A Study of Inertial Migration of a Neutrally Buoyant Sphere in Channel Flow: On the Roles of Confinement and Inertia

The inertial migration of finite-size particles in channel and pipe flows is a fundamental phenomenon in particulate flows, with applications spanning microfluidics, biomedical devices, and industrial slurry transport. Due to finite-size and inertial effects, neutrally buoyant particles experience lateral migration and settle at well-defined equilibrium positions, features that can be leveraged for particle focusing and size-based separation. First observed by Segré and Silberberg (1962) in pipe flow, this behaviour has since been the subject of extensive investigation. However, key questions remain, especially under conditions of strong confinement and high fluid inertia. In this study, we employ Particle-Resolved Direct Numerical Simulations (PR-DNS) using a Volume-Filtering Immersed Boundary Method (IBM) to examine the inertial migration of neutrally buoyant rigid spheres in pressure-driven channel flow. We investigate a wide range of Reynolds numbers (Re ≈ 10–2000), spanning moderate to high-inertia regimes, while focusing on a strongly confined system with a fixed confinement ratio (λ = a/H), where a is the particle radius and H is the channel height. Our simulations show that, irrespective of their initial positions, particles consistently migrate to a unique, steady-state equilibrium location governed by both λ and Re. Furthermore, we explore how the presence of a finite-size particle alters the stability of the background flow and potentially influences the onset of transition.