Multiphase flows: Rich physics, challenging theory, and big simulations

Understanding multiphase flows is vital to addressing some of our most pressing human needs: clean air, clean water, and the sustainable production of food and energy. This article focuses on a subset of multiphase flows called particle-laden suspensions involving nondeforming particles in a carrier fluid. The hydrodynamic interactions in these flows result in rich multiscale physics, such as clustering and pseudo-turbulence, with important practical implications. Theoretical formulations to represent, explain, and predict these phenomena encounter peculiar challenges that multiphase flows pose for classical statistical mechanics. A critical analysis of existing approaches leads to the identification of key desirable characteristics that a formulation must possess in order to be successful at representing these physical phenomena. The need to build accurate closure models for unclosed terms that arise in statistical theories has motivated the development of particle-resolved direct numerical simulations (PR-DNS) for model-free simulation at the microscale. A critical perspective on outstanding questions and potential limitations of PR-DNS for model development is provided. Selected highlights of recent progress using PR-DNS to discover new multiphase flow physics and develop models are reviewed. Alternative theoretical formulations and extensions to current formulations are outlined as promising future research directions. The article concludes with a summary perspective on the importance of integrating theoretical, modeling, computational, and experimental efforts at different scales.