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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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Friction fingers and stick-slip bubbles.(a) At low granular filling fraction ϕ, air slowly displaces the granular-fluid mixture in a creeping fingering process. (b) A transition to highly intermittent dynamics occurs at high ϕ. A single bubble of air suddenly inflates after a long static period. Both experiments: Vair=30 ml, q=0.02 ml min−1, scale bar, 5 cm. (c) Gas pressure, (d) invaded volume V and (e) the flow rate  as a function of time for the bubbles labelled 1–7 in b (Supplementary Movie 1).
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f2: Friction fingers and stick-slip bubbles.(a) At low granular filling fraction ϕ, air slowly displaces the granular-fluid mixture in a creeping fingering process. (b) A transition to highly intermittent dynamics occurs at high ϕ. A single bubble of air suddenly inflates after a long static period. Both experiments: Vair=30 ml, q=0.02 ml min−1, scale bar, 5 cm. (c) Gas pressure, (d) invaded volume V and (e) the flow rate as a function of time for the bubbles labelled 1–7 in b (Supplementary Movie 1).

Mentions: At low granular filling fraction the injected air advances in a slow and quasi-continuous fingering process where side-branching of fingers and a random growth direction produces a branched labyrinthine structure as seen in Figure 2a. The front of compacted grains, compiled by the advancing interface, can be seen along the entire front as a narrow, dark band. We have previously shown that a characteristic finger width emerges as a result of the force balance between the gas pressure on the inside of the finger and the capillary forces and friction at the interface. This characteristic width gives rise to the uniform wavelength of the labyrinths seen in fully drained systems32 and decreases with increasing ϕ.


Patterns and flow in frictional fluid dynamics.

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

Friction fingers and stick-slip bubbles.(a) At low granular filling fraction ϕ, air slowly displaces the granular-fluid mixture in a creeping fingering process. (b) A transition to highly intermittent dynamics occurs at high ϕ. A single bubble of air suddenly inflates after a long static period. Both experiments: Vair=30 ml, q=0.02 ml min−1, scale bar, 5 cm. (c) Gas pressure, (d) invaded volume V and (e) the flow rate  as a function of time for the bubbles labelled 1–7 in b (Supplementary Movie 1).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Friction fingers and stick-slip bubbles.(a) At low granular filling fraction ϕ, air slowly displaces the granular-fluid mixture in a creeping fingering process. (b) A transition to highly intermittent dynamics occurs at high ϕ. A single bubble of air suddenly inflates after a long static period. Both experiments: Vair=30 ml, q=0.02 ml min−1, scale bar, 5 cm. (c) Gas pressure, (d) invaded volume V and (e) the flow rate as a function of time for the bubbles labelled 1–7 in b (Supplementary Movie 1).
Mentions: At low granular filling fraction the injected air advances in a slow and quasi-continuous fingering process where side-branching of fingers and a random growth direction produces a branched labyrinthine structure as seen in Figure 2a. The front of compacted grains, compiled by the advancing interface, can be seen along the entire front as a narrow, dark band. We have previously shown that a characteristic finger width emerges as a result of the force balance between the gas pressure on the inside of the finger and the capillary forces and friction at the interface. This characteristic width gives rise to the uniform wavelength of the labyrinths seen in fully drained systems32 and decreases with increasing ϕ.

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