Toward Rational Design of Drug Delivery Substrates: II. Mixture Theory for Three-Scale Biocompatible Polymers and a Computational Example

Abstract

In Part I of this article we focused on glassy-state biocompatible polymers (two-scale) that may possess charges. Here we extend these results to a three-scale setting for polymers that contain two liquid phases. On the microscale the three phases each behave as a continuum occupying distinct regions of space. On the mesoscale the polymer is homogenized with the sorbed liquid phase to form a particle wherein both homogenized phases are assumed to simultaneously occupy each point in space within the particle. On the macroscale, the mesoscale particles are homogenized with two bulk-phase liquids, one being the same as the sorbed liquid. Conceptually, throughout all space, each macroscale homogenized phase exists everywhere. A theory of constitution is developed at the macroscale by exploiting the entropy inequality, and the resultant constitutive equations are inserted into the macroscale field equations and simplifications made so that a solution may be obtained via finite elements. A simple imbibition problem is studied in detail.