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• W2087386124 abstract "Abstract Analytical solutions with algebraic expressions are proposed for one-dimensional nonlinear mass diffusion problems. The solutions proposed to solve sorption/desorption problems are rigorously exact for piecewise linear isotherms. They provide an efficient methodology to devise analytical solutions to nonlinear isotherms, and instantly time-varying boundary conditions, with arbitrary accuracy. An exact solution is calculated for each linear piece of the isotherm and is then propagated iteratively to the next linear piece. For end-user convenience and efficiency, three exact analytical expansions are proposed: a new short and intermediate contact time expansion obtained using the Laplace transform (erfc solution), a modified version of Eq. (33) in Sagiv (2002) with improved stability (Sagiv solution), and a new expansion with a decreasing energy norm (energy solution). All expansions are compared in terms of their accuracy and number of terms for typical nonlinear isotherms, mass Biot numbers and volume ratios covering a broad range of applications. When the thermodynamic conditions are changed at the interface, only the “erfc” and the “energy” solutions retain overall accuracy (machine precision) with few terms (" @default.
• W2087386124 created "2016-06-24" @default.
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• W2087386124 date "2013-08-01" @default.
• W2087386124 modified "2023-10-11" @default.
• W2087386124 title "Extension to nonlinear adsorption isotherms of exact analytical solutions to mass diffusion problems" @default.
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• W2087386124 doi "https://doi.org/10.1016/j.ces.2013.05.017" @default.
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