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Fluid transport in thin liquid films using traveling thermal waves
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10.1063/1.4811829
/content/aip/journal/pof2/25/7/10.1063/1.4811829
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4811829

Figures

Image of FIG. 1.
FIG. 1.

(a) Velocity and temperature distributions in a liquid film heated from below by a stationary thermal wave at the bottom wall with = 25, = 0.1, = 100, δ = 3, = 0.0152. The thick curve indicates the position of the liquid-gas interface in the steady state. (b) The temperature profile at the bottom wall. The vertical dashed line indicates the border line between the counter-rotating vortices in the liquid film, namely, counterclockwise near the ends of the periodic domain and clockwise in the center of the domain. The bright and dark shades correspond to high and low temperatures, respectively.

Image of FIG. 2.
FIG. 2.

(a) Time evolution of the film deformation. (b) Film interface deformation at the steady state. The dashed and solid curves denote the results obtained from LW theory and VOF simulation, respectively. The parameter set is = 25, = 0.1, = 100, δ = 3, = 0.0152.

Image of FIG. 3.
FIG. 3.

The case of a stationary temperature wave at the solid-liquid boundary. (a) Film interface deformation Δ = as a function of Marangoni number for different wave periods and a fixed temperature amplitude = 0.1. (b) Film deformation Δ as a function of for different wave amplitudes and a fixed wave period = 10. Empty and filled symbols represent the results obtained from LW theory and VOF simulations, respectively. All parameter sets shown in the figure correspond to linearly stable films with = 1 in the case of a uniform temperature with = 0 at the solid-liquid boundary. Curves serve to guide the reader's eye.

Image of FIG. 4.
FIG. 4.

Snapshot of the velocity and temperature fields for a traveling thermal wave at the solid-liquid boundary for = 25, = 0.1, = 150, ω = 0.0136, δ = 3, = 0.0152. The bottom panel shows the instantaneous temperature profile at the solid-liquid boundary. Phase lag Δϕ denotes the phase difference between the thermal wave and the film interface. The vertical dashed lines indicate the border line between the counter-rotating vortices, namely counterclockwise is on the left of the center line and clockwise is on the right. The bright and dark shades correspond to high and low temperatures, respectively.

Image of FIG. 5.
FIG. 5.

Evolution of the liquid film in the case of = 25, = 0.1, = 150, δ = 3, = 0.0152, and different values of the wave frequency ω of propagating thermal wave. (a) Interface profile of the film at the saturated (steady for ω = 0) state. The inset shows the maximum and the minimum thickness of the film, and the interface deformation as a function of the wave frequency ω. (b) Variation of the interface velocity at the saturated state. The inset shows the magnitudes of positive and negative interface velocities, and the difference between them as a function of wave frequency ω. In both panels, the dashed and solid curves correspond to the results obtained from LW and VOF, respectively. In the insets, the empty and filled symbols correspond to the results obtained with LW and VOF, respectively.

Image of FIG. 6.
FIG. 6.

Film evolution for = 25, = 0.1, δ = 3, = 0.0152 with different wave frequencies ω. (a) Effect of the Marangoni number on the flow rate averaged over the periodic domain. (b) Phase difference between the traveling thermal wave and the interfacial wave. (c) Film interface deformation relative to the case of a static thermal wave with the same . Empty and filled symbols correspond to the results obtained from LW theory and VOF simulations, respectively. Curves serve to guide the reader's eye.

Image of FIG. 7.
FIG. 7.

Film evolution for = 10, = 400, δ = 3, = 0.0152 with different wave frequencies ω. (a) Effect of the wave amplitude on the flow rate. (b) Phase difference between the traveling thermal wave and the interfacial wave. (c) Film interface deformation relative to the case of a static thermal wave. Empty and filled symbols correspond to LW and VOF, respectively. Curves serve to guide the reader's eye.

Image of FIG. 8.
FIG. 8.

Film evolution for = 0.1, = 150, δ = 3, = 0.0152 with different wave frequencies ω. Note that the horizontal axis is in logarithmic scale. (a) Effect of the thermal wave period on the flow rate . (b) Phase difference between the traveling thermal wave and the interfacial wave. (c) Variation of the interface deformation relative to the case of a static thermal wave. Empty and filled symbols correspond to LW and VOF, respectively. Curves serve to guide the reader's eye.

Image of FIG. 9.
FIG. 9.

Optimal wave frequency as a function of the wave period . Circle and square symbols represent LW theory and VOF simulations, respectively. The range of parameters is 0.1 ⩽ ⩽ 0.3 and 100 ⩽ ⩽ 1500.

Tables

Generic image for table
Table I.

Dimensionless parameters.

Generic image for table
Table II.

Material properties for the bilayer liquid-gas system.

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/content/aip/journal/pof2/25/7/10.1063/1.4811829
2013-07-01
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Fluid transport in thin liquid films using traveling thermal waves
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4811829
10.1063/1.4811829
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