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Pattern formation in rectilinear flows of noncolloidal suspensions

Parham Poureslami

Ranit Mukherjee

Sungyon Lee*

  • *Contact author: sungyon@umn.edu

Phys. Rev. Fluids 11, 064303 – Published 10 June, 2026

DOI: https://doi.org/10.1103/tgvb-bh1n

Abstract

The displacement of air by a noncolloidal particulate suspension between two parallel plates can trigger interfacial instabilities and two seemingly intertwined patterns: deformation of the fluid-fluid interface and dense particle clusters within the suspension, hereafter referred to as plumes. While prior studies have primarily examined the onset and source of this instability, the emergence and coupling of these patterns remain unresolved. Notably, existing investigations have been limited to radial geometries, where continuous outward expansion of the interface weakens plume-plume interactions. Here, we experimentally displace air with an oil suspension in a rectangular Hele-Shaw cell. Confinement within a constant-width channel amplifies interactions between neighboring plumes, giving rise to previously unreported regimes of pattern formation, including plume merging and plume shedding. Image analysis reveals strong coupling between interfacial deformation and plumes and characterizes the interaction between adjacent plumes. Employing the suspension balance model, we demonstrate how net particle flux toward the interface drives particle accumulation and establishes the conditions for pattern formation. Namely, particle clustering at the interface locally slows the advancing interface and produces concave plume tips that become preferential sites for plume initiation. In addition, we develop a simple scaling for the size of the interfacial deformation based on the interplay between upstream pressure, interface concentration, and plume concentration.

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