Solving the inverse Knudsen problem: Gas diffusion in random fibrous media

Journal of Membrane Science - Tập 620 - Trang 118728 - 2021
Wojciech Szmyt1,2,3,4, Carlos Guerra-Nuñez5, Clemens Dransfeld6, Ivo Utke5
1Institute of Polymer Engineering, FHNW University of Applied Sciences and Arts Northwestern Switzerland, Klosterzelgstrasse 2, CH 5210, Windisch, Switzerland
2Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, CH 5232, Villigen PSI, Switzerland
3Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
4Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, CH 4056, Basel, Switzerland
5Mechanics of Materials and Nanostructures Laboratory, EMPA Swiss Federal Laboratories for Materials Science and Technology, Feuerwerkerstrasse 39, Thun, CH 3602, Switzerland
6Aerospace Manufacturing Technologies, Delft University of Technology, Kluyverweg 1, 2629, HS Delft, the Netherlands

Tài liệu tham khảo

Chan, 2012, Experimental measurement of effective diffusion coefficient of gas diffusion layer/microporous layer in PEM fuel cells, Electrochim. Acta, 65, 13, 10.1016/j.electacta.2011.12.110 Cash, 2019 Lee, 2014 Gilron, 2002, Knudsen diffusion in microporous carbon membranes with molecular sieving character, J. Membr. Sci., 209, 339, 10.1016/S0376-7388(02)00074-1 Phattaranawik, 2003, Effect of pore size distribution and air flux on mass transport in direct contact membrane distillation, J. Membr. Sci., 215, 75, 10.1016/S0376-7388(02)00603-8 Li, 2016, Influence of microporous membrane properties on the desalination performance in direct contact membrane distillation, J. Membr. Sci., 513, 280, 10.1016/j.memsci.2016.04.015 Kim, 2017, Self-adjusting, combined diffusion in direct contact and vacuum membrane distillation, J. Membr. Sci., 543, 255, 10.1016/j.memsci.2017.08.059 2006 Elam, 2012, Coatings on high aspect ratio structures, 227 Yazdani, 2014, Modeling and optimization of atomic layer deposition processes on vertically aligned carbon nanotubes, Beilstein J. Nanotechnol., 5, 234, 10.3762/bjnano.5.25 Guerra-Nuñez, 2015, Morphology and crystallinity control of ultrathin TiO 2 layers deposited on carbon nanotubes by temperature-step atomic layer deposition, Nanoscale, 7, 10622, 10.1039/C5NR02106E Guerra-Nuñez, 2017, Reaction and growth mechanisms in Al 2 O 3 deposited via atomic layer deposition: elucidating the hydrogen source, Chem. Mater., 29, 8690, 10.1021/acs.chemmater.7b02759 Elam, 2003, Conformal coating on ultrahigh-aspect-ratio nanopores of anodic alumina by atomic layer deposition, Chem. Mater., 15, 3507, 10.1021/cm0303080 Gordon, 2003, A kinetic model for step coverage by atomic layer deposition in narrow holes or trenches, Chem. Vap. Depos., 9, 73, 10.1002/cvde.200390005 Dendooven, 2017, Basics of atomic layer deposition: growth characteristics and conformality, 1 Baxamusa, 2008, Thin polymer films with high step coverage in microtrenches by initiated CVD, Chem. Vap. Depos., 14, 313, 10.1002/cvde.200806713 Li, 2000, Densification of unidirectional carbon–carbon composites by isothermal chemical vapor infiltration, Carbon, 38, 423, 10.1016/S0008-6223(99)00122-0 Sun, 2015, Gas transport mode criteria in ultra-tight porous media, Int. J. Heat Mass Tran., 83, 192, 10.1016/j.ijheatmasstransfer.2014.11.075 Knudsen, 1909, Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren, Ann. Phys., 333, 75, 10.1002/andp.19093330106 Knudsen, 1909, Die Molekularströmung der Gase durch Offnungen und die Effusion, Ann. Phys., 333, 999, 10.1002/andp.19093330505 Knudsen, 1916, Das Cosinusgesetz in der kinetischen Gastheorie, Ann. Phys., 353, 1113, 10.1002/andp.19163532409 Malek, 2003, Knudsen self- and Fickian diffusion in rough nanoporous media, J. Chem. Phys., 119, 2801, 10.1063/1.1584652 Dreyer, 2014, Simulation of gas diffusion in highly porous nanostructures by direct simulation Monte Carlo, Chem. Eng. Sci., 105, 69, 10.1016/j.ces.2013.10.038 Shi, 2012, Knudsen diffusion through cylindrical tubes of varying radii: theory and Monte Carlo simulations, Transport Porous Media, 93, 517, 10.1007/s11242-012-9966-3 Vignoles, 2011, A Brownian motion algorithm for tow scale modeling of chemical vapor infiltration, Comput. Mater. Sci., 50, 1871, 10.1016/j.commatsci.2011.01.031 Feres, 2004, Knudsen's cosine law and random billiards, Chem. Eng. Sci., 59, 1541, 10.1016/j.ces.2004.01.016 Welty, 2015 Ylilammi, 2018, Modeling growth kinetics of thin films made by atomic layer deposition in lateral high-aspect-ratio structures, J. Appl. Phys., 123, 205301, 10.1063/1.5028178 Zheng, 2012, A diffusivity model for gas diffusion through fractal porous media, Chem. Eng. Sci., 68, 650, 10.1016/j.ces.2011.10.031 Levitz, 1993, Knudsen diffusion and excitation transfer in random porous media, J. Phys. Chem., 97, 3813, 10.1021/j100117a030 Szmyt, 2017, Diffusion of dilute gas in arrays of randomly distributed, vertically aligned, high-aspect-ratio cylinders, Beilstein J. Nanotechnol., 8, 64, 10.3762/bjnano.8.7 Shou, 2014, An analytical model for gas diffusion though nanoscale and microscale fibrous media, Microfluid. Nanofluidics, 16, 381, 10.1007/s10404-013-1215-8 Zhu, 2006, Monitoring carbon nanotube growth by formation of nanotube stacks and investigation of the diffusion-controlled kinetics, J. Phys. Chem. B, 110, 5445, 10.1021/jp060027q Tomadakis, 1993, Ordinary and transition regime diffusion in random fiber structures, AIChE J., 39, 397, 10.1002/aic.690390304 Melkote, 1989, Gas diffusion in random-fiber substrates, AIChE J., 35, 1942, 10.1002/aic.690351205 Tomadakis, 1991, Effective Kundsen diffusivities in structures of randomly overlapping fibers, AIChE J., 37, 74, 10.1002/aic.690370107 Poodt, 2017, Effect of reactor pressure on the conformal coating inside porous substrates by atomic layer deposition, J. Vac. Sci. Technol. Vac. Surf. Films., 35, 10.1116/1.4973350 O'Hanlon, 2005 Cieplak, 2000, Molecular dynamics of flows in the Knudsen regime, Phys. Stat. Mech. Its Appl., 287, 153, 10.1016/S0378-4371(00)00353-8 Steckelmacher, 1986, Knudsen flow 75 years on: the current state of the art for flow of rarefied gases in tubes and systems, Rep. Prog. Phys., 49, 1083, 10.1088/0034-4885/49/10/001 Einstein, 1905, Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Ann. Phys., 322, 549, 10.1002/andp.19053220806 von Smoluchowski, 1906, Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen, Ann. Phys., 326, 756, 10.1002/andp.19063261405 Colson, 2019, Statistical method for modeling Knudsen diffusion in nanopores, Phys. Rev. E., 100, 10.1103/PhysRevE.100.062125 2009 Hwang, 2012, Effective-diffusivity measurement of partially-saturated fuel-cell gas-diffusion layers, J. Electrochem. Soc., 159, F683, 10.1149/2.024211jes Burganos, 1998, Gas diffusion in random binary media, J. Chem. Phys., 109, 6772, 10.1063/1.477323 Mu, 2008, Determination of the effective diffusion coefficient in porous media including Knudsen effects, Microfluid, Nanofluidics, 4, 257, 10.1007/s10404-007-0182-3 Zhang, 1994, Evaluation of tortuosity factors and effective diffusivities in biofilms, Water Res., 28, 2279, 10.1016/0043-1354(94)90043-4 Szmyt, 2017, Protective effect of ultrathin alumina film against diffusion of iron into carbon fiber during growth of carbon nanotubes for hierarchical composites investigated by ptychographic X-ray computed tomography, Carbon, 115, 347, 10.1016/j.carbon.2016.12.085 Jin, 2004, Nanofibrillar cellulose aerogels, Colloids Surf. Physicochem. Eng. Asp., 240, 63, 10.1016/j.colsurfa.2004.03.007 He, 2016, Ultra-low thermal conductivity and high strength of aerogels/fibrous ceramic composites, J. Eur. Ceram. Soc., 36, 1487, 10.1016/j.jeurceramsoc.2015.11.021 Clennell, 1997, Tortuosity: a guide through the maze, Geol. Soc. Lond. Spec. Publ., 122, 299, 10.1144/GSL.SP.1997.122.01.18 Puurunen, 2005, Surface chemistry of atomic layer deposition: a case study for the trimethylaluminum/water process, J. Appl. Phys., 97, 121301, 10.1063/1.1940727 Carlsson, 1991, Thermodynamics of the homogeneous and heterogeneous decomposition of trimethylaluminum, monomethylaluminum, and dimethylaluminumhydride: effects of scavengers and ultraviolet-laser photolysis, J. Vac. Sci. Technol. B Microelectron. Nanometer Struct., 9, 2759, 10.1116/1.585642 Nagy, 2019, Membrane gas separation, 457 Breck, 1984