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Nonmodal and nonlinear dynamics of a volatile liquid film flowing over a locally heated surface
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10.1063/1.3241967
/content/aip/journal/pof2/21/10/10.1063/1.3241967
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/10/10.1063/1.3241967

Figures

Image of FIG. 1.
FIG. 1.

Schematic diagram of a thin liquid film flowing over a heater. The Marangoni stress at the upstream edge of the heater opposes the gravitational flow, which leads to the formation of a capillary ridge.

Image of FIG. 2.
FIG. 2.

Base profiles for for different values of and . The curves with symbols are the corresponding temperature profiles at the interface.

Image of FIG. 3.
FIG. 3.

(a) Leading eigenvalues of for , , and . (b) Real part of the leading eigenvalues of for , , and .

Image of FIG. 4.
FIG. 4.

Leading eigenfunctions for , , and .

Image of FIG. 5.
FIG. 5.

Maximum transient amplification of spanwise perturbations to the film with and (a) and and (b) and .

Image of FIG. 6.
FIG. 6.

(a) Maximal nonmodal amplification, , vs and (b) vs for the linearly stable film with , , and .

Image of FIG. 7.
FIG. 7.

Optimal perturbations for the unstable base state with , , and . (a) Optimal initial perturbation and (b) corresponding evolved state after time for a perturbation with wave number . (c) and (d) for .

Image of FIG. 8.
FIG. 8.

(a) Optimal initial perturbation and (b) corresponding evolved state after time for a perturbation with wave number applied to the linearly stable base state with , , and .

Image of FIG. 9.
FIG. 9.

Plot of the pseudospectra given by for the linearly stable film with , , , and (a) (least stable eigenvalue) and (b) (repeated eigenvalue). The abscissa is , and the ordinate is . Contours are plotted for [the contour is not visible in (a)]. The symbols are the leading eigenvalues of .

Image of FIG. 10.
FIG. 10.

(a) Maximum instantaneous growth rate vs for , , and several . (b) Corresponding eigenvectors for , , and . The curve with symbols is .

Image of FIG. 11.
FIG. 11.

(a) Nonlinear amplification ratio of perturbations to the linearly unstable film with , , and . (b) Contour plot of of the nonlinear film evolution after rivulet formation. Contours are shown for , 0.75, 1.25, 1.5, 2.0, 2.5, and 3.0. (c) Nonlinear amplification ratio for the linearly stable film with , , and . (d) Magnitude of perturbation that destabilizes the linearly stable film with , , and .

Image of FIG. 12.
FIG. 12.

(a) Oscillations above the heater after a perturbation is applied to the steady film profile at . The dashed curves indicate the maximum and minimum values of the film thickness after the oscillations evolve into a time-periodic profile. (b) Profiles at intervals of after the film reaches the time-periodic state. The dark curve is the steady base state. (c) Phase space plots at . (d) Dimensionless heat transfer coefficient after the time-periodic state is reached relative to that for the steady profile at intervals of .

Image of FIG. 13.
FIG. 13.

Asymptotic exponential growth rate of transverse perturbations to the time-periodic film.

Tables

Generic image for table
Table I.

Definition and physical interpretation of dimensionless groups.

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/content/aip/journal/pof2/21/10/10.1063/1.3241967
2009-10-01
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonmodal and nonlinear dynamics of a volatile liquid film flowing over a locally heated surface
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/10/10.1063/1.3241967
10.1063/1.3241967
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