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Patterns and flow in frictional fluid dynamics.

Sandnes B, Flekkøy EG, Knudsen HA, Måløy KJ, See H - Nat Commun (2011)

Bottom Line: Here we consider Coulomb friction and compressibility in the fluid dynamics, and discover surprising responses including highly intermittent flow and a transition to quasi-continuous dynamics.Moreover, by varying the injection rate over several orders of magnitude, we characterize new dynamic modes ranging from stick-slip bubbles at low rate to destabilized viscous fingers at high rate.We classify the fluid dynamics into frictional and viscous regimes, and present a unified description of emerging morphologies in granular mixtures in the form of extended phase diagrams.

View Article: PubMed Central - PubMed

Affiliation: School of Chemical and Biomolecular Engineering, University of Sydney, Sydney, New South Wales 2006, Australia. bjornar.sandnes@fys.uio.no

ABSTRACT
Pattern-forming processes in simple fluids and suspensions have been studied extensively, and the basic displacement structures, similar to viscous fingers and fractals in capillary dominated flows, have been identified. However, the fundamental displacement morphologies in frictional fluids and granular mixtures have not been mapped out. Here we consider Coulomb friction and compressibility in the fluid dynamics, and discover surprising responses including highly intermittent flow and a transition to quasi-continuous dynamics. Moreover, by varying the injection rate over several orders of magnitude, we characterize new dynamic modes ranging from stick-slip bubbles at low rate to destabilized viscous fingers at high rate. We classify the fluid dynamics into frictional and viscous regimes, and present a unified description of emerging morphologies in granular mixtures in the form of extended phase diagrams.

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Related in: MedlinePlus

Setup and displacement process.(a) Air is slowly injected into a linear Hele-Shaw cell loaded with polydisperse glass beads (∼100 μm diameter) submersed in a water/glycerol solution. The gap is Δz=0.5 mm and the cell forms a channel 20 cm wide and 30 cm long. The granular material settles after loading. (b) The invading air/fluid interface accumulates a front of close-packed grains in the gap between the plates.
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f1: Setup and displacement process.(a) Air is slowly injected into a linear Hele-Shaw cell loaded with polydisperse glass beads (∼100 μm diameter) submersed in a water/glycerol solution. The gap is Δz=0.5 mm and the cell forms a channel 20 cm wide and 30 cm long. The granular material settles after loading. (b) The invading air/fluid interface accumulates a front of close-packed grains in the gap between the plates.

Mentions: Pressurized air is injected into a confined, settled granular mixture using a syringe pump driven at a constant rate (Fig. 1a). The height of granular material in the gap depends on the initial filling fraction ϕ of the mixture (where ϕ is normalized with the filling fraction of close-packed grains). The syringe contains a reservoir of air of volume Vair. The air/fluid interface advances and accumulates a front of compacted granular material of thickness L as illustrated in Figure 1b. Here, horizontal stress imposed by capillary forces at the interface is transmitted through force chains within the packing. As the granular packing is unable to dilate, the normal force on the confining plates increases. We adopt a Janssen model30 for the stress in the packing, such that σzz=κσxx, where κ is the Janssen proportionality constant giving the ratio of transverse to in-plane granular pressure. The frictional stress σ at the interface that must be overcome to move the front is derived31, and takes the form σ∼Δz[exp(L/Δz)−1].


Patterns and flow in frictional fluid dynamics.

Sandnes B, Flekkøy EG, Knudsen HA, Måløy KJ, See H - Nat Commun (2011)

Setup and displacement process.(a) Air is slowly injected into a linear Hele-Shaw cell loaded with polydisperse glass beads (∼100 μm diameter) submersed in a water/glycerol solution. The gap is Δz=0.5 mm and the cell forms a channel 20 cm wide and 30 cm long. The granular material settles after loading. (b) The invading air/fluid interface accumulates a front of close-packed grains in the gap between the plates.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3104512&req=5

f1: Setup and displacement process.(a) Air is slowly injected into a linear Hele-Shaw cell loaded with polydisperse glass beads (∼100 μm diameter) submersed in a water/glycerol solution. The gap is Δz=0.5 mm and the cell forms a channel 20 cm wide and 30 cm long. The granular material settles after loading. (b) The invading air/fluid interface accumulates a front of close-packed grains in the gap between the plates.
Mentions: Pressurized air is injected into a confined, settled granular mixture using a syringe pump driven at a constant rate (Fig. 1a). The height of granular material in the gap depends on the initial filling fraction ϕ of the mixture (where ϕ is normalized with the filling fraction of close-packed grains). The syringe contains a reservoir of air of volume Vair. The air/fluid interface advances and accumulates a front of compacted granular material of thickness L as illustrated in Figure 1b. Here, horizontal stress imposed by capillary forces at the interface is transmitted through force chains within the packing. As the granular packing is unable to dilate, the normal force on the confining plates increases. We adopt a Janssen model30 for the stress in the packing, such that σzz=κσxx, where κ is the Janssen proportionality constant giving the ratio of transverse to in-plane granular pressure. The frictional stress σ at the interface that must be overcome to move the front is derived31, and takes the form σ∼Δz[exp(L/Δz)−1].

Bottom Line: Here we consider Coulomb friction and compressibility in the fluid dynamics, and discover surprising responses including highly intermittent flow and a transition to quasi-continuous dynamics.Moreover, by varying the injection rate over several orders of magnitude, we characterize new dynamic modes ranging from stick-slip bubbles at low rate to destabilized viscous fingers at high rate.We classify the fluid dynamics into frictional and viscous regimes, and present a unified description of emerging morphologies in granular mixtures in the form of extended phase diagrams.

View Article: PubMed Central - PubMed

Affiliation: School of Chemical and Biomolecular Engineering, University of Sydney, Sydney, New South Wales 2006, Australia. bjornar.sandnes@fys.uio.no

ABSTRACT
Pattern-forming processes in simple fluids and suspensions have been studied extensively, and the basic displacement structures, similar to viscous fingers and fractals in capillary dominated flows, have been identified. However, the fundamental displacement morphologies in frictional fluids and granular mixtures have not been mapped out. Here we consider Coulomb friction and compressibility in the fluid dynamics, and discover surprising responses including highly intermittent flow and a transition to quasi-continuous dynamics. Moreover, by varying the injection rate over several orders of magnitude, we characterize new dynamic modes ranging from stick-slip bubbles at low rate to destabilized viscous fingers at high rate. We classify the fluid dynamics into frictional and viscous regimes, and present a unified description of emerging morphologies in granular mixtures in the form of extended phase diagrams.

Show MeSH
Related in: MedlinePlus