Formation and Destabilization of the Particle Band on the Fluid-Fluid Interface Jungchul Kim, † Feng Xu, and Sungyon Lee * Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843, USA (Received 5 August 2016; revised manuscript received 1 December 2016; published 13 February 2017) An inclusion of particles in a Newtonian liquid can fundamentally change the interfacial dynamics and even cause interfacial instabilities. For instance, viscous fingering can arise even in the absence of the destabilizing viscosity ratio between invading and defending phases, when particles are added to the viscous invading fluid inside a Hele-Shaw cell. In the same flow configuration, the formation and breakup of a dense particle band are observed on the interface, only when the particle diameter d becomes comparable to the channel gap thickness h. We experimentally characterize the evolution of the fluid-fluid interface in this new physical regime and propose a simple model for the particle band that successfully captures the fingering onset as a function of the particle concentration and h=d. DOI: 10.1103/PhysRevLett.118.074501 Controlling interfacial instabilities [1] is of critical importance in many engineering and geophysical proc- esses, ranging from droplet microfluidics [2], lung airways [3,4], enhanced oil recovery [5], to volcanic flows [6]. The manipulation of viscous fingering was recently achieved by modulating the channel properties [7,8], or by employing time-dependent injection strategies [9]. The development in particle design and production provides another tool for modifying fluid-fluid interfaces [10–14]. For instance, when particles adsorb on the inter- face, they assemble into a dense monolayer via capillary attractions [15,16] and rigidify interfaces [16–21] against interfacial instabilities. The stabilizing effects of adsorbed particles on the interface have led to a number of techno- logical advances, from stabilizing emulsions [22] to form- ing “liquid marbles” [23]. More recently, the wettability of particles was utilized to control viscous fingering, as Trojer and colleagues [24] suppressed viscous fingering by injecting air into a saturated packing of hydrophobic particles. In the reverse scenario, oil injection into a channel containing hydrophilic particles was shown to induce viscous fingering [25]. In all aforementioned studies, particles directly affect the surface energy of the interface. Particles entrained in a fluid flow can also indirectly alter the interfacial dynamics and even cause or delay instabilities. Yet, only a limited number of studies examine this coupling between suspensions and fluid-fluid interfaces. For instance, the addition of particles to a viscous liquid is shown to accelerate the droplet pinch-off [26–31], and the exact physical mechanism remains unknown. Thin, free-surface flows of the negatively buoyant particle and oil mixture exhibit particle concentration-dependent fingering behaviors down an incline [32–41]. In particular, at high particle concentrations, fingering of the suspension-air interface becomes suppressed as particles aggregate near the free surface instead of settling. More recently, Kulkarni and colleagues [42] demonstrated that adding noncolloidal particles to a spreading thin film on a rotating surface can initially enhance fingering (resulting in shorter wavelengths), before unstable wavelengths increase at higher particle concentrations. This nonmonotonic dependence of fingering instability on the particle concentration alludes to the com- plex relationship between suspended particles and interfaces. Distinct from previous examples of thin suspension flows that are inherently susceptible to fingering, particles immersed in a fluid can also destabilize the fluid-fluid interface that is otherwise stable, when the suspension is injected into a Hele-Shaw cell [43,45]. In this radial flow, particles accumulate near the interface, which locally increases the effective viscosity [43–45] and leads to miscible fingering inside the suspension [46]. The resultant inhomogeneous distribution of particles causes interfacial deformations, while the analogous experiments with a clear liquid exhibit stable, circular interfaces [Fig. 1(a)]. In this Letter, we focus on the destabilizing effect of particles on the fluid-fluid interface, as particles in a wetting liquid spontaneously form a dense band near the interface and break up into fingers in the radial source flow. This new fingering regime arises unexpectedly when the channel confinement becomes important, or if d ∼ h, where d and h are the particle diameter and channel gap thickness, respectively. We experimentally observe the spreading of a mixture of oil and neutrally buoyant, noncolloidal particles in a Hele-Shaw cell, and quantify the onset of this particle band formation and breakup. Based on the rate of particle band growth as the suspension expands, a simple model successfully predicts this onset as a function of h=d and the suspension volume fraction ϕ 0 . As depicted in Fig. 1(b), the Hele-Shaw cell consists of two Plexiglas plates (30.5 × 30.5 × 3.8 cm) that are separated by h ranging from 0.2 to 1.4 mm. The silicone oil (density ρ l ¼ 0.96 g=cm 3 and viscosity μ l ¼ 0.096 Pa · s, UCT) wets the cell walls and particles completely, so that particles remain immersed inside the liquid. Two sets of polyethylene particles PRL 118, 074501 (2017) PHYSICAL REVIEW LETTERS week ending 17 FEBRUARY 2017 0031-9007=17=118(7)=074501(6) 074501-1 © 2017 American Physical Society