scholarly journals Impact of water vapor diffusion and latent heat on the effective thermal conductivity of snow

2021 ◽  
Vol 15 (6) ◽  
pp. 2739-2755
Author(s):  
Kévin Fourteau ◽  
Florent Domine ◽  
Pascal Hagenmuller
Keyword(s):  
Thermal Conductivity ◽  
Diffusion Coefficient ◽  
Heat Conduction ◽  
Water Vapor ◽  
Effective Thermal Conductivity ◽  
Latent Heat ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Water Vapor Transport ◽  
Fast Kinetics

Abstract. Heat transport in snowpacks is understood to occur through the two processes of heat conduction and latent heat transport carried by water vapor, which are generally treated as decoupled from one another. This paper investigates the coupling between both these processes in snow, with an emphasis on the impacts of the kinetics of the sublimation and deposition of water vapor onto ice. In the case when kinetics is fast, latent heat exchanges at ice surfaces modify their temperature and therefore the thermal gradient within ice crystals and the heat conduction through the entire microstructure. Furthermore, in this case, the effective thermal conductivity of snow can be expressed by a purely conductive term complemented by a term directly proportional to the effective diffusion coefficient of water vapor in snow, which illustrates the inextricable coupling between heat conduction and water vapor transport. Numerical simulations on measured three-dimensional snow microstructures reveal that the effective thermal conductivity of snow can be significantly larger, by up to about 50 % for low-density snow, than if water vapor transport is neglected. A comparison of our numerical simulations with literature data suggests that the fast kinetics hypothesis could be a reasonable assumption for modeling heat and mass transport in snow. Lastly, we demonstrate that under the fast kinetics hypothesis the effective diffusion coefficient of water vapor is related to the effective thermal conductivity by a simple linear relationship. Under such a condition, the effective diffusion coefficient of water vapor is expected to lie in the narrow 100 % to about 80 % range of the value of the diffusion coefficient of water vapor in air for most seasonal snows. This may greatly facilitate the parameterization of water vapor diffusion of snow in models.

scholarly journals Impact of water vapor diffusion and latent heat on the effective thermal conductivity of snow

2020 ◽  
Author(s):  
Kévin Fourteau ◽  
Florent Domine ◽  
Pascal Hagenmuller
Keyword(s):  
Thermal Conductivity ◽  
Diffusion Coefficient ◽  
Heat Conduction ◽  
Water Vapor ◽  
Effective Thermal Conductivity ◽  
Latent Heat ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Water Vapor Transport ◽  
Fast Kinetics

Abstract. Heat transport in snowpacks is generally thought to occur through two independent processes: heat conduction and latent heat transport carried by water vapor. This paper investigates the coupling between both these processes in snow, with an emphasis on the impacts of the kinetics of the sublimation and deposition of water vapor onto ice. In the case where kinetics is fast, latent heat exchanges at ice surfaces modify their temperature, and therefore the thermal gradient within ice crystals and the heat conduction through the entire microstructure. Furthermore, in this case, the effective thermal conductivity of snow can be expressed by a purely conductive term complemented by a term directly proportional to the effective diffusion coefficient of water vapor in snow, which illustrates the inextricable coupling between heat conduction and water vapor transport. Numerical simulations on measured three-dimensional snow microstructures reveal that the effective thermal conductivity of snow can be significantly larger, up to about 50 % for low-density snow, than if water vapor transport is neglected. Comparison of our numerical simulations with literature data suggests that the fast kinetics hypothesis could be a reasonable assumption to model snow physical properties. Lastly, we demonstrate that under the fast kinetics hypothesis the effective diffusion coefficient of water vapor is related to the effective thermal conductivity by a simple linear relationship. Under such condition, the effective diffusion coefficient of water vapor is expected to lie in the narrow 100 % to about 80 % range of the value of the diffusion coefficient of water vapor in air for most seasonal snows. This may greatly facilitate the parameterization of water vapor diffusion of snow in models.

scholarly journals Macroscopic water vapor diffusion is not enhanced in snow

2020 ◽  
Author(s):  
Kévin Fourteau ◽  
Florent Domine ◽  
Pascal Hagenmuller
Keyword(s):  
Diffusion Coefficient ◽  
Water Vapor ◽  
Effective Diffusion Coefficient ◽  
Molecular Diffusion ◽  
Pore Space ◽  
Effective Diffusion ◽  
Vapor Transport ◽  
Water Vapor Transport ◽  
Vapor Diffusion ◽  
Water Vapor Diffusion

Abstract. Water vapor transport in dry snowpacks plays a significant role for snow metamorphism and the mass and energy balance of snowpacks. The molecular diffusion of water vapor in the interstitial pores is usually considered as the main or only transport mechanism, and current detailed snow physics models therefore rely on the knowledge of the effective diffusion coefficient of water vapor in snow. Numerous previous studies have concluded that water vapor diffusion in snow is enhanced relative to that in air. Various field observations also indicate that for vapor transport in snow to be explained by diffusion alone, the effective diffusion coefficient should be larger than that in air. Here we show using theory and numerical simulations on idealized and measured snow microstructures that, although sublimation and condensation of water vapor onto snow crystal surfaces do enhance microscopic diffusion in the pore space, this effect is more than countered by the restriction of diffusion space due to ice. The interaction of water vapor with the ice results in water vapor diffusing more than inert molecules in snow, but still less than in free air, regardless of the value of the accommodation coefficient of water on ice. Our results imply that processes other than diffusion, probably convection, play a preponderant role in water vapor transport in dry snowpacks.

scholarly journals Macroscopic water vapor diffusion is not enhanced in snow

2021 ◽  
Vol 15 (1) ◽  
pp. 389-406
Author(s):  
Kévin Fourteau ◽  
Florent Domine ◽  
Pascal Hagenmuller
Keyword(s):  
Diffusion Coefficient ◽  
Water Vapor ◽  
Effective Diffusion Coefficient ◽  
Molecular Diffusion ◽  
Pore Space ◽  
Effective Diffusion ◽  
Vapor Transport ◽  
Water Vapor Transport ◽  
Vapor Diffusion ◽  
Water Vapor Diffusion

Abstract. Water vapor transport in dry snowpacks plays a significant role for snow metamorphism and the mass and energy balance of snowpacks. The molecular diffusion of water vapor in the interstitial pores is usually considered to be the main or only transport mechanism, and current detailed snow physics models therefore rely on the knowledge of the effective diffusion coefficient of water vapor in snow. Numerous previous studies have concluded that water vapor diffusion in snow is enhanced relative to that in air. Various field observations also indicate that for vapor transport in snow to be explained by diffusion alone, the effective diffusion coefficient should be larger than that in air. Here we show using theory and numerical simulations of idealized and measured snow microstructures that, although sublimation and deposition of water vapor onto snow crystal surfaces do enhance microscopic diffusion in the pore space, this effect is more than countered by the restriction of diffusion space due to ice. The interaction of water vapor with the ice results in water vapor diffusing more than inert molecules in snow but still less than in free air, regardless of the value of the sticking coefficient of water molecules on ice. Our results imply that processes other than diffusion play a predominant role in water vapor transport in dry snowpacks.

scholarly journals A macroscale mixture theory analysis of deposition and sublimation rates during heat and mass transfer in dry snow

2015 ◽  
Vol 9 (5) ◽  
pp. 1857-1878 ◽  
Author(s):  
A. C. Hansen ◽  
W. E. Foslien
Keyword(s):  
Thermal Conductivity ◽  
Mass Transfer ◽  
Diffusion Coefficient ◽  
Effective Thermal Conductivity ◽  
Heat And Mass Transfer ◽  
Effective Diffusion ◽  
Mixture Theory ◽  
Temperature Gradients ◽  
Snow Metamorphism ◽  
Sublimation Rates

Abstract. The microstructure of a dry alpine snowpack is a dynamic environment where microstructural evolution is driven by seasonal density profiles and weather conditions. Notably, temperature gradients on the order of 10–20 K m−1, or larger, are known to produce a faceted snow microstructure exhibiting little strength. However, while strong temperature gradients are widely accepted as the primary driver for kinetic growth, they do not fully account for the range of experimental observations. An additional factor influencing snow metamorphism is believed to be the rate of mass transfer at the macroscale. We develop a mixture theory capable of predicting macroscale deposition and/or sublimation in a snow cover under temperature gradient conditions. Temperature gradients and mass exchange are tracked over periods ranging from 1 to 10 days. Interesting heat and mass transfer behavior is observed near the ground, near the surface, as well as immediately above and below dense ice crusts. Information about deposition (condensation) and sublimation rates may help explain snow metamorphism phenomena that cannot be accounted for by temperature gradients alone. The macroscale heat and mass transfer analysis requires accurate representations of the effective thermal conductivity and the effective mass diffusion coefficient for snow. We develop analytical models for these parameters based on first principles at the microscale. The expressions derived contain no empirical adjustments, and further, provide self consistent values for effective thermal conductivity and the effective diffusion coefficient for the limiting cases of air and solid ice. The predicted values for these macroscale material parameters are also in excellent agreement with numerical results based on microscale finite element analyses of representative volume elements generated from X-ray tomography.

Latent Heat Fluxes Through Soft Materials With Microtruss Architectures

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Matthew J. Traum ◽  
Peter Griffith ◽  
Edwin L. Thomas ◽  
William A. Peters
Keyword(s):  
Diffusion Coefficient ◽  
Water Vapor ◽  
Latent Heat ◽  
Diffusion Coefficients ◽  
Evaporative Cooling ◽  
Vapor Transport ◽  
Water Vapor Transport ◽  
Vapor Concentration ◽  
Water Vapor Concentration ◽  
Evaporation Chamber

Microscale truss architectures provide high mechanical strength, light weight, and open porosity in polymer sheets. Liquid evaporation and transport of the resulting vapor through truss voids cool nearby surfaces. Thus, microtruss materials can simultaneously prevent mechanical and thermal damage. Assessment of promise requires quantitative understanding of vapor transport through microtruss pores for realistic heat loads and latent heat carriers. Pore size may complicate exegesis owing to vapor rarefaction or surface interactions. This paper quantifies the nonboiling evaporative cooling of a flat surface by water vapor transport through two different hydrophobic polymer membranes, 112–119μm (or 113–123μm) thick, with microtruss-like architectures, i.e., straight-through pores of average diameter of 1.0–1.4μm (or 12.6–14.2μm) and average overall porosity of 7.6% (or 9.9%). The surface, heated at 1350±20Wt∕m2 to mimic human thermal load in a desert (daytime solar plus metabolic), was the bottom of a 3.1cm inside diameter, 24.9cm3 cylindrical aluminum chamber capped by the membrane. Steady-state rates of water vapor transport through the membrane pores to ambient were measured by continuously weighing the evaporation chamber. The water vapor concentration at the membrane exit was maintained near zero by a cross flow of dry nitrogen (velocity=2.8m∕s). Each truss material enabled 13–14°C evaporative cooling of the surface, roughly 40% of the maximum evaporative cooling attainable, i.e., with an uncapped chamber. Intrinsic pore diffusion coefficients for dilute water vapor (<10.4mole%) in air (P total ∼112,000Pa) were deduced from the measured vapor fluxes by mathematically disaggregating the substantial mass transfer resistances of the boundary layers (∼50%) and correcting for radial variations in upstream water vapor concentration. The diffusion coefficients for the 1.0–1.4μm pores (Knudsen number ∼0.1) agree with literature for the water vapor-air mutual diffusion coefficient to within ±20%, but for the nominally 12.6–14.2μm pores (Kn ∼0.01), the diffusion coefficient values were smaller, possibly because considerable pore area resides in noncircular, i.e., narrow, wedge-shaped cross sections that impede diffusion owing to enhanced rarefaction. The present data, parameters, and mathematical models support the design and analysis of microtruss materials for thermal or simultaneous thermal-and-mechanical protection of microelectromechanical systems, nanoscale components, humans, and other macrosystems.

Diffusion of Heavy Oil in SiO2 Model Catalyst and FCC Catalyst

2012 ◽  
Vol 550-553 ◽  
pp. 158-163 ◽  
Author(s):  
Zi Yuan Liu ◽  
Sheng Li Chen ◽  
Peng Dong ◽  
Xiu Jun Ge
Keyword(s):  
Diffusion Coefficient ◽  
Pore Size ◽  
Effective Diffusion Coefficient ◽  
Pore Diameter ◽  
Effective Diffusion ◽  
Model Catalyst ◽  
Average Pore ◽  
Diffusion Factor ◽  
Fcc Catalyst ◽  
Fcc Catalysts

Through the measured effective diffusion coefficients of Dagang vacuum residue supercritical fluid extraction and fractionation (SFEF) fractions in FCC catalysts and SiO2model catalysts, the relation between pore size of catalyst and effective diffusion coefficient was researched and the restricted diffusion factor was calculated. The restricted diffusion factor in FCC catalysts is less than 1 and it is 1~2 times larger in catalyst with polystyrene (PS) template than in conventional FCC catalyst without template, indicating that the diffusion of SFEF fractions in the two FCC catalysts is restricted by the pore. When the average molecular diameter is less than 1.8 nm, the diffusion of SFEF fractions in SiO2model catalyst which average pore diameter larger than 5.6 nm is unrestricted. The diffusion is restricted in the catalyst pores of less than 8 nm for SFEF fractions which diameter more than 1.8 nm. The tortuosity factor of SiO2model catalyst is obtained to be 2.87, within the range of empirical value. The effective diffusion coefficient of the SFEF fractions in SiO2model catalyst is two orders of magnitude larger than that in FCC catalyst with the same average pore diameter. This indicate that besides the ratio of molecular diameter to the pore diameter λ, the effective diffusion coefficient is also closely related to the pore structure of catalyst. Because SiO2model catalyst has uniform pore size, the diffusion coefficient can be precisely correlated with pore size of catalyst, so it is a good model material for catalyst internal diffusion investigation.

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