A Nonlinear Diffusion Problem Relevant to Desalination by Reverse Osmosis
Various techniques are used to obtain approximate solutions to the one-dimensional, time-dependent diffusion equation in a semi-infinite, incompressible medium, subject to nonlinear boundary conditions that describe flow through a semipermeable membrane across which is applied a constant difference...
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| Published in | SIAM journal on applied mathematics Vol. 17; no. 1; pp. 59 - 73 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.1969
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0036-1399 1095-712X |
| DOI | 10.1137/0117006 |
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| Abstract | Various techniques are used to obtain approximate solutions to the one-dimensional, time-dependent diffusion equation in a semi-infinite, incompressible medium, subject to nonlinear boundary conditions that describe flow through a semipermeable membrane across which is applied a constant difference in hydrostatic pressure. A term describing the convective motion is included in the diffusion equation. A convective-diffusive region, in which time derivatives are negligible, develops and grows in the vicinity of the membrane, while a time-dependent diffusive region in which convection is negligible is established at large distances from the membrane. Theoretically predicted membrane fluxes are shown to be in reasonable agreement with experiment. |
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| AbstractList | Various techniques are used to obtain approximate solutions to the one-dimensional, time-dependent diffusion equation in a semi-infinite, incompressible medium, subject to nonlinear boundary conditions that describe flow through a semipermeable membrane across which is applied a constant difference in hydrostatic pressure. A term describing the convective motion is included in the diffusion equation. A convective-diffusive region, in which time derivatives are negligible, develops and grows in the vicinity of the membrane, while a time-dependent diffusive region in which convection is negligible is established at large distances from the membrane. Theoretically predicted membrane fluxes are shown to be in reasonable agreement with experiment. |
| Author | Williams, F. A. |
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| Cites_doi | 10.1002/aic.690130611 |
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| Copyright | Copyright 1969 Society for Industrial and Applied Mathematics [Copyright] © 1969 © Society for Industrial and Applied Mathematics |
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| References | R5 Udall S. L. (R3) Rickles R. M. (R2) 1966; 73 Rickles R. M. (R1) 1966; 73 |
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| SubjectTerms | Asymptotic value Boundary conditions Convection Desalination Fresh water Iterative solutions Laplace transforms Mathematical constants Osmosis Power series Reverse osmosis Salt Saltwater Water |
| Title | A Nonlinear Diffusion Problem Relevant to Desalination by Reverse Osmosis |
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