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Water entry of spheres with various contact angles

Published online by Cambridge University Press:  10 January 2019

Nathan B. Speirs ,
Mohammad M. Mansoor Open the ORCID record for Mohammad M. Mansoor [Opens in a new window] ,
Jesse Belden Open the ORCID record for Jesse Belden [Opens in a new window]  and
Tadd T. Truscott Open the ORCID record for Tadd T. Truscott [Opens in a new window]
Nathan B. Speirs
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
Mohammad M. Mansoor
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
Jesse Belden
Affiliation:
Naval Undersea Warfare Center, 1176 Howell Street, Newport, RI 02841, USA
Tadd T. Truscott*
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
*
†Email address for correspondence: [email protected]
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Abstract

It is well known that the water entry of a sphere causes cavity formation above a critical impact velocity as a function of the solid–liquid contact angle; Duez et al. (Nat. Phys., vol. 3 (3), 2007, pp. 180–183). Using a rough sphere with a contact angle of $120^{\circ }$, Aristoff & Bush (J. Fluid Mech., vol. 619, 2009, pp. 45–78) showed that there are four different cavity shapes dependent on the Bond and Weber numbers (i.e., quasistatic, shallow, deep and surface). We experimentally alter the Bond number, Weber number and contact angle of smooth spheres and find two key additions to the literature: (1) cavity shape also depends on the contact angle; (2) the absence of a splash crown at low Weber number results in cavity formation below the predicted critical velocity. In addition, we use alternate scales in defining the Bond, Weber and Froude numbers to predict the cavity shapes and scale pinch-off times for various impacting bodies (e.g., spheres, multidroplet streams and jets) on the same plots, merging the often separated studies of solid–liquid and liquid–liquid impact in the literature.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , R3
Copyright
© 2019 Cambridge University Press 

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References

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Speirs et al. supplementary movie 1

A 3 mm diameter sphere impacts a quiescent pool surface with velocity Uo=4.43 m/s and static contact angle θ=101.0˚ without forming a cavity. The movie is played back at 0.6% of real speed.

Download Speirs et al. supplementary movie 1(Video)
Video 616.4 KB

Speirs et al. supplementary movie 2

A 3 mm diameter sphere impacts a quiescent pool surface with velocity Uo=0.24 m/s and static contact angle θ=141.1˚ forming a quasi-static seal cavity. The movie is played back at 0.6% of real speed.

Download Speirs et al. supplementary movie 2(Video)
Video 1.9 MB

Speirs et al. supplementary movie 3

A 3 mm diameter sphere impacts a quiescent pool surface with velocity Uo=1.40 m/s and static contact angle θ=141.1˚ forming a shallow seal cavity. Deep seal quickly follows shallow seal in this case. The movie is played back at 0.6% of real speed.

Download Speirs et al. supplementary movie 3(Video)
Video 3.1 MB

Speirs et al. supplementary movie 4

A 3 mm diameter sphere impacts a quiescent pool surface with velocity Uo=2.80 m/s and static contact angle θ=141.1˚ forming a deep seal cavity. The movie is played back at 0.6% of real speed.

Download Speirs et al. supplementary movie 4(Video)
Video 1.4 MB

Speirs et al. supplementary movie 5

A 3 mm diameter sphere impacts a quiescent pool surface with velocity Uo=4.43 m/s and static contact angle θ=141.1˚ forming a surface seal cavity. The movie is played back at 0.6% of real speed.

Download Speirs et al. supplementary movie 5(Video)
Video 2.2 MB

Speirs et al. supplementary movie 6

A 10 mm diameter sphere impacts a quiescent pool surface with velocity Uo=6.26 m/s and static contact angle θ=101.1˚ forming a partial surface seal cavity. The movie is played back at 0.6% of real speed.

Download Speirs et al. supplementary movie 6(Video)
Video 1.7 MB