Wind-Driven Rivulet Breakoff and Droplet Flows in Microgravity and Terrestrial-Gravity Conditions

[+] Author and Article Information
G. McAlister, R. Ettema, J. S. Marshall

 IIHR—Hydroscience and Engineering, University of Iowa, Iowa City IA 52242

J. Fluids Eng 127(2), 257-266 (Aug 23, 2004) (10 pages) doi:10.1115/1.1881696 History: Received April 13, 2004; Revised August 23, 2004

A study is reported of the wind-driven breakoff of rivulets and subsequent droplet flows on a horizontal plate subject to different normal gravitational states, ranging from zero- to terrestrial-gravity conditions (1 g), and including some data for partial gravity conditions (between 0.1 g and 0.38 g). The study entailed experiments conducted in the authors’ laboratory at the University of Iowa and onboard the NASA KC-135, parabolic-flight aircraft. The wind-driven rivulets exhibited a breakoff phenomenon over a broad range of flow rates, in which a “head” at the tip of the rivulet broke off periodically to form a droplet that advected down the plate. The rivulet breakoff phenomena was sensitive to the normal gravitational force acting on the plate. For instance, the frequency of rivulet breakoff was nearly an order-of-magnitude greater for the 0 g condition than for the same flow in the 1 g condition. The droplet shape and behavior were observed to be quite different between the two cases. It was furthermore found in all cases examined that wind-driven rivulet and droplet flows are markedly different from gravitationally driven flows. These differences arise primarily from the role of form drag on the droplets and on the raised ridge of the rivulet and pool flows near the moving contact line.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Sketch of the rivulet wind tunnel showing (A) air inlet, (B) blower, (C) contraction, (D) honeycomb, (E) test section, (F) honeycomb water trap, (G) air outlet, (H) collapsible water storage tank, (I) positive-displacement pump, (J) needle valve, (K) water inlet hole, and (L) water collection box.

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Figure 2

Photographs of experimental runs with low airflow rates: (a) large puddle spreading downstream for a very low wind speed case (U=4.5m∕s); (b) fanshaped structure for a slightly higher wind speed case (U=6m∕s). Both experiments are performed with a water flow rate of Q=5mL∕min.

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Figure 3

Typical sequence of droplet detachment and roller development and bifurcation for the terrestrial gravity experiments

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Figure 4

Photographs showing breakoff of a rivulet head to form a droplet in 1 g, including (a) the rivulet at a time where it has stopped progressing and is beginning to form a large head, and (b) close-up of the head about to detach from the rivulet. Grid lines have a spacing of 6 mm.

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Figure 5

Data for (a) rivulet breakoff period T and (b) product of T and the water flow rate Q versus air speed U for the terrestrial gravity (1 g) case, for values of water flow rate of Q=10ml∕min (squares), 15ml∕min (triangles), 20ml∕min (circles), and 40ml∕min (diamonds). The solid line is the theoretical prediction from Eq. 6 for C=0.5.

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Figure 6

Average substrate surface area covered by rivulet head at time of breakoff versus air speed for terrestrial gravity experiments. Error bars indicate the standard deviation of the data. The curve represents the theoretical prediction from Eq. 7 with D=3.

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Figure 7

(a) Average time Trivulet for attached rivulet head to progress 300 mm downstream from the inlet versus air speed U for the terrestrial gravity experiments, with water flow rates Q=5ml∕min (crosses), 10ml∕min (squares), 15ml∕min (triangles), 20ml∕min (circles), and 40ml∕min (diamonds). The lines are best fit to the data. (b) Correlation, showing all data, obtained by plotting as a function of rivulet breakoff period.

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Figure 8

Examples of downstream-propagating rollers on a horizontal surface in 1 g: (a) droplet forming a roller shortly after breakoff from rivulet, (b) close-up view of the elongated, double-lobed structure of the roller, and (c) a larger roller overtaking two smaller droplets (Q=15ml∕min, U=11m∕s). Grid lines have a spacing of 6 mm.

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Figure 9

Average velocity of initial droplet versus air speed U for data with all water flow rates for the terrestrial gravity experiments. The error bars indicate the first quartile of velocity measurement around the mean.

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Figure 10

Graphs of droplet bifurcations and collisions for the terrestrial gravity experiments, showing average number of times a single droplet (a) bifurcates and (b) collides with another droplet as it traverses the test surface for cases with water flow rate Q=5ml∕min (crosses), 10ml∕min (squares), 15ml∕min (triangles), 20ml∕min (circles), and 40ml∕min (diamonds)

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Figure 11

Typical sequence of rivulet head growth and detachment for microgravity case

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Figure 12

Period of rivulet breakoff in microgravity versus the water discharge rate, for cases with Q=10.3ml∕min (squares), 11.4ml∕min (triangles), 11.9ml∕min (circles), and 12.5ml∕min (diamonds). The curves give the theoretical predictions from Eq. 6 with C=0.05 for U=10m∕s (dashed), 11m∕s (solid) and 12m∕s (dashed-dotted).

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Figure 13

The average height of the rivulet head at the breakoff time for all microgravity experiments, where Q=7ml∕min (squares), 10ml∕min (triangles), 12.5ml∕min (gradients), 18.5ml∕min (right triangles), 26.5ml∕min (crosses), 33ml∕min (circles). The curve represents the theoretical prediction from Eq. 8 with A=3.7.

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Figure 14

Periodic shedding showing two nearly hemispherical droplets with a third about to break off from the end of the rivulet for microgravity case (Q=15mL∕min, U=11.8m∕s). Grid lines have a spacing of 6 mm.

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Figure 15

Average droplet velocity versus air speed for the microgravity experiments, with Q=7ml∕min (squares), 10ml∕min (triangles), 12.5ml∕min (gradients), 15ml∕min (asterisks), 18.5ml∕min (crosses), 26.5ml∕min (diamonds), and 33ml∕min (circles)

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Figure 16

Typical sequence illustrating the inchworm phenomenon for microgravity droplet flows

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Figure 17

Photographs of the rivulet head and detached droplets for (a) 0.38g (Q=10ml∕min, U=11m∕s) and (b) 1.5 g (Q=10ml∕min, U=12.4m∕s)

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Figure 18

Period of rivulet breakoff for partial-gravity cases as a function of water flow rate with air speed held constant at 11m∕s, for cases with 0 g (squares), 0.16 g (gradients), 0.26 g (circles), and 0.38 g (diamonds). Curves are predictions from Eq. 6 with C=0.05 (lower dashed), 0.07 (lower solid), 0.09 (upper dashed), and 0.11 (upper solid), respectively.




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