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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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Frictional dynamics transition.(a) Displacement structures obtained by varying ϕ and Vair, keeping q constant (0.03 ml min−1). Frictional fingers are stable at low filling fraction and elasticity, whereas stick-slip bubbles prevail at high ϕ and Vair. The theoretical model for the phase boundary is superimposed on the images (black line), including the effect of a ±10% variation in the friction coefficient μ (red lines). Scale bar, 10 cm. (b) The finger width decreases with increasing ϕ (squares, experiments; solid line, theory). Inset: Bubble size increases with Vair, but varies considerably as evident from this box plot showing median, quartiles and extremes (whiskers). ϕ=0.58 for this data set. (c) Interface to area ratio S/A. Error bars on two data points denote standard deviations in replicate experiments. (d) Ratio of adjacent maximum to minimum width plotted as a function of ϕ. Mean and standard deviation obtained by 20 random measurements. Red line: theoretical result for the phase boundary.
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f3: Frictional dynamics transition.(a) Displacement structures obtained by varying ϕ and Vair, keeping q constant (0.03 ml min−1). Frictional fingers are stable at low filling fraction and elasticity, whereas stick-slip bubbles prevail at high ϕ and Vair. The theoretical model for the phase boundary is superimposed on the images (black line), including the effect of a ±10% variation in the friction coefficient μ (red lines). Scale bar, 10 cm. (b) The finger width decreases with increasing ϕ (squares, experiments; solid line, theory). Inset: Bubble size increases with Vair, but varies considerably as evident from this box plot showing median, quartiles and extremes (whiskers). ϕ=0.58 for this data set. (c) Interface to area ratio S/A. Error bars on two data points denote standard deviations in replicate experiments. (d) Ratio of adjacent maximum to minimum width plotted as a function of ϕ. Mean and standard deviation obtained by 20 random measurements. Red line: theoretical result for the phase boundary.

Mentions: Figure 3a shows images from experiments probing a phase space of ϕ and Vair. The fingering dynamics is stable for low filling fraction and small air volumes (high stiffness). A transition to the highly intermittent bubble phase can be achieved by increasing ϕ or by making the system more elastic (increasing Vair). This result mirrors the behaviour of the sliding block, in which the bifurcation from stick slip to smooth sliding occurs above a critical stiffness/weight ratio34.


Patterns and flow in frictional fluid dynamics.

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

Frictional dynamics transition.(a) Displacement structures obtained by varying ϕ and Vair, keeping q constant (0.03 ml min−1). Frictional fingers are stable at low filling fraction and elasticity, whereas stick-slip bubbles prevail at high ϕ and Vair. The theoretical model for the phase boundary is superimposed on the images (black line), including the effect of a ±10% variation in the friction coefficient μ (red lines). Scale bar, 10 cm. (b) The finger width decreases with increasing ϕ (squares, experiments; solid line, theory). Inset: Bubble size increases with Vair, but varies considerably as evident from this box plot showing median, quartiles and extremes (whiskers). ϕ=0.58 for this data set. (c) Interface to area ratio S/A. Error bars on two data points denote standard deviations in replicate experiments. (d) Ratio of adjacent maximum to minimum width plotted as a function of ϕ. Mean and standard deviation obtained by 20 random measurements. Red line: theoretical result for the phase boundary.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Frictional dynamics transition.(a) Displacement structures obtained by varying ϕ and Vair, keeping q constant (0.03 ml min−1). Frictional fingers are stable at low filling fraction and elasticity, whereas stick-slip bubbles prevail at high ϕ and Vair. The theoretical model for the phase boundary is superimposed on the images (black line), including the effect of a ±10% variation in the friction coefficient μ (red lines). Scale bar, 10 cm. (b) The finger width decreases with increasing ϕ (squares, experiments; solid line, theory). Inset: Bubble size increases with Vair, but varies considerably as evident from this box plot showing median, quartiles and extremes (whiskers). ϕ=0.58 for this data set. (c) Interface to area ratio S/A. Error bars on two data points denote standard deviations in replicate experiments. (d) Ratio of adjacent maximum to minimum width plotted as a function of ϕ. Mean and standard deviation obtained by 20 random measurements. Red line: theoretical result for the phase boundary.
Mentions: Figure 3a shows images from experiments probing a phase space of ϕ and Vair. The fingering dynamics is stable for low filling fraction and small air volumes (high stiffness). A transition to the highly intermittent bubble phase can be achieved by increasing ϕ or by making the system more elastic (increasing Vair). This result mirrors the behaviour of the sliding block, in which the bifurcation from stick slip to smooth sliding occurs above a critical stiffness/weight ratio34.

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