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The planar setup: a window through the complex interactions ingranular flows
Miguel Cabrera1,2*, Laura Cote1, and Santiago Caro1
1

Department of Civil and Environmental Engineering, Universidad de los Andes, 111711, Bogotá, Colombia
Department of Geoscience & Engineering, TU Delft, 5048, Stevinweg 1, Delft, The Netherlands

2Abstract. Granular flows are a complex process, involving a wide range of grain sizes, materials, varied
viscous fluids, among others. For this reason, the simulation of granular flows requires a certain level ofsimplification, allowing the isolated study of its governing variables and extending the global observations
to field events. Here, we present the planar setup as an alternative for studying simplified processes
associated to granular flows. The planar setup consists of two windows separated by a thin gap and enclosing
a granular assembly. We present two examples where the planar setup is adapted for the study of thecompeting action of segregation and disaggregation in a fractured grain under shear flow, and for the studyof the stability scenarios of a flow impacting a permeable obstacle. The close visualization of the kinematics
at the particle scale provides an ideal opportunity for describing the mechanisms behind the grain
disaggregation or controlling the obstacle stability. Both examples highlight the advantages of the planar
setup for the study of granular flows.

1 The power of simplification
Granular flows like debris flows, mudflows, andhyperconcentrated flows pose a latent thread tomountaincommunities,
interactingwithits
infrastructure and eventually causing fatalities [1-2].
Such granular flows are complex processes, involving awide range of grain sizes, materials with fluctuating
viscosity and varying density, erosion and deposition
processes changing the channel geometry, andtransitional flow regimes from initiation to deposition[3-5]. In consequence, simplification has been key inunderstanding and simulating granular flows for natural
hazard assessments and in the design of mitigation
systems, among others. Numerical simplifications range
from continuum constitutive models describing the flow
motion and runout [3-6] to micro-mechanical models
providing insights into the particle-fluid interactions [78]. Experimental simplifications range from large
configurations aiming at matching some features of field
scale events [9-11] to small laboratory scale models
isolating some of the governing processes in a granular
flow [12-15].
The similarity between field processes andnumerical and experimental models is explored at
different levels of abstraction (i.e., geometry, loading,materials) and chosen out of convenience of the process
under study [16]. Geometrical similarities come fromthe simplification of the macroscopic characteristics(e.g., channel cross section, channel slope) andmicroscopic features (e.g., grain shape, bed roughness)[17]; loading similarities aim at reproducing theassociated stresses and stress ratios of large field events(e.g., pore-pressure feedback) [16]; and material
similarities intend to reproduce closely the rheologicalbehavior of the materials involved in field events [18].
However, the introduction of these simplifications sets adistance with a detailed description of a particular field
event, requiring a careful consideration of theadvantages and disadvantages at each point of the model
design and simplification.
One example of intense simplification inexperimental models is the planar setup, similar to theHele-Shaw cell in fluid mechanics. A planar setup is anearly two-dimensional configuration, consisting of two
windows that enclose a granular assembly in a gap
slightly thicker than one particle diameter [19-23]. This
setup allows clear visualization of the granularassembly, its kinematics, and ambient fluid motion [24],while reducing the complexity of boundary and initialconditions to the interaction between the grains and themodel walls. Moreover, the richness of information
extracted from the visualization of the kinematics at theparticle scale overcomes in some instances thelimitations of studying monodisperse systems. The
visualization is obtained by a simple camera setup andrecent advances in open-source digital image analysis
tools (e.g., scikit-image, imageJ, napari) points to a costeffective strategy for the study of granular flows.
In this work, we present two examples where theplanar setup is adapted for the study of processes thatmight remain hidden in a three-dimensionalconfiguration. The first example studies the competing
action of segregation and disaggregation in a fractured* Corresponding author: miguel.cabrera.geo@gmail.com© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

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Fig. 1. (a) Planar Couette cell top view; and (b) snapshots of the disaggregation and segregation of a fragmented disk.

grain under shear flow [25], and the second example
studies the stability scenarios of a flow impacting apermeable obstacle [26]. Finally, the last section
summarizes and proposes a forecast on the alternatives
to be explored in a planar setup in future works.

initiate at the test start, but it is eventually triggered by
the shear flow agitation (see Fig. 1(c-d)). Further work
focuses on the role of the fragment pattern and on theformulation of a generalized model for fragments
disaggregation.

2 A look into a fractured grain

3 A look into a flow impacting apermeable obstacle

Highly fractured boulders, also known as Jigsaw-fit
blocks, are often found in volcanic debris avalanche
deposits with little separation between its fragments[27]. Despite the avalanche long runout and agitatedmotion, jigsaw-fit blocks appear to evade the expected
disaggregation within a gravity-driven shear flow. Themechanisms behind the fragments frustrated
disaggregation are explored in a planar Couette cell,
focusing on the interactions frustrating thedisaggregation of a fragmented grain in a steady state
shear flow. In this configuration, two horizontal annular
windows enclose a granular assembly of 2 mm ceramicbeads and 2 mm thick PMMA laser-cut plates of 30 mm
diameter (see Fig. 1(a)). The PMMA plates are cut in a
simplified pattern of a jigsaw fit block, assuming thatcracks found on the outer-surface concentrate at theblock center. The shear flow within the two annular
windows is driven by the rotation of the inner cylinderand the basal plate. The bottom annular window isbacklighted by a led panel and the beads and fragments
motion is monitored by a top high-speed camera (seeFig. 1(b)). The test is driven by a steady angular velocity
and lasts until complete disaggregation is reached.
After initiation, the fragmented plate starts spinningin a clockwise direction around its axis until a relative
displacement between fragments generates a void at its
center and the exposed edges are dragged apart by themoving beads. The asymmetrical distribution of normal
forces on the fragments and the equivalent volume
fraction gradient on the surrounding grains, creates a lift
force that sets a gradual disaggregation until nofragments are left in contact with each other.
Remarkably, the fragments disaggregation does not

Open mitigation structures like filter barriers and baffles
allow flow through a series of openings, resulting in adecrease of the mass flow kinematics [28-29]. Amongthese, baffles are a cost-effective alternative, requiring
less materials and of easier construction andreplacement. However, the basal fixture and single
stability of these elements is among their main
challenges. Here, the stability against impact of apermeable obstacle is simplified into a two-dimensional
planar setup. The obstacle is made of a lattice of 6 mm
perforated beads connected through their orifices with anylon thread. The planar setup consists of a 1.5 m longchannel, connected upstream to a 15 l tank that fills a0.28 m wide reservoir and impacts the obstacle at0.56 m from the reservoir outlet (see Fig. 2(a)). The flow
kinematics and obstacle motion are monitored by a sidehigh-sped camera, recording a back-lighted region. We
explore the obstacle stability as a function of the ratio
between its height H and width B.
After the water flow impacts the permeable obstacle,
three main scenarios are observed: (i) the obstacle
overturns once the flow upstream is just above 0.5H (seeFig. 2(b)); (ii) the obstacle slides before the flow
upstream is about H (see Fig. 2(c)); and (iii) the obstacle
remains in place when the flow upstream is at H (seeFig. 2(d)). The occurrence of each scenario isconditioned by the obstacle width and upstream fillingtime, resulting in stable outcomes for all obstacles witha ratio of H/B ≤ 0.75. Ongoing work aims at providing asimplified analytical model for describing the stabilityof permeable obstacles and guide the design of such
mitigation structures.

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and studying the flow impact against a permeable
obstacle. In both instances, the richness of informationcollected through digital image analysis, provides acomprehensive collection of information for describing
in detail the process under study. It is important tohighlight, that these simplified systems are a first orderapproach, aimed at setting a benchmark scenario for thevalidation of more complex tools.
Future works could aim at validating the observed
behaviours in a planar setup with three-dimensionalmodels instrumented with a visualization of its inner
kinematics (e.g., Planar laser-induced fluorescence[30]), or compare the observed patterns with field-scale
instrumented cases. Moreover, the advantages anddisadvantages of the planar setup require further
idealizations for including the study of polydisperse
systems, the role of non-Newtonian viscous fluids, andthe scaling of flexible mitigation structures. In thissense, it should be highlighted that the cost-effective
alternative of a planar setup should be tempting enoughfor driving more research and stablishing it as a common
tool for the study of granular flows.

Acknowledgments
The authors would like to thank the partial funding
provided by the Patrimonio Autónomo-Fondo Nacionalde Financiamiento para la Ciencia, la Tecnología y laInnovación Francisco José de Caldas, under grant
agreement No. 164–2019, Colombia.

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Fig. 2. Flow impact against a permeable obstacle. (a) Planar
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4 Perspectives and futures challenges
The simplification of the complex interactions in
granular flows poses the challenging task of identifying
the dominant variables of a given process and isolatingthem in a controlled system. This task is non-trivial anddemands a clear link between the abstraction and theidealized field event. In this work, we present two
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