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Falling liquid films on longitudinal grooved geometries: Integral boundary layer approach
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10.1063/1.3675568
/content/aip/journal/pof2/24/1/10.1063/1.3675568
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/1/10.1063/1.3675568
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Schematic representation of the fluid flow on a grooved topography.

Image of FIG. 2.
FIG. 2.

(Color online) Neutral stability curves of the IBL and long-wave model (LW) considered in Sadiq and Usha66 (see Fig. 6 in their paper). The solid curves correspond to the flow on a vertical plane and the broken lines represent the flow on a plane inclined at β = 45°. The weber number is taken as We = 44.96 to reproduce the result in Sadiq and Usha.66

Image of FIG. 3.
FIG. 3.

(Color online) Growth rate curves on a structured and unstructured topography for water at 20 °C when β = 90° (———–) and when β = 45° (- - - - - -) for different Reynolds numbers; (a) Re = 2, (b) Re = 5, (c) Re = 10, and (d) Re = 15.

Image of FIG. 4.
FIG. 4.

(Color online) Growth rate curves on the structured and unstructured topographies inclined at (a) β = 45° and (b) β = 60° for the water-glycerin mixture (—–), water at 20 °C (- - -), and nitrogen on the saturation line at the atmospheric pressure (-.-.-.-) when Re = 20.

Image of FIG. 5.
FIG. 5.

(Color online) (a) Phase velocity and (b) frequency as a function of wavenumber for water at 20 °C when β = 90°: (—–) Re = 5 and (- - -) Re = 15.

Image of FIG. 6.
FIG. 6.

(Color online) Neutral stability curves for water at 20 °C when β = π/2 as a function of groove measure and Reynolds numbers and (b) linear stability curves corresponding to maximal growth rate.

Image of FIG. 7.
FIG. 7.

(Color online) Growth rate corresponding to the mode where the maximum instability is attained, and the frequency and phase velocity curves at maximum linear growth rate for water at 20 °C when β = π/2.

Image of FIG. 8.
FIG. 8.

(Color online) Surface wave instability and amplitude profiles reproduced from Sadiq and Usha78 and compared with the IBL model corresponding to the two-dimensional flow for Re = 5, β = π/4, We = 4496, and k = 0.14.

Image of FIG. 9.
FIG. 9.

(Color online) Two-dimensional view of the surface wave instability and the amplitude profiles for the flow at Re = 5, We = 4496, and k = 0.14: (1) β = π/2, (2) β = π/3, and (3) β = π/4.

Image of FIG. 10.
FIG. 10.

(Color online) Maximum and minimum amplitude profiles for a film flow on a vertical planar surface for water at 20 °C: (1) Re = 5, (2) Re = 10, and (3) Re = 15.

Image of FIG. 11.
FIG. 11.

(Color online) Free surface profiles for a film flow on a vertical planar surface for water at 20 °C at Re = 5.

Image of FIG. 12.
FIG. 12.

(Color online) Maximum amplitude profiles for the flow on a complex topography: (a) Re = 5, (b) Re = 10, and (c) Re = 15. In (b), numbers “1” and “2” correspond to water at 20 °C and the liquid nitrogen on the saturation line at the atmospheric pressure. In (a) and (c), the curves correspond to water at 20 °C.

Image of FIG. 13.
FIG. 13.

(Color online) Snap shots of the evolution of waves on a vertically falling film at Re = 10 corresponding to water at 20 °C: (a) L 0 = 0, (b) L 0 = 0.2, and (c) L 0 = 0.4; Figures (i) and (ii) represent the wave evolution at time t = 0 and t = 100, respectively, whereas (iii) corresponds to the time at which saturation is attained and the simulations are stopped.

Image of FIG. 14.
FIG. 14.

(Color online) Wave evolution of a film on a vertical wall at Re = 15 and L 0 = 0.2.

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/content/aip/journal/pof2/24/1/10.1063/1.3675568
2012-01-09
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Falling liquid films on longitudinal grooved geometries: Integral boundary layer approach
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/1/10.1063/1.3675568
10.1063/1.3675568
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