Gels and Microfluidic Devices

Gels are materials that consist of a solid, crosslinked system in a fluid solvent. They are over-whelmingly present in biological systems and also occur in many aspects of materials applications. Some gels are mostly characterized by their mechanical properties whereas for the large class of {\it hydrogels}, the electric effect of ions is the signature feature. In the biomedical industry, mechanical properties of gels are relevant to the prediction of the life-cycle of body implantable devices such as pacemaker, bone-replacement systems and artifcial skin. Upon body implantation, devices swell due to the moisture of the environment, resulting in stress concentrations that may cause failure of the device. A main goal is to determine the time evolution of stresses at interfaces between different materials of the device, and controlability conditions that ensure that the stress values will remain below an allowed threshold. The proposed governing equations involve transport, diffusion, elasticity and dissipation. To study hydrogels, we explore the coupling of the mechanics of gels with the {\it Poisson-Nernst-Planck equations} governing the transport and diffusion of ions in the solvent, and in the presence of the electric potential of the system. We focus on two types of microuidic models that emerge from such a setting, cyclic drug-delivery devices and microvalves.

M. Carme Calderer, University of Minnesota

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