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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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 17; no. 1; pp. 59 - 73
Main Author Williams, F. A.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.1969
Subjects
Asymptotic value
Boundary conditions
Convection
Desalination
Fresh water
Iterative solutions
Laplace transforms
Mathematical constants
Osmosis
Power series
Reverse osmosis
Salt
Saltwater
Water
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ISSN0036-1399
1095-712X
DOI10.1137/0117006

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Summary: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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ISSN:0036-1399
1095-712X
DOI:10.1137/0117006