Simulations show that the kinetics of permeant fluids in viscoelastic matrices depends on the rheological and chemical properties of the material. Fick's law fails to describe transport through viscoelastic materials because of the stress exerted on the incoming fluid which causes a delay. Reversible binding to immobilizing sites also retards permeation of molecules. The effects of mechanical properties and chemical affinities of materials on the transport of solutes are studied. An integro-partial-differential equation is used to model the transport. While the differential part of the equation is represented by an elliptic operator, the integral part describes the contributions of stress and reversible binding. The stability of the model is investigated. The steady-state flux and effective time constant are calculated. The lag time is also studied using multiple integration. Subsequent analyses reveal the dependence of the steady-state flux, the effective time constant, and the lag time on the Young modulus, the viscosity, and the binding/unbinding rates. The results presented in this paper make it possible to tune the mechanical and chemical properties to achieve a desired transport profile.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Integro-partial-differential equation
- Laplace transform