The Role of the Area Averaging Approach to Derive Macroscopic Scaled Transport Equations for Hydrogel Capillaries

Abstract

A hydrogel is a three-dimensional network of chemically or physically cross-linked polymers. Hydrogels have porous structures at the nanometer scale and are able to contain large amounts of water without changing their structure. Hydrogels are widely used for gel electrophoresis, which is a technique to separate biomolecules, such as proteins, nucleic acids, and pharmaceuticals, for industrial, biological, and environmental processes. During gel electrophoresis, biomolecules migrate through pores of varying shapes and sizes in the presence of an electric field and separate according to their size and charge.
This research aims to develop and systematize a technique for the analysis of the microscopic transport equations that describe gel electrophoresis at a local level, within a capillary of the hydrogel material, and upscale them to macroscopic equations using a technique known as area averaging. The results of the research efforts will be twofold. First, the research efforts will develop a systematization of the area averaging technique that is currently disorganized in the literature and difficult to apply and generalize. Second, the research efforts will produce constitutive equations for the effective transport coefficients including the effective diffusivity and the effective mobility of the biomolecules in the material capillaries.
The migration of a biomolecule through a pore during gel electrophoresis may be modeled using these transport equations and other anticipated equations, allowing for connection to macroscale parameters that are able to be measured experimentally.