@article{30323,
  author = {David M Lorenzetti and Michael D Sohn},
  title = {Numerical Solution of the Polanyi-DR Isotherm in Linear Driving Force Models},
  abstract = {<p>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.</p>},
  year = {2011},
  journal = {Environmental Science & Technology},
  volume = {45},
  pages = {10091 - 10095},
  month = {09/2011},
  issn = {0013-936X},
  doi = {10.1021/es202359j},
  language = {eng},
}