The finger-like branching pattern that occurs when a less viscous fluid displaces a more viscous one confined between two parallel plates has been widely studied as a classical example of a mathematically-tractable hydrodynamic instability since the time of Saffman and Taylor. Fingering in such Hele-Shaw geometries have been generated not only with Newtonian fluids but also with various non-Newtonian fluids including fine granular material displaced by gas, liquid, or large grains. Here we study a granular Hele-Shaw system to explore whether the absence of cohesive forces in dry granular material can produce an ideal venue for studying the hitherto-unrealizable singular hydrodynamics predicted in the zero-surface-tension limit. We demonstrate that the grain-gas interface does indeed exhibit fractal structure and sharp cusps associated with finite-time singularities. Above the yield stress, the scaling for the finger width is distinct from that for ordinary fluids, reflecting unique granular properties such as friction-induced dissipation as opposed to viscous damping. Despite such differences, the dimension of the global fractal structure and the shape of the singular cusps on the interface agree with the theories based on simple Laplacian growth of conventional fluid fingering in the zero-surface-tension limit. Our study provides new insights not only on the dynamics of two-phase dense granular flows and granular pattern formation, but also on the fluid dynamics in the zero-surface-tension limit.
We experimentally study the viscous fingering instability in a fluid-fluid phase separated colloid-polymer mixture by means of laser scanning confocal microscopy and microfluidics. We focus on three aspects of the instability. (i) The interface between the two demixed phases has an ultralow surface tension, such that we can address the role of thermal interface fluctuations. (ii) We image the interface in three dimensions allowing us to study the interplay between interface curvature and flow. (iii) The displacing fluid wets all walls completely, in contrast to traditional viscous fingering ex…
Fingering instabilities akin to the Rayleigh-Taylor (RT) instability in fluids have been observed in a binary granular system consisting of dense and small particles layered on top of lighter and larger particles, when the system is subjected to vertical vibration and fluidizing gas flow. Using observations from experiments and numerical modelling we explore whether the theory developed to describe the Rayleigh-Taylor (RT) instability in fluids is also applicable to binary granular systems. Our results confirm the applicability of the classic RT instability theory for binary granular systems d…
We identify and characterize a new class of fingering instabilities in liquid metals; these instabilities are unexpected due to the large interfacial tension of metals. Electrochemical oxidation lowers the effective interfacial tension of a gallium-based liquid metal alloy to values approaching zero, thereby inducing drastic shape changes, including the formation of fractals. The measured fractal dimension ($D = 1.3 \pm 0.05$) places the instability in a different universality class than other fingering instabilities. By characterizing changes in morphology and dynamics as a function of drople…
We show that a minimal model for viscous fingering with a nematic liquid crystal in which anisotropy is considered to enter through two different viscosities in two perpendicular directions can be mapped to a two-fold anisotropy in the surface tension. We numerically integrate the dynamics of the resulting problem with the phase-field approach to find and characterize a transition between tip-splitting and side-branching as a function of both anisotropy and dimensionless surface tension. This anisotropy dependence could explain the experimentally observed (reentrant) transition as temperature …
Eutectic gallium-indium (EGaIn), a room-temperature liquid metal alloy, has the largest tension of any liquid at room temperature, and yet can nonetheless undergo fingering instabilities. This effect arises because, under an applied voltage, oxides deposit on the surface of the metal, which leads to a lowering of the interfacial tension, allowing spreading under gravity. Understanding the spreading dynamics of room temperature liquid metals is important for developing soft electronics and understanding fluid dynamics of liquids with extreme surface tensions. When the applied voltage or the oxi…
Viscous flows in a quasi-two-dimensional Hele-Shaw geometry can lead to an interfacial instability when one fluid, of viscosity $η_{in}$ displaces another of higher viscosity, $η_{out}$. Recent studies have shown that there is a delay in the onset of fingering in miscible fluids as the viscosity ratio, $η_{in}/η_{out}$, increases and approaches unity; the interface can remain stable even though the displacing liquid is less viscous. This paper shows that a delayed onset and stable pattern can occur in immiscible fluids as well. However, there are two significant differences between the two cas…
Our experiments on viscous fingering of air into oil contained between closely spaced plates reveal two selection rules for the fjords of oil that separate fingers of air. (Fjords are the building blocks of solutions of the zero-surface-tension Laplacian growth equation.) Experiments in rectangular and circular geometries yield fjords with base widths 1/2 lambda_c, where lambda_c is the most unstable wavelength from a linear stability analysis. Further, fjords open at an angle of 8.0 degrees plus or minus 1.0 degree. These selection rules hold for a wide range of pumping rates and fjord length…
The spreading of a thin film of suspension on a spinning disk and the accompanying contact line instability is studied through flow visualization experiments. The critical radius for the onset of instability shows an increase with increase in the particle fraction ($ϕ_{p}$) before decreasing slightly at the highest value of $ϕ_{p}$ studied, while the instability wavelength ($λ$) exhibits a non-monotonic dependence. The value of $λ$ is close to that for a partially wetting liquid at lower $ϕ_{p}$, it decreases with increasing $ϕ_{p}$ to a minimum before increasing again at largest $ϕ_{p}$. The …
During the spreading of epithelial tissues, the advancing tissue front often develops fingerlike protrusions. Their resemblance to traditional viscous fingering patterns in driven fluids suggests that epithelial fingers could arise from an interfacial instability. However, the existence and physical mechanism of such a putative instability remain unclear. Here, based on an active polar fluid model for epithelial spreading, we analytically predict a generic instability of the tissue front. On the one hand, active cellular traction forces impose a velocity gradient that leads to an accelerated f…
We study viscous fingering of an air-nematic interface in a radial Hele-Shaw cell when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). We observe undulations at the sides of the fingers which correlate with the switching frequency and with tip oscillations which give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise-induced) side branching. We conclude that the lateral…
Avalanche experiments on an erodible substrate are treated in the framework of ``partial fluidization'' model of dense granular flows. The model identifies a family of propagating soliton-like avalanches with shape and velocity controlled by the inclination angle and the depth of substrate. At high inclination angles the solitons display a transverse instability, followed by coarsening and fingering similar to recent experimental observation. A primary cause for the transverse instability is directly related to the dependence of soliton velocity on the granular mass trapped in the avalanche.
In Hele-Shaw flows, boundaries between fluids develop unstable viscous fingers. At vanishing surface tension, the fingers further evolve to cusp-like singularities. We show that the problem admits a {\it weak solution} where shock fronts triggered by a singularity propagate together with a fluid. Shocks form a growing, branching tree of a mass deficit, and a line distribution of vorticity where pressure and velocity of the fluid have finite discontinuities. Imposing that the flow remain curl-free at macroscale determines the shock graph structure. We present a self-similar solution describing …
Viscous fingering (VF) is an interfacial instability that occurs in a narrow confinement or porous medium when a less-viscous fluid pushes a more viscous one, producing finger-like patterns. Controlling the VF instability is essential to enhance the efficiency of various technological applications. However, the control of VF instability has been challenging and so far focused on simple Newtonian fluids of constant viscosity. Here, we extend to complex yield-stress fluids and examine the controlling feasibility by carrying out a linear stability analysis using a radial cell with a converging ga…
We study the fingering instability of the interface between two miscible fluids, a colloidal suspension and its own solvent. The temporal evolution of the interface in a Hele-Shaw cell is found to be governed by the competition between the non-linear viscosity of the suspension and an off-equilibrium, effective surface tension $Γ_e$. By studying suspensions in a wide range of volume fractions, $Φ_\mathrm{C}$, we show that $Γ_e \sim Φ_\mathrm{C}^2$, in agreement with Korteweg's theory for miscible fluids. The surface tension exhibits an anomalous increase with particle size, which we account fo…
We perform the analog to the "water bell" experiment using non-cohesive granular material. When a jet of granular material, many particles wide, rebounds from a fixed cylindrical target, it deforms into a sharply-defined sheet or cone with a shape that mimics a liquid with zero surface tension. The particulate nature of granular material becomes apparent when the number of particles in the cross-section of the jet is decreased and the emerging sheets and cones broaden and gradually disintegrate into a broad spray. This experiment has its counterpart in the behavior of the quark-gluon plasma ge…
We study the injection of air in a granular suspension. We use a linear Hele-Saw cell filled with a suspension which is displaced by air, leading to a Saffman-Taylor (fingering) instability. For the suspension, we use an iso-dense mixture where the fluid and the particles have the same density. The volume fraction of particles can thus be adjusted over a wide range. We discuss the question of an effective rheology inside the cell as well as the pattern formation as a function of the granular compacity. We finally report results on the finger width for stable fingers and the thresholds for thei…
An experimental study of liquid drop impacts on a granular medium is proposed. Four fluids were used to vary physical properties: pure distilled water, water with glycerol at 2 concentrations 1:1 and 1:2 v/v and water with Tween 20 at the concentration of 0.1g/l. The drop free fall height was varied to obtain a Weber number (We) between 10 and 2000. Results showed that obtained crater morphologies highly depend on the impacting drop kinetic energy E_{K}. Different behaviours during the drop spreading, receding and absorption are highlighted as function of the fluids viscosity and surface tensi…
Motivated by studies suggesting that the patterns exhibited by the collectively expanding fronts of thin cells during the closing of a wound [Mark et al., Biophys. J., 98:361-370, 2010] and the shapes of single cells crawling on surfaces [Callan-Jones et al., Phys. Rev. Lett., 100:258106, 2008] are due to fingering instabilities, we investigate the stability of actively driven interfaces under Hele-Shaw confinement. An initially radial interface between a pair of viscous fluids is driven by active agents. Surface tension and bending rigidity resist deformation of the interface. A point source …
We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting liquid and crystal phases. Measurements of the orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-crystal one. The interplay of boundary inelasticity and geometry, either order-promoting or inhibiting, controls the wetting of the gra…
We present experimental evidence, which contradicts the the standard boundary conditions used in continuum theories of non-cohesive granular flows for the velocity normal to a boundary u.n=0, where n points into the fluid. We propose and experimentally verify a new boundary condition for u.n, based on the observation that the boundary cannot exert a tension force Fb on the fluid. The new boundary condition is u.n=0 if Fb.n>=0 else n.P.n=0, where P is the pressure tensor. This is the analog of cavitation in ordinary fluids, but due the lack of attractive forces and dissipation it occurs frequen…
Despite the ubiquitousness and technological and scientific importance of granular matter, our understanding is still very poor compared to molecular fluids and solids. Until today, there is no unified description, which indeed seems unreachable. However, it has been proposed that important advances could be attained for noncohesive, hard-sphere like systems, by combining fluid dynamics with phase-field modeling through an appropriate order parameter (Aranson and Tsimring, 2006). Here, we present a review of the dynamics of confined granular matter, for which this systematic approach has prove…
A highly sheared dense aqueous suspension of granular cornstarch particles displays rich nonlinear rheology. We had previously demonstrated the growth and onset of interfacial instabilities when shear-thinning cornstarch suspensions were displaced by a Newtonian fluid, and had suggested methods to maximise displacement efficiency [Palak, R. Sathayanath, S. K. Kalpathy and R. Bandyopadhyay, Colloids Surf. A Physicochem. Eng. Asp., 629 (2021) 127405]. In the present work, we explore the miscible displacement of a dense aqueous cornstarch suspension in its discontinuous shear-thickening regime in…
We study the effect of fluids on the angle of repose and the segregation of granular matter poured into a silo. The experiments are conducted in two regimes where: (i) the volume fraction of the fluid is small and it forms liquid bridges between particles, and (ii) the particles are completely immersed in the fluid. The data is obtained by imaging the pile formed inside a quasi-two dimensional silo through the transparent glass side walls. In the first series of experiments, the angle of repose is observed to increase sharply with the volume fraction of the fluid and then saturates at a value …
This article deals with the Hadamard instability of the so-called $μ(I)$ model of dense rapidly-sheared granular flow, as reported recently by Barker et al. (2015,this journal, ${\bf 779}$, 794-818). The present paper presents a more comprehensive study of the linear stability of planar simple shearing and pure shearing flows, with account taken of convective Kelvin wave-vector stretching by the base flow. We provide a closed form solution for the linear stability problem and show that wave-vector stretching leads to asymptotic stabilization of the non-convective instability found by Barker et…
During detachment of a viscous fluid extruded from a nozzle a filament linking the droplet to the latter is formed. Under the effect of surface tension the filament thins until pinch off and final detachment of the droplet. In this paper we study the effect of the presence of individual particles trapped in the filament on the detachment dynamics using granular suspensions of small volume fractions (ϕ < 6%). We show that even a single particle strongly modifies the detachment dynamics. The particle perturbs the thinning of the thread and a large droplet of fluid around the particle is formed. …
