Bridging shallow flow theory and microfluidics: The role of confinement in shaping wake lengths and pressure loss

Abstract

Flow past obstacle clusters in micro-channels is central to a wide range of microfluidic applications, yet its fundamental hydrodynamics remain poorly understood under strong geometric confinement. No-slip boundary conditions on all walls enforce inherently three-dimensional (3D) flow structures in fully confined micro-channels, fundamentally altering wake formation, momentum transport, and drag mechanisms. A combined experimental and numerical investigation of wake dynamics behind obstacle clusters in laminar micro-channel flows is presented. High-resolution micro-particle image velocimetry and resolved 3D computational fluid dynamics simulations are employed to systematically explore the effects of Reynolds number and cluster porosity. We demonstrate that full wall confinement sup­presses classical wake–regime transitions commonly observed in shallow and unconfined flows, including shear layer instabilities and vortex shedding. Instead, wake recovery is governed primarily by secondary flows that promote rapid momentum redistribution across the channel depth. As a result, wake length exhibits only weak dependence on Reynolds number and is controlled predominantly by cluster porosity. We further introduce the relative bleeding velocity as a unifying metric to characterize the transition from macro-particle to individual par­ticle behavior. The relative bleeding velocity is the ratio of the mean velocity through the cluster’s main axis perpendicular to the inflow and the mean inflow velocity. These findings establish a distinct physical regime of confined wake flows, bridging the gap between classical shal­low flow theory and microfluidic hydrodynamics, and provide a foundation for improved prediction of pressure losses, transport, and mix­ing in micro-reactors and porous microfluidic systems.