{"id":104,"date":"2021-10-02T23:37:32","date_gmt":"2021-10-02T23:37:32","guid":{"rendered":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/?post_type=part&p=104"},"modified":"2022-01-10T19:23:24","modified_gmt":"2022-01-10T19:23:24","slug":"flux-equations","status":"publish","type":"part","link":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/part\/flux-equations\/","title":{"raw":"5 Flux Equations","rendered":"5 Flux Equations"},"content":{"raw":"
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With Equation 14<\/a> now understood in the context of conservation of momentum, we replace partial pressure, p<\/em>A<\/em><\/sub>, with the more familiar molar concentration, C<\/em>A<\/em><\/sub> and use Equation 10<\/a> to replace J<\/em>A<\/em><\/sub> and obtain Equation 22.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle -D\\frac{dC_{A}}{dl}=\\left ( x_{B}N_{A}^{D}-x_{A}N_{B}^{D} \\right )+\\frac{D}{D_{A}^{K}}N_{A}^{D}[\/latex]<\/td>\r\n(22)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Equation 22 and the corresponding equation for species B<\/em> (interchange the subscripts) apply in both the molecular and transition regimes under both isobaric and non-isobaric conditions. The total diffusive fluxes are expressed by Equations 20<\/a> and 21<\/a> for the non-isobaric and isobaric condition, respectively.<\/p>\r\n\r\n<\/div>","rendered":"

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With Equation 14<\/a> now understood in the context of conservation of momentum, we replace partial pressure, p<\/em>A<\/em><\/sub>, with the more familiar molar concentration, C<\/em>A<\/em><\/sub> and use Equation 10<\/a> to replace J<\/em>A<\/em><\/sub> and obtain Equation 22.<\/a><\/p>\n\n\n\n
<\/td>\n\"\displaystyle -D\frac{dC_{A}}{dl}=\left ( x_{B}N_{A}^{D}-x_{A}N_{B}^{D} \right )+\frac{D}{D_{A}^{K}}N_{A}^{D}\"<\/td>\n(22)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Equation 22 and the corresponding equation for species B<\/em> (interchange the subscripts) apply in both the molecular and transition regimes under both isobaric and non-isobaric conditions. The total diffusive fluxes are expressed by Equations 20<\/a> and 21<\/a> for the non-isobaric and isobaric condition, respectively.<\/p>\n<\/div>\n","protected":false},"parent":0,"menu_order":5,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-104","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/wp-json\/pressbooks\/v2\/parts\/104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":7,"href":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/wp-json\/pressbooks\/v2\/parts\/104\/revisions"}],"predecessor-version":[{"id":400,"href":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/wp-json\/pressbooks\/v2\/parts\/104\/revisions\/400"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/wp-json\/wp\/v2\/media?parent=104"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/wp-json\/wp\/v2\/contributor?post=104"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/wp-json\/wp\/v2\/license?post=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}