title: Numerical solution of the Polanyi-DR isotherm in linear driving force models.
abstract: The Polanyi-Dubinin-Radushkevich isotherm has proven useful for modeling the adsorption of volatile organic compounds on microporous materials such as activated carbon. When embedded in a larger dynamic simulation--e.g., of whole-building pollutant transport--it is important to solve the sorption relations as quickly as possible. This work compares numerical methods for solving the Polanyi-DR model, in cases where transport to the surface is assumed linear in the bulk-to-surface concentration differences. We focus on developing numerically stable algorithms that converge across a wide range of inputs, including zero concentrations, where the isotherm is undefined. We identify several methods, including a modified Newton-Raphson search, that solve the system 3-4 times faster than simple bisection. Finally, we present a rule of thumb for identifying when boundary-layer diffusion limits the transport rate enough to justify reducing the model complexity.
authors.affiliation: Indoor Environment Department, Lawrence Berkeley National Laboratory, Berkeley, California, United States. dmlorenzetti@lbl.gov
authors.forename: David M
authors.initials: DM
authors.lastname: Lorenzetti
authors.forename: Michael D
authors.initials: MD
authors.lastname: Sohn
mesh_terms: D000327:Adsorption; D000393:Air Pollutants / Q000737:chemistry; D000465:Algorithms; D008962:Models, Theoretical; D056004:Molecular Dynamics Simulation
chemical_list: D000393:Air Pollutants