Polydisperse multiphase flows arise in many applications, and almost always involve a disperse phase with particles of different sizes, compositions, etc., present over a wide range for volume fractions. In this presentation, I will review recent advances in combining quadrature-based moment methods with a well-posed Eulerian two-fluid model derived from a kinetic theory that includes mass and velocity distributions. This approach relies on formulating a disperse-phase kinetic equation valid from close-packed to dilute conditions, coupled to a modified Navier-Stokes equation for the continuous phase. A critical component of the computational approach for treating polydispersity is the formulation of the numerical fluxes for the mass-velocity moments found from the kinetic equation. For the mass moments, the recently developed generalized quadrature method of moments provides a robust reconstruction of the mass distribution. Then, using the conditional and hyperbolic quadrature method of moments for the mass-conditioned velocity moments of the disperse phase, well-posed spatial fluxes are formulated and implemented in a hyperbolic flow solver. Through numerical examples, we demonstrate that by including added mass and pseudoturbulence, this well-posed modeling approach extends to polydisperse flows with arbitrary material density ratios (e.g., bubbly flows).

Professor Fox joined Iowa State University as the Glenn Murphy Professor of Engineering in 1999, and was the Herbert L. Stiles Professor of Chemical Engineering from 2003-2012. He was promoted to Distinguished Professor in Engineering in 2010. Fox has held visiting professorships in Belgium, Denmark, France, Italy, Switzerland and The Netherlands. From 1987-88, he was a NATO Postdoctoral Fellow at LSGC in Nancy, France. His numerous professional awards include a NSF Presidential Young Investigator Award in 1992 and the ISU Outstanding Achievement in Research Award in 2007. From 2012-14, he was a Marie-Curie Senior Fellow at the Ecole Centrale in Paris, France. In 2015 he was selected as an International Francqui Professor by the Francqui Foundation in Belgium, and awarded a Chaire d’Attractivité at the Université Fédérale Toulouse Midi-Pyrénées, France. In 2016 he was selected for the North American Mixing Forum Award for Excellence and Sustained Contributions to Mixing Science and Practice, and the Shell Particle Technology Forum Thomas Baron Award. In 2022 he was named the Fulbright-Tocqueville Distinguished Chair and D’Alembert Senior Fellow at the University of Paris-Saclay, CentraleSupélec. Professor Fox is a Fellow of the American Physical Society and of the American Institute of Chemical Engineering.
Professor Fox has made numerous ground-breaking contributions to the field of multiphase and reactive flow modeling. The Fox group spearheaded many fundamental advances in the development of novel computational fluid dynamics (CFD) models to overcome specific scientific challenges faced in the chemical and petroleum industries. He developed powerful quadrature-based moment methods (CQMOM, GQMOM, HyQMOM) for treating distribution functions (particle size, bubble size, velocity, etc.). The impact of Fox’s work extends far beyond chemical engineering and touches every technological area dealing with turbulent flow and chemical reactions. His first book, Computational Models for Turbulent Reacting Flows, published by Cambridge University Press (CUP) in 2003, offers an authoritative treatment of the field. His second CUP book in 2013, Computational Models for Polydisperse Particulate and Multiphase Systems, provides a comprehensive treatment of CFD model for disperse multiphase flows. His current research is focused on well-posed multifluid models for polydisperse systems and multiphase turbulent flows.

Nearly 70 years ago, R.A. Bagnold published his seminal findings on the rheological properties of liquid-solid suspensions. The Bagnold work provided the basis for many granular and particle flow studies on the transition from the viscous regime to a grain-inertia regime that involves particle collisions; an analysis of the experiments, however, showed the transition was a result of a turbulent transition rather than a transition involving particle collisions. This presentation overviews other studies on the rheology of liquid-solid flows and presents new results from experiments at Caltech. The new experiments involve a coaxial cylindrical rheometer and use the Reynolds number based on particle diameter and the velocity of the moving wall and not on the square of the particle diameter and the shear rate. For Reynolds numbers great than 10, the effective viscosity shows a linear increase with Reynolds number for solid fraction less than 40%; this increase results from inertial effects and not from particle-to-particle collisions. At higher sheer rates, the flow can transition to turbulence with smaller particles suppressing the transition and larger particles enhancing the turbulence. Additional experiments also consider cases with unmatched densities between the fluid and solid phases. The results are compared with recent numerical simulations using the diameter-based Reynolds number.

Melany L. Hunt is the Dotty and Dick Hayman Professor of Mechanical Engineering. Her research work involves transport and mechanics in multiphase systems, including granular material flows, dense liquid-solid flows, fluidized beds, powders, and booming sand dunes. She received her bachelor's degree from the University of Minnesota, Minneapolis and her masters and doctorate from the University of California, Berkeley. At Caltech she has served in a variety of roles, including executive officer of mechanical engineering and vice provost. She has won awards for teaching, research, and mentoring, including Caltech’s 2019 Richard P. Feynman Teaching Prize and the 2022 Agent of Change Award for her efforts around diversity, equity, and inclusion. She was recently elected vice chair of the US National Committee on Theoretical and Applied Mechanics of the National Academies.

The understanding of the random fluctuations generated by the motion of a population of bodies dispersed in a fluid is a fundamental issue for many multiphase configurations, including bubbly flows, droplet emulsions and particulate flows. In this talk, we mainly focus on inertial situations where a wake develops at the rear of the dispersed bodies. From the examination of gravity-driven flows (bubble columns and fluidized beds), the singular properties of the body-induced fluctuations, in terms of statistical moments and spectra, is revealed. It turns out that the dynamics of these fluctuations emerge from collective effects and cannot be derived from the dynamics of a single, or a few, particles. They can neither be understood in the framework of single-phase turbulence. The aim of this lecture is to present the concepts that have been introduced to understand the mechanisms responsible for various specific features, such as anisotropy, exponential tails of probability density functions, and k-3 spectral subrange. The relative importance of each mechanism with the volume fraction, the Reynolds number and the nature of the dispersed bodies will also be discussed, as well as the modeling of the body-induced agitation and its interaction with single-phase flow turbulence.

Frédéric Risso (56 years) is a senior researcher at the CNRS (French National Center for Research). He received his PhD in Fluid Dynamics in 1994 from the National Polytechnique Institute of Toulouse and has been studying multiphase flows at IMFT (Institute of Fluids Mechanics of Toulouse) since then. His research is structured around two main axes: Agitation, mixing and transfers in bubbly flows, droplet emulsions and dense suspensions; Dynamics of fluid interfaces (deformation, breakup and coalescence) involving complex interfacial rheology due to the presence of surfactants or membranes. In this context, he particularly focuses on the understanding of fundamental physical mechanisms from the analysis of original experiments and simulations, with the aim to develop models for applications to chemical processes, geophysics and biological flows. He has published 78 articles in peer-reviewed journal (Google scholar page), supervised 17 PhD and 13 postdocs, and be associated editor of the Int. J. Multiphase Flow (2010-2016).

The behaviors of a single bubble and bubble clusters are drastically changed by small amounts of surfactant. It is well-known that a bubble in aqueous surfactant solution rises much slower than one in purified water. This phenomenon is explained by the so-called Marangoni effect caused by a nonuniform concentration distribution of surfactant along the bubble surface. More interestingly, this Marangoni effect also influences the lateral migration in the presence of mean shear. These phenomena influence the multiscale nature of bubbly flows and cause a drastic change in the large scale bubbly flow structures. In the present talk, bubble clustering phenomena in upward bubbly channel flows are discussed with the emphasis on the detail description of single bubble behaviors and bubble-bubble interactions. The direct numerical simulations and the PIV measurement were conducted to clarify the spatiotemporal change of flow structures. It is shown that large scale turbulent vortical structures disappears by suppressing the growth of a small vortical structure near the wall, where the quasi 2-dimensional bubble clusters are passing by.

Shu Takagi is a Professor at the Department of Mechanical Engineering and Department of Bioengineering, The University of Tokyo since 2010. He received Doctor of Engineering from the University of Tokyo in 1995. His areas of expertise include numerical simulations and experimental investigations on dispersed multiphase flows, especially bubbly flows and blood cell flows, medical ultrasound, hierarchical integrated simulation of human body, molecular thermo-fluid mechanics and multiscale analysis of thermo-fluid phenomena. He has written over 20 review articles including Annual Review of Fluid Mechanics and has given more than 30 keynote lectures in conferences. He has been contributing as an associate editor of IJMF and journal FLOW. He is currently the President of Japan Society of Multiphase Flows and the vice President of Japan Society of Fluid Mechanics. He is also a IUTAM Congress Committee member and contributing for the international activity in the field of mechanics.