%0 DATA
%A David M., Lorenzetti
%A Michael D., Sohn
%D 2016
%T Numerical Solution of the Polanyi-DR Isotherm in Linear Driving Force Models
%U https://acs.figshare.com/articles/Numerical_Solution_of_the_Polanyi_DR_Isotherm_in_Linear_Driving_Force_Models/2577769
%R 10.1021/es202359j.s001
%2 https://ndownloader.figshare.com/files/4221490
%K sorption relations
%K concentration
%K isotherm
%K model complexity
%K method
%K Numerical Solution
%K transport rate
%K microporous materials
%X 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 simulatione.g., of whole-building pollutant transportit 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.