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Interfacial instability of two rotating viscous immiscible fluids in a cylinder
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10.1063/1.3599507
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Affiliations:
1 DETEC, Università di Napoli “Federico II,” Naples 80125, Italy
2 Linné Flow Centre, KTH Mechanics, SE-100-44 Stockholm, Sweden
a) Electronic mail: gcoppola@unina.it.
b) Electronic mail: onofrio@mech.kth.se.
Phys. Fluids 23, 064105 (2011)
/content/aip/journal/pof2/23/6/10.1063/1.3599507
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/6/10.1063/1.3599507
View: Figures

## Figures

FIG. 1.

Geometric configuration: inner surface of radius R 1 is the base flow interface, outer surface of radius R 2 is the rigid boundary.

FIG. 2.

(Color online) Growth rate vs wavenumber for the rotating annulus at different values of the Hocking number L2 and of the radius ratio b. (a): b = 1.2, L2 = 1.5, (b): b = 1.2, L2 = 10, (c): b = 12, L2 = 1.5, and (d): b = 12, L2 = 10. Dashed lines correspond to the inviscid solution of Weidman et al. (Ref. 8).

FIG. 3.

(Color online) Variation with the Reynolds number Re2 of the maximum growth rate and wavenumber of maximum growth rate for the rotating annulus at different values of the radius ratio b and at L2 = 1.5. Dashed line corresponds to the prediction of the theory of de Hoog and Lekkerkerker (Ref. 10).

FIG. 4.

(Color online) Variation with the Reynolds number Re2 of the maximum growth rate and wavenumber of maximum growth rate for the rotating annulus at different values of the radius ratio b and at L2 = 10. Dashed line corresponds to the prediction of the theory of de Hoog and Lekkerkerker (Ref. 10).

FIG. 5.

Variation with the Reynolds number Re2 of the maximum growth rate and wavenumber of maximum growth rate for the rotating annulus at different values of the radius ratio b for L2 = 2. Lines denoted with + symbols are relative to computations in which Coriolis terms are artificially suppressed.

FIG. 6.

(Color online) Variation with the Reynolds number Re2 of the maximum growth rate and wavenumber of maximum growth rate for the rotating annulus at different values of the Ohnesorge number Oh2 and for b = 20. Continuous line is the prediction of Tomotika (Ref. 4) theory. Dashed lines are the predictions of de Hoog and Lekkerkerker theory (Ref. 10) for the first three values of Oh2.

FIG. 7.

(Color online) Variation with the Hocking number L2 of the maximum growth rate and wavenumber of maximum growth rate for the rotating annulus at different values of the Reynolds number Re2. (a) and (b): b = 20, (c) and (d): b = 1.2. Dashed lines are the predictions of de Hoog and Lekkerkerker theory (Ref. 10) for the first three values of Re2. Dash-dotted line is the prediction of Rayleigh (Ref. 2) theory.

FIG. 8.

(Color online) Variation with the radius ratio b of the maximum growth rate and wavenumber of maximum growth rate for the rotating annulus at different values of the Reynolds number Re2. (a) and (b): L2 = 1.5, (c) and (d): L2 = 10. Dashed lines are the inviscid solutions of Weidman et al. (Ref. 8).

FIG. 9.

(Color online) Maximum growth rate and critical wavenumber as functions of Re2 for the two-fluid rotating system. λ = χ = 1, b = 12. Continuous lines are the predictions of Ashmore and Stone’s (Ref. 11) large-Taylor number asymptotic theory. Thick lines are the predictions of Tomotika (Ref. 4) theory.

FIG. 10.

(Color online) Maximum growth rate and critical wavenumber as functions of Re2 for the two-fluid rotating system. λ = 0.5, χ = 1, b = 12. Continuous lines are the predictions of Ashmore and Stone’s (Ref. 11) large-Taylor number asymptotic theory, thick line are the predictions of Tomotika (Ref. 4) theory, and dashed lines are the prediction of de Hoog and Lekkerkerker theory (Ref. 10) for the first three values of Oh2.

FIG. 11.

Maximum growth rate and critical wavenumber as functions of Re2 for the two-fluid rotating system for χ = 0.5, b = 5 and various λ. (a) and (b): L2 = 1, (c) and (d): L2 = 5.

FIG. 12.

(Color online) Maximum growth rate and critical wavenumber as functions of λ for the two-fluid rotating system for χ = 0.5, L2 = 5, b = 5 and various Re2. Dashed lines are the inviscid solution of Weidman et al. (Ref. 8).

FIG. 13.

(Color online) Maximum growth rate and critical wavenumber as functions of L2 for the two-fluid rotating system for χ = 0.5, b = 2 and various λ. Continuous lines are computed for Re2 = 10, dashed lines are the inviscid solution of Weidman et al. (Ref. 8).

FIG. 14.

(Color online) Variation of L2c (a) and σ Mc (b) as functions of Re2. Symbol legends are: Δ: b = 1.2, ○: b = 5. Continuous lines are for χ = 1, dashed lines are for χ = 0.5, and dash-dotted lines are for χ = 0.1.

FIG. 15.

Maximum growth rate and critical wavenumber as functions of χ for the two-fluid rotating system for Re2 = 1, L2 = 5, b = 5 and various λ.

/content/aip/journal/pof2/23/6/10.1063/1.3599507
2011-06-22
2014-04-19

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