title: Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions.
abstract: The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.
authors.affiliation: Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland, United States of America.
authors.forename: Preston
authors.initials: P
authors.lastname: Donovan
authors.affiliation: Department of Biomedical Engineering, Saint Louis University, St. Louis, Missouri, United States of America.
authors.forename: Yasaman
authors.initials: Y
authors.lastname: Chehreghanianzabi
authors.affiliation: Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland, United States of America.
authors.forename: Muruhan
authors.initials: M
authors.lastname: Rathinam
authors.affiliation: Department of Biomedical Engineering, Saint Louis University, St. Louis, Missouri, United States of America.
authors.forename: Silviya Petrova
authors.initials: SP
authors.lastname: Zustiak
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D009010:Monte Carlo Method; D011108:Polymers / Q000737:chemistry*; D012996:Solutions / Q000737:chemistry; D012997:Solvents / Q000737:chemistry
chemical_list: D011108:Polymers; D012996:Solutions; D012997:Solvents