inferred from the temperature field by assuming vapor concentrations in local thermodynamic equilibrium with the temperature. Here we give evidence that, at the pore scale, this picture is in clear contradiction with the observed evolution of the specific surface area (SSA) under temperature gradient metamorphism. To this end, we have calculated pore-scale temperature fields using the Finite Element Method on micro-tomography images. Subsequently, we utilized the exact volume-averaged evolution equation for the SSA to infer that the disagreement stems from the employed diffusion-limited growth law which manifests in local thermodynamic equilibrium of vapor and temperature. Via sensitivity studies we confirm that this conclusion is not affected by the involved image analysis and numerical procedures. We outline how and why attachment kinetics may resolve the observed contradiction.

Evaporation kinetics of volatile liquids and release kinetics of water from a smectite clay: comparison between experiments and finite element calculations

Pascal Clausen, Jan-Anders Månson, John Christopher Plummer

Numerical calculations of the evaporation kinetics of bulk volatile liquids and of water from smectite clay granules are compared with experimental results. The weight loss of the volatiles is analyzed by thermogravimetry and differential calorimetry. Under the thermodynamic conditions of the experiments, finite element calculations are in good agreement with the experimental data, and an approximate semi-analytical model is developed in order to explain the dependence of the rate of evaporation on the temperature, the chemical species and the carrier gas flow rate. The initial rate of evaporation of water from the clay granule is close to that for bulk water. Its decrease with time is determined mainly by changes in the gas/condensed phase partition given by the equilibrium desorption isotherm, with little limitations due to internal diffusion effects for the present experimental conditions. Its temperature dependence could also be approximately described by an Arrhenius-type equation derived from the semi-analytical model. Further analysis of the experimental measurements reveals steps in the heat of vaporization of water as a function of water concentration, that could be related to the equilibrium desorption isotherm. (C) 2011 Published by Elsevier Ltd.

2010

Evaporation kinetics of volatile liquids and release kinetics of water from a smectite clay: Comparison between experiments and finite element calculations

Pascal Clausen, Jan-Anders Månson, John Christopher Plummer

2011

Propriétés hors-équilibre d'une paroi adiabatique

Séverine Pache

We study the evolution of a system composed of N non-interacting particles of mass m distributed in a cylinder of length L. The cylinder is separated into two parts by an adiabatic piston of a mass M ≫ m. The length of the cylinder is a fix parameter and can be finite or infinite (in this case N is infinite). For the infinite case we carry out a perturbative analysis using Boltzmann's equation based on a development of the velocity distribution of the piston in function of a small dimensionless parameter ε = √(m/M). The non-stationary case is solved up to the order ε ;; our analysis shows that the system tends exponentially fast towards a stationary state where the piston has an average velocity V. The characteristic time scale for this relaxation is proportional to the mass of the piston (τ0 = M/A where A is the cross-section of the piston). We show that for equal pressures the collisions of the particles induce asymmetric fluctuations of the velocity of the piston which leads to a macroscopic movement of the piston in the direction of the higher temperature. In the case of the finite model a perturbative approach based on Liouville's equation (using the parameter α = 2m/(M + m)) shows that the evolution towards thermal equilibrium happens on two well separated time scales. The first relaxation step is a fast, deterministic and adiabatic evolution towards a state of mechanical equilibrium with approximately equal pressures but different temperatures. The movement of the piston is more or less damped. This damping qualitatively depends on whether the ratio R = Mgas/M between the total mass of the gas and the mass of the piston is small (R < 2) or large (R > 4). The second part of the evolution is much slower ; the typical time scales are proportional to the mass of the piston. There is a stochastic evolution including heat transfer leading to thermal equilibrium. A microscopic analysis yields the relation XM(t) = L(1/2 - ξ(at)) where the function ξ is independent of M. Using the hypothesis of homogeneity (i.e. the values of the densities, pressures and temperatures at the surface of the piston can be replaced by their respective average values) introduced in the previous analysis the observed damping does not show up. This can be explained by shock waves propagating between the piston and the walls at the extremities of the cylinder. In order to study the behaviour of the system there is hence a need to adequately describe the non-equilibrium fluids around the piston. We carry out an analysis of the infinite case, based on the perturbative approach introduced earlier. In this case the initial conditions are chosen in such a manner that the piston on average stays at the origin. It is shown that it is possible to describe the evolution of the fluids in such a way that it is coherent with the two laws of thermodynamics and the phenomenological relationships. Finally we study the case of a constant velocity of the piston in a finite cylinder. Such a condition and elastic collisions allow us to derive an explicit expression for the distribution of the fluids and hence for the hydrodynamics fields. This expression reveals the presence of shock waves between the piston and the extremities of the cylinder.

EPFL2004

Propriétés hors-équilibre d'une paroi adiabatique

Séverine Pache

EPFL2004