Collaborative Research on Mathematical Constructs for Multiphase Complex Fluids

点击翻译按钮获取中文摘要

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This research project will develop a suite of mathematical constructs for the hydrodynamics of multiphase complex fluids. Complex fluids are distinguished from viscous fluids (e.g., water, oil) in that they require resolution of microstructure to resolve behavior in even the simplest of experiments. For single-phase complex fluids, the signature phenomena of shear thinning (viscosity falls with increased shear rate) and normal stress generation in shear (oppositely translating parallel plates experience a force along their mutual normal) are not captured by the Navier-Stokes model for viscous fluids. Yet, these features are successfully predicted by the kinetic theory of single-phase polymeric liquids. When combined to form multiphase mixtures, either in Nature (biofilms or lung airway mucosal layers) or synthetically (nano-rods or nano-platelets dispersed in a polymer matrix), the different fluid phases are prone to separate. Other forces (chemical bonds and weaker attractive potentials) compete with phase separation to sustain the mixture, which are only reasonably understood for equilibrium states. Outstanding challenges arise, and predictive tools do not yet exist, in far-from-equilibrium conditions typical of biofilms in streams or pipes, lung airway mucus layers propelled toward the larynx by coordinated cilia and tidal breathing, and flow processing of polymer nano-composites into films or molds. A mathematically consistent kinetic theory for generic multiphase complex fluids, incorporating the physics and chemistry of individual phases, their mixtures and their hydrodynamics, will be developed in this research project. A kinetic theory is only useful when accompanied by clear protocols for the derivation of reduced models applicable to benchmark experiments, numerical algorithms for each model reduction, and direct simulations to test the predictive capability of the theory with blind experiments. These constructs will be developed, along with inference methods so that all physical parameters of a multiphase complex fluid model can be experimentally determined. The generality and diversity of the theory will be demonstrated by detailed specificity to hydrodynamics of biofilms, mucosal layers, and polymer nano-composites. Polymer nano-composites are new synthetic materials with extraordinary promise, consisting of a cocktail of a traditional polymer with property-boosting nano-rods or platelets. Insight into why nano-composites are truly special can be appreciated from a simple fact: one percent volume fraction of nano-platelets in a single raindrop of polymer matrix introduces an entire football field of new surface area! The novel features of number and size of particles together with new surface contact between the particle phase and the polymer phase overwhelm current experimental and theoretical capabilities. Flow is impossible to probe experimentally (particles are too small and too numerous to track orientation and position) and there is no predictive theory, and therefore no simulation tools, to guide material design. This project will develop the requisite theoretical and computational capabilities. Similar challenges and limitations exist for mixtures of multiphase complex fluids arising in Nature, such as biofilms in streams, ponds, and pipes and mucosal layers between the air and tissue in lung airways. This research project will develop a mathematical blueprint for theory and simulation of the hydrodynamics of generic multiphase complex fluid mixtures. In this strategy, details of each phase in the mixture and the chemical and physical interactions between phases serve as inputs, together with the necessary experimental data to test the theory. The formalism will produce the theory specific to the multiphase fluid, the approach to derive model reductions for benchmark experiments, and numerical methods and simulations. The general methods will be brought to bear on three diverse multiphase materials: biofilms, mucosal layers, and polymer nano-composites. These mathematical constructs will provide predictive tools for: the design of novel high performance polymer nano-composite materials for defense and the aerospace industry; remediation strategies for biofilms in industrial pipelines; and, improved pulmonary health through simulations of mucus transport prior to and during drug and physical therapies.