Estimates for deformation induced flow in fluid-elastomer composites with application to self-healing materials

Self-healing polymers enhance the durability of polymeric products. In extrinsic systems, healing fluid stored within embedded vasculature is transported to the damage site, typically driven by capillary action, facilitating autonomous repair and material recovery. This capillary-driven flow limits fluid to attain required coverage of damage region and also results in the unavailability of the healing fluid for multiple damage events. The fluid flow behavior in the micro channels is complex and it is a function of boundary conditions and material, geometrical properties of the composite system. In this work, an extrinsic type composite is proposed which stores the healing fluid in randomly positioned, uni-disperse, parallel, cylindrical channels inside the elastomer matrix. This fluid is initially pressurized by means of compression of elastomer matrix. Upon damage, this pressurized fluid is released and heals the cut. A mathematical framework is presented for characterizing the flow of healing fluid in terms of elastomer, fluid properties, initial elastomer compression, channel geometry, fluid fraction, etc in a semi-analytical manner. To validate the results, numerical simulations are performed in the COMSOL multiphysics software. The semi-analytical method can be used to design the self-healing composites on the basis of the properties of elastomer and healing fluid, offering a very substantial computational advantage over corresponding numerical simulations.