Interfacial patterns of stretching suspension
Phys. Rev. Fluids 10, 104004 – Published 15 October, 2025
DOI: https://doi.org/10.1103/wk72-dkxd
Abstract
Particle-mediated multiphase flow in confined geometries is common in natural processes and industrial applications. Here, we study air-suspension interfacial patterns under the impact of particle dynamics through a combination of experiments and theory in a lifting Hele-Shaw cell where the suspension is undergoing stretching deformation. We observe a transition of interfacial morphology from wavy pattern with noticeable wiggles, to blobby fingering featured by blunt tips, and eventually to dendritic fingering pattern characterized by densely spaced side branching. Three particle effects are identified in the pattern formation, including rheological modification, nonuniform spatial distribution, and particle perturbations. Notably, the emergence of dendritic fingering is rarely observed in pure fluids under comparable conditions. To explain this phenomenon, we quantify the particle-induced perturbations using linear stability theory. The particle-induced perturbations correspond to higher wave-number modes than cell roughness-induced perturbation. Once their amplitudes become comparable, tip splitting is continuously triggered and evolves into side branching during finger propagation, ultimately leading to the formation of dendritic morphology. On this basis, we propose a perturbation amplitude-based criterion to predict the emergence of dendritic pattern, and further establish a regime diagram of interfacial patterns in the parameter space of capillary number and aspect ratio. The proposed criterion and the phase diagram are in good agreement with our experiments. This study elucidates the crucial role of particle dynamics in shaping the interface morphologies of suspensions, offering insights into controlling interfacial instability in relevant engineering applications.