From frictional to viscous behavior: Three-dimensional imaging and rheology of gravitational suspensions

Abstract

We probe the three dimensional flow structure and rheology of gravitational (non-density matched) suspensions for a range of driving rates in a split-bottom geometry. We establish that for sufficiently slow flows, the suspension flows as if it were a dry granular medium, and confirm recent theoretical modelling on the rheology of split-bottom flows. For faster driving, the flow behavior is shown to be consistent with the rheological behavior predicted by the recently developed "inertial number" approaches for suspension flows.PACS numbers: 83.80. Fg, 82.70.Kj, 47.57.Gc Flows of granular materials submersed in a liquid of unequal density have started to attract considerable attention [1][2][3][4][5] and are relevant in many practical applications [6]. These materials, which we will refer to as "gravitational" suspensions, clearly differ from density matched suspensions, which have been studied in great detail [7][8][9][10]. Gravitational suspensions exhibit sedimentation, large packing fractions and jamming of the material, which suggests a description similar to dry granular matter [11,12].In the last two decades, various flow regimes have been identified for dry granular matter. Sufficiently slow flows are frictional: the ratio of shear (driving) to normal (confining) stresses becomes independent of flow rate if the material is allowed to dilate [12,13]. Faster flows are referred to as inertial: here the effective friction coefficient µ depends on the so-called "inertial" number I, which is a non-dimensional measure of the local flow rate [12,14,15].For gravitational suspensions, the presence of liquid instead of gas as interstitial medium strongly affects the microscopic picture -how should we think of the flow of such suspensions? Pouliquen and coworkers proposed that the ratio of the strain rate and settling time, I S , would play a similar role as the inertial number in dry granular flows [5]. They furthermore conjectured a dependence of the effective friction coefficient µ on I S similar to the dry case, and applied this rheological law to capture the behavior of underwater avalanches [16].Here we test this picture by combining 3D imaging and rheological measurements of the flow of gravitational suspensions in a so-called split-bottom geometry (Fig. 1). This geometry has two main advantages. First, the flow rate, which is the key control parameter in the inertial number framework, can be varied over several orders of magnitude, allowing us to access slow flows as seen in plane shear [3,17], faster flows as seen in gravity driven flows [5,18], and the crossover regime in between -some- thing not achieved in previous studies of gravitational suspensions [3,5,17,18]. Second, extensive experimental and numerical work [19][20][21][22][23][24] has shown that the split bottom geometry produces highly nontrivial slow dry granular flows. A simple frictional picture is not sufficient to capture these flows [25,26], so that testing whether these profiles also arise in slowly sheared gravitational suspensions is a ...

Dense annular flows of granular media

“…This result compares well with the measurements at onset of flow by Dijksman et al [9] for submersed (circles) or dry (squares in Fig. 5) experiments.…”

“…In the case of an orthoradial flow due to the rotation of an inner disk of diameter b, placed at the bottom of (8) and (9). Each line gives a set of homothetic iso-ω lines.…”

Viscoelasticity of vibrated granular suspensions

“…(7) reduces to rðtÞ ¼ Gc c þ r M ðtÞ. The rheological behavior of a granular suspension in these conditions has already been studied by , Coussot and Ancey (1999), Mills et al (2009), or Dijksman et al (2010, leading to rðtÞ ¼ r f þ g_ cðtÞ, with r f being the frictional stress and g being the suspension viscosity. The identification of the two relations shows that Gc c ¼ r f ¼ cst and r M ðtÞ ¼ g_ c. Therefore, Gc c equals the frictional stress as in dry granular media [Marchal et al (2009);Marchal et al (2013)] or in saturated granular suspensions ].…”

“…In this paper, we focus our attention on the rheology of vibrated gravitational suspensions, i.e., suspensions where particles are denser than the suspending fluid, relevant for understanding most of the above mentioned applications. Although such suspensions have received much attention over the past few years ; Cassar et al (2005); Lemaître et al (2009); Pailha et al (2009);Dijksman et al (2010); Boyer et al (2011)], no universal law currently exists to describe their flow behavior in complex geometries. This is mainly linked to the fact that such systems, being athermal in nature can, at rest, be jammed far from equilibrium, which makes tricky the preparation of a sample in a repeatable initial state.…”

Path to fracture in granular flows: Dynamics of contact networks

“…The split-cell geometry as described in [13] consists of a (15cm) 3 cell with a 9cm diameter disk embedded in the bottom. The cell contains 5mm diameter acrylic beads immersed in an index matched triton and laser dye (Nile Blue 690 Perchlorate) solution, and is filled to a height of 10 particle diameters.…”