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An analysis of head-on droplet collision with large deformation in gaseous medium
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10.1063/1.3580754
/content/aip/journal/pof2/23/4/10.1063/1.3580754
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/4/10.1063/1.3580754

Figures

Image of FIG. 1.
FIG. 1.

Schematic of collision regimes of hydrocarbon droplets in atmospheric pressure.

Image of FIG. 2.
FIG. 2.

Schematic of the droplet configuration analyzed. Only one droplet is shown here because of symmetry. The four time-dependent variables describing the droplet geometry and dynamics are the radius of the flattened interface , the perpendicular distance from the center of the spherical surface to the flattened interface , the droplet radius , and the distance between the impacting interfaces . The distance between the center of mass of the droplet to the flattened interface can be expressed in terms of and .

Image of FIG. 3.
FIG. 3.

Schematic of the induced flow by an expanding disk. The outward velocity on the disk is given by and is the strain rate.

Image of FIG. 4.
FIG. 4.

Comparison of the three solutions for the droplet internal motion: the series solution (dash line), the numerical solution (solid line), and the approximate solution (dash dot line).

Image of FIG. 5.
FIG. 5.

Schematic of the Poiseuille flow between two expanding flattened interfaces. The radial dimension is much larger than the axial dimension .

Image of FIG. 6.
FIG. 6.

Variation of the pressure correction due to rarefied gas effect with the Knudsen number. Comparison between the numerical integration of Eq. (68) for (circle), first approximation (69) for , which is extended to (asterisk) and composite expression (73) (solid line).

Image of FIG. 7.
FIG. 7.

Evolution of the time-dependent variables , , , and describing the tetradecane droplet coalescence at .

Image of FIG. 8.
FIG. 8.

Evolution of the time-dependent variables , , , and describing the tetradecane droplet coalescence at .

Image of FIG. 9.
FIG. 9.

Evolution of the time-dependent variables , , , and describing the tetradecane droplet coalescence at .

Image of FIG. 10.
FIG. 10.

Evolution of the gap distance with time for the collision of tetradecane droplets in 1 atm air.

Image of FIG. 11.
FIG. 11.

Evolution of the gap distance with time for the soft collision of tetradecane droplets in one atmosphere air around the transition state .

Image of FIG. 12.
FIG. 12.

Evolution of the time-dependent variables , , , and describing the soft coalescence of tetradecane droplets in 1 atm air at the transition state , with manifest nonmonotonic evolution behavior of , , and .

Image of FIG. 13.
FIG. 13.

Evolution of the gap distance with time for the hard collision of tetradecane droplets in 1 atm air around the transition state .

Image of FIG. 14.
FIG. 14.

Evolution of the time-dependent variables , , , and describing the hard coalescence of tetradecane droplets in 1 atm air at the transition state , with manifest nonmonotonic evolution behavior of , , and .

Image of FIG. 15.
FIG. 15.

Evolution of the gap distance with time for the collision of tetradecane droplets in reduced pressure (0.6 atm).

Image of FIG. 16.
FIG. 16.

Evolution of the gap distance with time for the collision of tetradecane droplets in elevated pressure (2.4 atm).

Image of FIG. 17.
FIG. 17.

Evolution of the gap width with time normalized by the natural oscillation time of the droplet for the collision of tetradecane droplets in reduced pressure (0.6 atm).

Image of FIG. 18.
FIG. 18.

The variation of the coalescence time normalized by the natural oscillation time with Weber number We. The solid and dashed lines correspond to droplet coalescence at 1.0 and 0.6 atm pressures, respectively.

Image of FIG. 19.
FIG. 19.

Evolution of the gap distance with time for the collision of water droplets in 1 atm air.

Image of FIG. 20.
FIG. 20.

Evolution of the gap distance with time for the collision of water droplets in 2.7 atm air.

Image of FIG. 21.
FIG. 21.

Evolution of the gap distance with time for the collision of water droplets in 8.0 atm air.

Image of FIG. 22.
FIG. 22.

(Left) Evolution of the gap distance with time for the collision of tetradecane droplets in 1 atm air, without including the viscous dissipation in droplets. (Right) Evolution of the radius of the flattened interface with time for and 34.1, with and without including the viscous dissipation.

Image of FIG. 23.
FIG. 23.

Evolution of the gap distance with time for the collision of tetradecane droplets in 1 atm air, with and without including the rarefied gas effect.

Image of FIG. 24.
FIG. 24.

Evolution of the gap distance with time for the collision of tetradecane droplets in 1 atm air, (left) without including the van der Waals force and (right) with different Hamaker constants.

Image of FIG. 25.
FIG. 25.

Change of the maximum deformation with the Weber number We. The solid line is the present theoretical results and circles denote experimental values from Ref. 8.

Tables

Generic image for table
Table I.

Physical properties and relevant nondimensional parameters for the collision of tetradecane and water droplets in air.

Generic image for table
Table II.

Comparison of the predicted and experimental transition We for the collision of tetradecane and water droplets in air.

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/content/aip/journal/pof2/23/4/10.1063/1.3580754
2011-04-26
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: An analysis of head-on droplet collision with large deformation in gaseous medium
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/4/10.1063/1.3580754
10.1063/1.3580754
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