A comprehensive review of particle-laden flows modeling: Single/multiphase modeling approaches, benchmarks, heat transfer, intermolecular interactions, recent advances and future directions

Abstract

Understanding the profound complexity of particle-laden flows is critical to advances across multiple disciplines. This review aims to provide a comprehensive framework for understanding these multiphase systems, addressing both their fundamental physics and diverse modeling approaches. By beginning with effective single-phase models that are characterized by their homogeneous​ mixture properties, the review sets a foundation for exploring more advanced techniques.

The presentation then transitions to multiphase models, where advancements seek to overcome the limitations of single-phase approaches. The mixture model, valued for its simplicity and computational efficiency, struggles to capture detailed interphase interactions. This challenge leads to the multiphase Eulerian models, which treat fluid and particle phases as interpenetrating continua. The Eulerian–Lagrangian approach emerges to address the need for higher fidelity, enabling detailed tracking of individual particles, whether point-like or resolved, in the fluid. Fully Lagrangian models further refine the focus on particle dynamics, offering specialized insights despite significant computational demands.

The dynamics of particle-laden flows are shaped by the interplay of forces among particles, fluids, and surfaces. Forces such as drag, lift, Magnus, and Brownian, along with thermophoretic, van der Waals, and electrostatic interactions, govern the individual particle motions. External influences, including acoustic radiation, Lorentz forces, and gravity, add complexity to these interactions. Scaling analyses provide clarity by identifying dominant dynamics across varying spatial and temporal scales.

Benchmark studies play a pivotal role in validating these models. Classical test cases, ranging from single-particle sedimentation to particle–particle dynamics, thermal migration, and Brownian motion, highlight the challenges of integrating particle transport phenomena across scales. Heat transfer mechanisms in particle-laden flows introduce another layer of complexity. Conduction, convection, and radiation interact with particle motion to shape the thermal behavior of particle–fluid suspension. At higher speeds, the multiphase mixture transitions to turbulent flow, and turbulence modeling approaches are used to analyze the chaotic flow regimes.

The techniques described in this article deepen the understanding of the complex hydrodynamic and thermal behavior of particle-laden systems, which are critical in numerous engineering and scientific applications. In addition, the review systematically explores the applications of particle-laden flows, identifying commonly used modeling approaches for various conditions. It further highlights the key forces influencing specific applications, offering critical insights into their significance and practical implications.

Ultimately, this review attempts to provide an essential and thorough guide for researchers and scholars exploring particle-laden flow and heat transfer dynamics. It also aims to critically examine the underlying physics of particle-laden flows, offering insights into the intricate and multifaceted nature of this widely studied yet challenging phenomenon.