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Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers
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10.1063/1.4747711
/content/aip/journal/chaos/22/3/10.1063/1.4747711
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/3/10.1063/1.4747711
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic of the system.

Image of FIG. 2.
FIG. 2.

Time evolution of the concentration field in the presence of cooperative solutal and thermal Marangoni effects: and . The other parameters are Le = 10 and .

Image of FIG. 3.
FIG. 3.

Time evolution of the concentration field in the presence of antagonistic solutal and thermal Marangoni effects when the system reaches a steady regime propagating at a constant speed: and . The other parameters are Le = 10 and .

Image of FIG. 4.
FIG. 4.

Periodic time evolution of the concentration field in the presence of antagonistic solutal and thermal Marangoni effects when the front remains unsteady in the co-moving frame: and . The other parameters are Le = 10 and .

Image of FIG. 5.
FIG. 5.

Streamlines superimposed on the concentration field in the presence of antagonistic solutal and thermal Marangoni effects for , Le = 10, , t = 40 for (a) a steady case, , and (b) an unsteady case, . The concentration ranges here from c = 1 (products to the left) shown in red to c = 0 (reactants to the right) shown in blue. The streamlines correspond to iso-contours of the streamfunction, , equally spaced between the maximum value of and 0.

Image of FIG. 6.
FIG. 6.

Surface tension along the surface for , Le = 10, , t = 40 in (a) a steady antagonistic case, , and (b) an unsteady antagonistic case, .

Image of FIG. 7.
FIG. 7.

Periodic time evolution of the concentration field in the presence of antagonistic solutal and thermal Marangoni effects when the front remains unsteady in the co-moving frame: and . The other parameters are Le = 10 and .

Image of FIG. 8.
FIG. 8.

Mixing length as a function of time for , Le = 10, , and various .

Image of FIG. 9.
FIG. 9.

(a) Mixing length as a function of for Le = 10 and various . Zones where the curve is splitted correspond to situations where the front is unsteady in the co-moving frame. (b) Solutal Marangoni range, Z, for which the front is unsteady as a function of . In both figures, the thickness of the layer is .

Image of FIG. 10.
FIG. 10.

(a) Mixing length as a function of for and various Le = 1, 5,10, 30, 50, 120. Zones where the curve is splitted correspond to situations where the front is unsteady in the co-moving frame. (b) Solutal Marangoni range, Z, for which the front is unsteady as a function of Le when . In both figures, the thickness of the layer is .

Image of FIG. 11.
FIG. 11.

Mixing length as a function of Le for and , in (a) the cooperative case, , and (b) the antagonistic case, .

Image of FIG. 12.
FIG. 12.

Mixing length as a function of the layer thickness for and Le = 10 in both a cooperative () and a steady antagonistic () case.

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/content/aip/journal/chaos/22/3/10.1063/1.4747711
2012-09-28
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/3/10.1063/1.4747711
10.1063/1.4747711
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