  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 non-deforming 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.
  This article is based on an invited talk given at the 2019 Annual Meeting of
the American Physical Society's Division of Fluid Dynamics in Seattle, WA.
