Improved pressure mathematical models for the flow and infiltration of healing agents in microvascular self-healing composite materials

Abstract This study addresses a critical challenge in microvascular self-healing composite systems, which is determining the precise applied pressure that is required to drive different healing agents into damaged regions within a defined timeframe. It found that the generalized derived pressure formulas for Newtonian and non-Newtonian healing agents were accumulated based on the integration of experimental rheological testing (healing agent properties), damage dimensions (slit or aperture scaling), and a combination of four fluid-mechanics constitutive models, which provides practical guidance for pressure selection and filling time. These prediction models were validated by using two-phase flow simulations, which demonstrated strong agreement between the calculated pressure values and simulated results. The extracted data highlight that the rheological nature of each agent significantly influences infiltration efficiency, with low-viscosity Newtonian fluids ensuring uniform filling at modest pressures with 99.725% filling efficiency, while non-Newtonian shear-thinning agents showed acceptable infiltration under the exact required pressure. These findings confirm the accuracy of the improved models and offer practical guidance for selecting healing agents and optimizing pressure-delivery strategies for real-world self-healing composite structures.