Mason–Weaver theory: Revised and extended for a semi-infinite domain
Mason and Weaver developed equations to describe small particles settling under the influence of gravity and Brownian motion, including the limiting case for an infinitely deep suspension. We encountered this common convection–diffusion equation and no-flux boundary conditions in a model for dynamic...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2022-07-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0100060 |
| _version_ | 1818487084476792832 |
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| author | Ziqiu Chen Baron Peters |
| author_facet | Ziqiu Chen Baron Peters |
| author_sort | Ziqiu Chen |
| collection | DOAJ |
| description | Mason and Weaver developed equations to describe small particles settling under the influence of gravity and Brownian motion, including the limiting case for an infinitely deep suspension. We encountered this common convection–diffusion equation and no-flux boundary conditions in a model for dynamics of adsorbed polymers in dead end pores of a depolymerization catalyst. Close examination reveals that the Mason–Weaver solution is not correct for the infinite domain with a non-uniform initial condition. In this paper, we obtain the time dependent Green’s function for the no flux boundary condition and also for a more general reactive boundary condition. We demonstrate how the results provide solutions, via superposition, which provide solutions for several boundary conditions and all initial conditions. |
| first_indexed | 2024-12-10T16:32:39Z |
| format | Article |
| id | doaj.art-32ab7a11291a419cbf129ee529446de4 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-12-10T16:32:39Z |
| publishDate | 2022-07-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-32ab7a11291a419cbf129ee529446de42022-12-22T01:41:30ZengAIP Publishing LLCAIP Advances2158-32262022-07-01127075215075215-510.1063/5.0100060Mason–Weaver theory: Revised and extended for a semi-infinite domainZiqiu Chen0Baron Peters1Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USAChemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USAMason and Weaver developed equations to describe small particles settling under the influence of gravity and Brownian motion, including the limiting case for an infinitely deep suspension. We encountered this common convection–diffusion equation and no-flux boundary conditions in a model for dynamics of adsorbed polymers in dead end pores of a depolymerization catalyst. Close examination reveals that the Mason–Weaver solution is not correct for the infinite domain with a non-uniform initial condition. In this paper, we obtain the time dependent Green’s function for the no flux boundary condition and also for a more general reactive boundary condition. We demonstrate how the results provide solutions, via superposition, which provide solutions for several boundary conditions and all initial conditions.http://dx.doi.org/10.1063/5.0100060 |
| spellingShingle | Ziqiu Chen Baron Peters Mason–Weaver theory: Revised and extended for a semi-infinite domain AIP Advances |
| title | Mason–Weaver theory: Revised and extended for a semi-infinite domain |
| title_full | Mason–Weaver theory: Revised and extended for a semi-infinite domain |
| title_fullStr | Mason–Weaver theory: Revised and extended for a semi-infinite domain |
| title_full_unstemmed | Mason–Weaver theory: Revised and extended for a semi-infinite domain |
| title_short | Mason–Weaver theory: Revised and extended for a semi-infinite domain |
| title_sort | mason weaver theory revised and extended for a semi infinite domain |
| url | http://dx.doi.org/10.1063/5.0100060 |
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