DOCSLIB.ORG

Gaseous Diffusion and Pore Structure in Nuclear Graphites

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Gaseous Diffusion and Pore Structure in Nuclear Graphites GASEOUS DIFFUSION AND PORE STRUCTURE IN NUCLEAR GRAPHITES T.J. MAYS, B. McENANEY, B.T. KELLY School of Materials Science, Bath University, XA9642926 Bath, United Kingdom Abstract With the incentive of providing more information for oxidation and lifecycle studies of moderators in thermal reactors, a new method has been developed to estimate pore structure in nuclear graphites. This method involves the measurement of room-temperature binary gas diffusion in graphite samples using an apparatus that was specially-built to operate at pressures below 100 Torr In these conditions diffusion in graphite pores is in the transition regime between Knudsen and bulk or molecular diffusion. Transition diffusion measurements are analysed for nuclear-grade graphites to yield pore size distributions. Results from the new method are compared with pore structure data obtained using porosimetry. pycnometry and established gas flow techniques. 1. INTRODUCTION Synthetic graphites used as moderators in thermal nuclear reactors contain pores, mostly in the macropore size range (larger than 50 nm [1]), which arise initially during their manufacture. Subsequently these pores are developed by radiolytic oxidation in the CO2 coolant during service. This leads to a reduction in graphite density, and hence to degradations in mechanical and other properties which have implications for moderator lifecycles. It is therefore important to determine pore structure in nuclear graphites in order to understand and predict radiolytic oxidation and property changes in moderators [2]. The nuclear industry in the UK recognised the need for this approach, and consequently used and developed methods such as porosimetry and permeability for macropore structure determination in moderator graphites. However, certain problems with these methods are well-known, such as the limited information available from permeability data [3]. This paper describes a new method to estimate pore structure that might supplement established methods. The new method is based on room-temperature measurements of gas diffusion in graphite samples that are made at pressures < 100 Torr. In these conditions flow in macropores is in the transition regime between Knudsen and bulk or molecular diffusion [4]. This compares with established fluid flow methods for pore structure determination which work at higher pressures where transport is mainly in the bulk regime. The structure of this paper is as follows. First, a simple theory of gaseous diffusion in porous solids is outlined. From this theory, a generalised, transition diffusion equation is obtained which lays the ground for experimental measurements. The second part of the paper deals briefly with the apparatus that was built to measure transition diffusion in graphites. Third, results from the new apparatus - essentially pore size distributions - are reported and discussed, and compared with results from established pore structure techniques, such as porosimetry 2. THEORY OF GASEOUS DIFFUSION IN POROUS SOLIDS A gas flow conductivity, C, may be defined as the molar flux through a solid sample per unit concentration gradient. For component i in a gas mixture, C may be written as 329 C =JlLL2_ (!) 1 Ac, / L where J! is the molar flow rate of i through the sampie, A is the cross-section area of the sample perpendicular to the macroscopic direction of flow and Ac; is the concentration difference of i across the length, LT of the sample parallel to flow The gas flow conductivity is a measure of the ease with which a component of a gas mixture flows through a solid, and is analogous to the thermal conductivity for the flow of heat. For the isothermal, isobaric, steady-state diffusion of component i in an ideal mixture of ideal gases, Eqn (1) becomes r =D =—* (T\ where D! is the effective diffusivity of the solid for component i. R is the gas constant, T is absolute temperature, p is pressure and Ayj is the mole fraction difference of i across L. The effective diffusivity depends on the flowing gas, the pore and surface structure of the solid and on environmental conditions (pressure, temperature and external gas composition). Experimentally, Dj can be calculated from Eqn (2) using experimental measurements of Ji, T, p and Ay; and sample dimensions. A cornerstone of this paper is the relationship between effective diffusivity and pore structure, using which experimental measurements of the former can yield estimates of the latter. This relationship involves a model of gaseous diffusion in porous solids. The model used here for nuclear graphites, which was originally proposed by Hewitt [5] and has more recently been described critically in [3], is as follows. The first part of the model refers to the pore structure. The transport porosity in graphites, i. e., that part of the accessible or open porosity through which fluid flows in the steady state, is assumed to comprise Nv non-intersecting, straight, cylindrical capillaries per unit volume. Isotropy is also assumed, so that there are Nv / 3 capillaries per face of a unit cube of material. The length, 1, of each capillary is assumed to be constant but may exceed the length, L, of the sample, by a factor q = 1 / L > 1, called the tortuosity. Finally, capillary radii, r, are assume to be distributed with a probability density function, f(r). In this model, the fractional transport pore volume, Vj, is given by 2 VT =7tNv < r >q (3) where < > denotes a mean value. It should be recognised that this model is a necessary simplification of the complicated pore structure in graphites. The second part of the model of gaseous diffusion in porous solids refers to flow in capillaries. From simple kinetic theory arguments, see [4], the isothermal, steady-state molar flow rate, ji, of a component i in an inert, ideal, binary mixture of ideal gases diffusing through a single, straight capillary of radius r and length 1» r is given by = 7trpDm rinyl2mKil Jl amRTl U-ainyli+Dm/DKJ where D^ is the bulk or molecular binary diffusion coefficient for the mixture (i = 1, n = 2 or i = 2, n =1). The sub-subscripts 1 and 2 for mole fraction, y, refer to opposite ends of the capillary. The flow rate ratio a is given by 330 (5) where M is molecular weight. Assuming completely diffuse (random) reflection of molecules after collision with pore walls, the Knudsen diffusion coefficient DK is given by DK, = | r < v, > (6) where the mean molecular speed, < v; >, of gas molecules is given by < v, > = ^RT/TIM,) (7) It is useful at this stage to note that bulk or molecular diffusion refers to flow that involves only intermolecular collisions in the gas phase (i. e., for high pressures and large pores) and Knudsen diffusion refers to flow that only involves molecule-pore wall collisions (low pressures, small pores). Transition diffusion refers to the case where both gas-gas and gas-solid collisions are important in flow. It should also be noted that capillary diffusion, Eq (4), depends in a complex way on pore radius, mainly due to the radius-dependence of the Knudsen diffusion coefficient in the logarithmic term. The total molar flow rate, Ji, through an area A of material is simply the sum of flows through each of the (Nv A / 3) capillaries in this area. Accounting for the distribution of pore radii, f(r), this gives (8) Combining Eqns (2), (4) and (8), remembering that q = 1 / L and for convenience defining the diffusivity ratio X, = D i / D in, gives two equations S() (9) J +D ainAy1 Q U /D J which in the model diffusivity ratio equation, and JRTL (10) ApAyiD m which is the experimental diffusivity ratio equation. A detailed derivation of these equations in contained in [6], together with a commentary on the properties of the generalised transition diffusion equation, Eqn (9). But here it is sufficient to note that, in principle, it appears to be possible to estimate the unknown, characteristic pore structure function [(Ny / q) f(r)] from the use of Eqn (9) as a model for experimental values of diffusivity ratio that are calculated using Eqn (10). The following sections summarise how this estimation is carried out. 331 3 EXPERIMENTAL Experimentally the aim is to measure the factors on the right hand side of Eq (10) and hence to calculate the diffusivity ratio as a function of pressure. In this work the only unknown is the molar flow rate since all other factors are fixed (R = 8.314 J K"1 mol" , T = 300 K, L / A « 0.012, Ay; « 1 and Din can be calculated for binary gases from empirical functions of p and T [6]). For He-Ar diffusion, it turns out for this work that X, /1000 = 3.914 (V^imols"1), i = HeorAr (11) Measurements of molar flow rate for each gas were made using a Wicke-Kallenbach cell [3], that operated at pressures < 100 Torr (13.3 kPa), in which conditions mean free path calculations indicated that transition diffusion would occur in the graphites. In this cell, pure He was directed through a mass flowmeter to one side of a sample, pure Ar was directed to the other side through another mass flowmeter, and the amounts of each gas diffusing through the sample into the other stream were determined using a mass spectrometer. Details of the apparatus that was built specially for this work are in [7]. The three nuclear-grade graphites selected for study are: AXF (a moulded, petroleum coke filler-coal tar pitch binder graphite made by POCO Graphite Inc., Decateur, TX, USA); Isograph-50 or IG-50 (an isostatically-pressed graphite made in Osaka, Japan by Toyo Tanso Co. Ltd.) and ATJ (similar to AXP but made by Union Carbide in Sheffield, UK). 4. RESULTS AND DISCUSSION Fig.
Load more

Recommended publications
  • Air-Sea Gas Exchange
    Air-Sea Gas Exchange OCN 623 – Chemical Oceanography 17 March 2015 Readings: Libes, Chapter 6 – pp. 158 -168 Wanninkhof et al. (2009) Advances in quantifying air-sea gas exchange and environmental forcing, Annual Reviews of Marine Science © 2015 David Ho and Frank Sansone Overview • Introduction • Theory/models of gas exchange • Mechanisms/lab studies of gas exchange • Field measurements • Parameterizations Why do we care about air-water gas exchange? . Globally, to understand cycling of biogeochemically important trace gases (e.g., CO2, DMS, CH4, N2O, CH3Br) . Regionally and locally . To understand indicators of water quality (e.g., dissolved O2) . To predict evasion rates of volatile pollutants (e.g., VOCs, PAHs, PCBs) Factors Influencing Air-water Transfer of Mass, Momentum, Heat From SOLAS Science Plan and Implementation Strategy Basic flux equation Concentration gradient Flux (mol cm-3) (mol cm-2 s-1) “driving force” Gas transfer velocity (cm s-1) “resistance” k: Gas transfer velocity, piston velocity, gas exchange coefficient Cw: Concentration in water near the surface Ca: Concentration in air near the surface α: Ostwald solubility coefficient (temp-compensated Bunsen coeff) Basic conceptual model Turbulent atmosphere C Atmosphere a Laminar Stagnant Cas Boundary Layer zFilm Cws (transport by Ocean molecular diffusion) Cw Turbulent bulk liquid F = k(Cw-αCa) Air/water side resistance Magnitude of typical Ostwald solubility coefficients He ≈ 0.01 Water-side resistance O2 ≈ 0.03 CO2 ≈ 0.7 DMS ≈ 10 Air- and water-side resistance CH3Br
    [Show full text]
  • Modes of Mass Transfer Chapter Objectives
    MODES OF MASS TRANSFER CHAPTER OBJECTIVES - After you have studied this chapter, you should be able to: 1. Explain the process of molecular diffusion and its dependence on molecular mobility. 2. Explain the process of capillary diffusion 3. Explain the process of dispersion in a fluid or in a porous solid. 4. Understand the process of convective mass transfer as due to bulk flow added to diffusion or dispersion. 5. Explain saturated flow and unsaturated capillary flow in a porous solid 6. Have an idea of the relative rates of the different modes of mass transfer. 7. Explain osmotic flow. KEY TERMS diffusion, diffusivity, and. diffusion coefficient dispersion and dispersion coefficient hydraulic conductivity capillarity osmotic flow mass and molar flux Fick's law Darcy's law 1. A Primer on Porous Media Flow Physical Interpretation of Hydraulic Conductivity K and Permeability k Figure 1. Idealization of a porous media as bundle of tubes of varying diameter and tortuosity. Capillarity and Unsaturated Flow in a Porous Media Figure 2.Capillary attraction between the tube walls and the fluid causes the fluid to rise. Osmotic Flow in a Porous Media Figure 3.Osmotic flow from a dilute to a concentrated solution through a semi-permeable membrane. 2. Molecular Diffusion • In a material with two or more mass species whose concentrations vary within the material, there is tendency for mass to move. Diffusive mass transfer is the transport of one mass component from a region of higher concentration to a region of lower concentration. Physical interpretation of diffusivity Figure 4. Concentration profiles at different times from an instantaneous source placed at zero distance.
    [Show full text]
  • Visualizing Molecular Diffusion Through Passive Permeability
    COCHBI-1072; NO. OF PAGES 9 Available online at www.sciencedirect.com Visualizing molecular diffusion through passive permeability barriers in cells: conventional and novel approaches 1 1 1,2 1,3 Yu-Chun Lin , Siew Cheng Phua , Benjamin Lin and Takanari Inoue Diffusion barriers are universal solutions for cells to achieve exist at a variety of cellular structures, including the distinct organizations, compositions, and activities within a nuclear envelope, the annulus of spermatozoa, the lead- limited space. The influence of diffusion barriers on the ing edge of migrating cells, the cleavage furrow of divid- spatiotemporal dynamics of signaling molecules often ing cells, and the budding neck of yeast, as well as in determines cellular physiology and functions. Over the years, cellular extensions such as primary cilia, dendritic spines, the passive permeability barriers in various subcellular locales and the initial segment of the neuronal axon [1 ,6 ,7]. have been characterized using elaborate analytical techniques. While some diffusion barriers exist constitutively in cells, In this review, we will summarize the current state of knowledge others are highly dynamic. The importance of diffusion on the various passive permeability barriers present in barriers is further underscored by the various human mammalian cells. We will conclude with a description of several diseases which result from their dysfunction [3,6 ,8,9]. conventional techniques and one new approach based on chemically inducible diffusion trap (CIDT) for probing Diffusion barriers can be categorized into two major permeable barriers. classes based on the substrates they affect: lateral diffu- Addresses sion barriers and permeability barriers. Lateral diffusion 1 Department of Cell Biology, Center for Cell Dynamics, School of barriers localize in membranes and restrict the movement Medicine, Johns Hopkins University, United States 2 of molecules within the membrane plane such as trans- Department of Biomedical Engineering, Johns Hopkins University, membrane proteins and membrane lipids [1 ].
    [Show full text]
  • On the Molecular Diffusion Coefficients of Dissolved , And
    Available online at www.sciencedirect.com Geochimica et Cosmochimica Acta 75 (2011) 2483–2498 www.elsevier.com/locate/gca À On the molecular diffusion coefficients of dissolved CO2; HCO3 , 2À and CO3 and their dependence on isotopic mass Richard E. Zeebe ⇑ School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 1000 Pope Road, MSB 504, Honolulu, HI 96822, USA Received 21 August 2010; accepted in revised form 7 February 2011; available online 13 February 2011 Abstract À The molecular diffusion coefficients of dissolved carbon dioxide ðCO2Þ, bicarbonate ion ðHCO3 Þ, and carbonate ion 2À ðCO3 Þ are fundamental physico-chemical constants and are of practical significance in various disciplines including geochem- istry, biology, and medicine. Yet, very little experimental data is available, for instance, on the bicarbonate and carbonate ion diffusion coefficient. Furthermore, it appears that no information was hitherto available on the mass-dependence of the dif- fusion coefficients of the ionic carbonate species in water. Here I use molecular dynamics simulations to study the diffusion of the dissolved carbonate species in water, including their dependence on temperature and isotopic mass. Based on the simu- À 2À lations, I provide equations to calculate the diffusion coefficients of dissolved CO2; HCO3 , and CO3 over the temperature range from 0° to 100 °C. The results indicate a mass-dependence of CO2 diffusion that is consistent with the observed 12 13 CO2= CO2 diffusion ratio at 25 °C. No significant isotope fractionation appears to be associated with the diffusion of À 2À the naturally occurring isotopologues of HCO3 and CO3 at 25 °C.
    [Show full text]
  • Diffusion in Porous Media – Measurement and Modeling
    Fakultät Maschinenwesen | Institut für Energietechnik | Professur für Technische Thermodynamik Institutslogo Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 09.12.2011 Diffusion in porous media – measurement and modeling Cornelia Breitkopf for personal use only! Diffusion – what is that? Diffusion – what is that? From G. Gamow „One, Two, Three…Infinity“ The Viking Press, New York, 1955. Dresden, Frauenkirche 2010 Diffusion – application to societies in: Diffusion – application to societies Diffusion – first experiment Robert Brown Robert Brown, (1773-1958) “Scottish botanist best known for his description of the natural continuous motion of minute particles in solution, which came to be called Brownian movement.” http://www.britannica.com/EBchecked/topic/81618/Robert-Brown Diffusion – first experiment Robert Brown “In 1827, while examining grains of pollen of the plant Clarkia pulchella suspended in water under a microscope, Brown observed minute particles, now known to be amyloplasts (starch organelles) and spherosomes (lipid organelles), ejected from the pollen grains, executing a continuous jittery motion. He then observed the same motion in particles of inorganic matter, enabling him to rule out the hypothesis that the effect was life- related…..” http://en.wikipedia.org/wiki/Robert_Brown_(botanist) Diffusion – short history http://www.uni-leipzig.de/diffusion/pdf/volume4/diff_fund_4(2006)6.pdf Diffusion – short history A. E. Fick “Adolf Eugen Fick (1829-1901) was a German physiologist. He started to study mathematics and physics, but then realized he was more interested in medicine. He earned his doctorate in medicine at Marburg in 1851.” “In 1855 he introduced Fick's law of diffusion, which governs the diffusion of a gas across a fluid membrane.” http://en.wikipedia.org/wiki/Adolf_Fick Diffusion – short history Albert Einstein (1879-1955) Marian von Smoluchowski (1872-1917 was a phyiscist.
    [Show full text]
  • Augmenting CO2 Absorption Flux Through a Gas–Liquid Membrane Module by Inserting Carbon-Fiber Spacers
    membranes Article Augmenting CO2 Absorption Flux through a Gas–Liquid Membrane Module by Inserting Carbon-Fiber Spacers Luke Chen 1 , Chii-Dong Ho 2,*, Li-Yang Jen 2, Jun-Wei Lim 3,* and Yu-Han Chen 2 1 Department of Water Resources and Environmental Engineering, Tamkang University, Tamsui, New Taipei 251, Taiwan; [email protected] 2 Department of Chemical and Materials Engineering, Tamkang University, Tamsui, New Taipei 251, Taiwan; [email protected] (L.-Y.J.); [email protected] (Y.-H.C.) 3 Department of Fundamental and Applied Sciences, HICoE-Centre for Biofuel and Biochemical Research, Institute of Self-Sustainable Building, Universiti Teknologi PETRONAS, Seri Iskandar, Perak Darul Ridzuan 32610, Malaysia * Correspondence: [email protected] (C.-D.H.); [email protected] (J.-W.L.); Tel.: +886-2-26215656 (ext. 2724) (C.-D.H.) Received: 18 September 2020; Accepted: 19 October 2020; Published: 22 October 2020 Abstract: We investigated the insertion of eddy promoters into a parallel-plate gas–liquid polytetrafluoroethylene (PTFE) membrane contactor to effectively enhance carbon dioxide absorption through aqueous amine solutions (monoethanolamide—MEA). In this study, a theoretical model was established and experimental work was performed to predict and to compare carbon dioxide absorption efficiency under concurrent- and countercurrent-flow operations for various MEA feed flow rates, inlet CO2 concentrations, and channel design conditions. A Sherwood number’s correlated expression was formulated, incorporating experimental data to estimate the mass transfer coefficient of the CO2 absorption in MEA flowing through a PTFE membrane. Theoretical predictions were calculated and validated through experimental data for the augmented CO2 absorption efficiency by inserting carbon-fiber spacers as an eddy promoter to reduce the concentration polarization effect.
    [Show full text]
  • Effect of Molecular Structure on Diffusion of Alcohols Through Type-A Zeolite Pores (0.5 Nm)
    Journal of Materials Science and Engineering A 11 (4-6) (2021) 48-55 doi: 10.17265/2161-6213/2021.4-6.003 D DAVID PUBLISHING Effect of Molecular Structure on Diffusion of Alcohols through Type-A Zeolite Pores (0.5 nm) Bryan Fernández-Solano and Julio F. Mata-Segreda Biomass Laboratory, School of Chemistry, University of Costa Rica 11501-2060, Costa Rica Abstract: Drying kinetics for alcohol-soaked type-A zeolite (pore size 0.5 nm) was determined at 50 °C for 12 small-molecule alcohols (from C1 to C10). The second-phase of drying of wet porous materials reports on the mass-transfer characteristics within the solid matrices. This stage follows pseudo first-order kinetics (k1), and the second-order rate constant k2 = k1/(fluxional area) was found to correlate with the surface tension of the liquids imbibing the solid matrix (p < 0.002). k2 values decrease along the homologous linear alcohols, and branched-chain alcohols diffuse faster than their linear analogues due to their lower surface tensions. No independent contribution was found from the molecular size of the alcohols in the experiment reported here. Characteristic velocity and enthalpy of vaporisation of the liquids were not found to be significant independent variables, either. The find agrees with the notion that liquid movement in pores is governed during the drying processes by the liquid chemical potential gradient between the pore space and gas phase above the porous particle surfaces, this gradient being a function of the molecular cohesion of -1 -2 the moving liquid front (surface tension, ). The results can be expressed by the linear Gibbs-energy relation log (k2/s ·m ) = (2.5 ± 0.5) - (1.6 ± 0.2) 102 (/J·m-2).
    [Show full text]
  • Determination of Diffusion Coefficient in Droplet Evaporation Experiment
    Determination of Diffusion Coefficient in Droplet Evaporation Experiment Using Response Surface Method Xue Chen, Xun Wang, Paul G. Chen, Qiusheng Liu To cite this version: Xue Chen, Xun Wang, Paul G. Chen, Qiusheng Liu. Determination of Diffusion Coefficient in Droplet Evaporation Experiment Using Response Surface Method. Microgravity Science and Technology, Springer, 2018, 30, pp.675-682. 10.1007/s12217-018-9645-2. hal-02112826 HAL Id: hal-02112826 https://hal.archives-ouvertes.fr/hal-02112826 Submitted on 29 Apr 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Determination of Diffusion Coefficient in Droplet Evaporation Experiment Using Response Surface Method Xue Chen1 · Xun Wang2 · Paul G. Chen3 · Qiusheng Liu4,5 Abstract Evaporation of a liquid droplet resting on a heated substrate is a complex free-surface advection-diffusion problem, in which the main driving force of the evaporation is the vapor concentration gradient across the droplet surface. Given the uncertainty associated with the diffusion coefficient of the vapor in the atmosphere during space evaporation experiments due to the environmental conditions, a simple and accurate determination of its value is of paramount importance for a better understanding of the evaporation process.
    [Show full text]
  • Membrane Gas Separation
    Membrane Gas Separation Membrane Gas Separation YURI YAMPOLSKII A.V. Topchiev Institute of Petrochemical Synthesis, Moscow, Russia BENNY FREEMAN University of Texas at Austin, Austin, TX, USA A John Wiley & Sons, Ltd., Publication This edition fi rst published 2010 © (2010) John Wiley & Sons Ltd Registered offi ce John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offi ces, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identifi ed as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered.
    [Show full text]
  • Models for Air–Water Gas Transfer
    Tellus (1984), 36B, 92-100 Models for air-water gas transfer: an experimental investigation By KIM HOLMEN, Department of Meteorology,' University of Stockholm, Arrhenius Laboratory, S-106 91 Stockholm, Sweden and PETER LISS, School of Environmental Sciences, University of East Anglia, Norwich, NR4 7TJ, England (Manuscript received August 16; in final form November 14, 1983) ABSTRACT The air-water transfer velocities for H,, He and Xe have been measured simultaneously in laboratory-tank experiments. Using average values from the existing literature data for the molecular diffusivities of the gases, the transfer velocities are found to vary with the diffusivity raised to the power 0.57. This exponent is in reasonable agreement with the findings from other laboratories, as well as field studies, provided average diffusivities are used consistently. Although interpretation is limited by uncertainties in presently available diffusion coefficients, the results may be interpreted as supportive of both the surface-renewal and boundary-layer models of air-water gas exchange, but they provide little evidence for the appropriateness of the film model. 1. Introduction In it, the main body of the fluid (liquid or gaseous) is assumed to be well mixed, the rate of interfacial The air-water transfer of gases which are transfer being determined by molecular diffusion of sparingly soluble in water and do not react rapidly the gas molecules across a stagnant layer (or film) in the aqueous phase is controlled by processes in of fluid (thickness z) adjacent to the surface. In this the near-surface water (Liss, 1973). Gases for model, the rate of gas exchange, expressed in terms which this applies include 0,, CO,, the inert gases, of a transfer velocity k, (defined as the flux of gas CO, CH,, CHJ, (CH,),S, freons and other low 'x' per unit of concentration gradient driving its molecular weight halocarbons.
    [Show full text]
  • Investigating Fuel-Cell Transport Limitations Using Hydrogen Limiting Current
    Lawrence Berkeley National Laboratory Recent Work Title Investigating fuel-cell transport limitations using hydrogen limiting current Permalink https://escholarship.org/uc/item/1f9147nv Journal International Journal of Hydrogen Energy, 42(19) ISSN 0360-3199 Authors Spingler, FB Phillips, A Schuler, T et al. Publication Date 2017-05-11 DOI 10.1016/j.ijhydene.2017.01.036 License https://creativecommons.org/licenses/by-nc-nd/4.0/ 4.0 Peer reviewed eScholarship.org Powered by the California Digital Library University of California Investigating Fuel-Cell Transport Limitations using Hydrogen Limiting Current Franz B. Spingler, Adam Phillips, Tobias Schuler, Michael C. Tucker, Adam Z. Weber Energy Conversion Group, Energy Technologies Area, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley CA 94720, USA Reducing mass-transport losses in polymer-electrolyte fuel cells (PEFCs) is essential to increase their power density and reduce overall stack cost. At the same time, cost also motivates the reduction in expensive precious-metal catalysts, which results in higher local transport losses in the catalyst layers. In this paper, we use a hydrogen-pump limiting- current setup to explore the gas-phase transport losses through PEFC catalyst layers and various gas-diffusion and microporous layers. It is shown that the effective diffusivity in the gas-diffusion layers is a strong function of liquid saturation. In addition, it is shown how the catalyst layer unexpectedly contributes significantly to the overall measured transport resistance. This is especially true at low catalyst loadings. It is also shown how the various losses can be separated into different mechanisms including diffusional processes and mass- dependent and independent ones, where the data suggests that a large part of the transport resistance in CLs cannot be attributed to a gas-phase diffusional process.
    [Show full text]
  • 1 3. Molecular Mass Transport 3.1 Introduction to Mass Transfer 3.2
    3. Molecular mass transport 3.1 Introduction to mass transfer 3.2 Properties of mixtures 3.2.1 Concentration of species 3.2.2 Mass Averaged velocity 3.3 Diffusion flux 3.3.1 Pick’s Law 3.3.2 Relation among molar fluxes 3.4 Diffusivity 3.4.1 Diffusivity in gases 3.4.2 Diffusivity in liquids 3.4.3 Diffusivity in solids 3.5 Steady state diffusion 3.5.1 Diffusion through a stagnant gas film 3.5.2 Pseudo – steady – state diffusion through a stagnant gas film. 3.5.3 Equimolar counter diffusion. 3.5.4 Diffusion into an infinite stagnant medium. 3.5.5 Diffusion in liquids 3.5.6 Mass diffusion with homogeneous chemical reaction. 3.5.7 Diffusion in solids 3.6 Transient Diffusion. 3.1 Introduction of Mass Transfer When a system contains two or more components whose concentrations vary from point to point, there is a natural tendency for mass to be transferred, minimizing the concentration differences within a system. The transport of one constituent from a region of higher concentration to that of a lower concentration is called mass transfer. The transfer of mass within a fluid mixture or across a phase boundary is a process that plays a major role in many industrial processes. Examples of such processes are: (i) Dispersion of gases from stacks (ii) Removal of pollutants from plant discharge streams by absorption (iii) Stripping of gases from waste water (iv) Neutron diffusion within nuclear reactors (v) Air conditioning Many of air day-by-day experiences also involve mass transfer, for example: 1 (i) A lump of sugar added to a cup of coffee eventually dissolves and then eventually diffuses to make the concentration uniform.
    [Show full text]