Particulate suspensions, consisting of solid particles dispersed in a fluid, exhibit complex flow behaviors influenced by multiple factors, including particle interactions, concentration gradients, and external forces. Suspensions play an important role in diverse processes, from sediment transport to food processing, and display instabilities triggered by shear-driven effects, frictional interactions, and viscous forces. These instabilities can often be understood by identifying the key mechanical quantities that govern the dynamics. Following hydrodynamic tradition, such mechanics can be characterized by dimensionless numbers, which encapsulate the interplay between geometric, kinematic, and mechanical factors. Many of these numbers represent competitions between opposing pairs of mechanical quantities, which we discuss in detail while also considering a few phenomena that require more complex combinations. By emphasizing the underlying mechanical principles, this review provides a perspective for understanding pattern formation and flow instabilities in confined particulate suspensions across different flow geometries.
Fardin et al. (2025) studied this question.