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The shape evolution of liquid droplets in miscible environments

Published online by Cambridge University Press:  07 August 2018

Daniel J. Walls Open the ORCID record for Daniel J. Walls [Opens in a new window] ,
Eckart Meiburg Open the ORCID record for Eckart Meiburg [Opens in a new window]  and
Gerald G. Fuller
Daniel J. Walls
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
Eckart Meiburg
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Gerald G. Fuller*
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
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Abstract

Miscible liquids often come into contact with one another in natural and technological situations, commonly as a drop of one liquid present in a second, miscible liquid. The shape of a liquid droplet present in a miscible environment evolves spontaneously in time, in a distinctly different fashion than drops present in immiscible environments, which have been reported previously. We consider drops of two classical types, pendant and sessile, in building upon our prior work with miscible systems. Here we present experimental findings of the shape evolution of pendant drops along with an expanded study of the spreading of sessile drops in miscible environments. We develop scalings considering the diffusion of mass to group volumetric data of the evolving pendant drops and the diffusion of momentum to group leading-edge radial data of the spreading sessile drops. These treatments are effective in obtaining single responses for the measurements of each type of droplet, where the volume of a pendant drop diminishes exponentially in time and the leading-edge radius of a sessile drop grows following a power law of $t^{1/2}$ at long times. A complementary numerical approach to compute the concentration and velocity fields of these systems using a simplified set of governing equations is paired with our experimental findings.

JFM classification

Convection: Buoyant boundary layers Drops and Bubbles: Drops Low-Reynolds-number flows: Stokesian dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 422 - 452
Copyright
© 2018 Cambridge University Press 

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Footnotes

‡

Present address: UC, Santa Barbara, USA.

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Walls et al. supplementary movie 1

Movie of image sequence shown in Figure 3a. Scale bar is 0.2 mm.

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Walls et al. supplementary movie 2

Movie from which a frame was taken to create Figure 3b. Scale bar is 0.2 mm.

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Walls et al. supplementary movie 3

Movie of image sequence shown in Figure 7a. Scale bar is 0.2 mm.

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Walls et al. supplementary movie 4

Movie of image sequence shown in Figure 7b. Scale bar is 0.2 mm.

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Walls et al. supplementary movie 5

Movie of image sequence shown in Figure 7c. Scale bar is 0.2 mm.

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Walls et al. supplementary movie 6

Movie of a physical pendant drop of 10,000 cSt silicone oil immersed in 1 cSt silicone oil, analogous to the image sequence shown in Figure 7a. Scale bar is 0.1 mm.

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Walls et al. supplementary movie 7

Movie of a simulated pendant drop of 10,000 cSt silicone oil immersed in 1 cSt silicone oil, analogous to the image sequence shown in Figure 7c. Scale bar is 0.1 mm.

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Walls et al. supplementary movie 8

Movie from which a frame was taken to create Figure 9a. Scale bar is 2.0 mm.

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Walls et al. supplementary movie 9

Movie from which a frame was taken to create Figure 9b. Scale bar is 2.0 mm.

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Walls et al. supplementary movie 10

Movie from which a frame was taken to create Figure 9c. Scale bar is 0.5 mm.

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Walls et al. supplementary movie 11

Movie from which a frame was taken to create Figure 9d. Scale bar is 25 μm.

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Walls et al. supplementary movie 12

Movie of image sequence shown in Figure 10a. Scale bar is 1.0 mm.

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Walls et al. supplementary movie 13

Movie of an image sequence shown in Figure 10b. Scale bar is 1.0 mm.

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