Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-10-29T21:40:55.135Z Has data issue: false hasContentIssue false
  • English
  • Français

Cavity formation in the wake of falling spheres submerging into a stratified two-layer system of immiscible liquids

Published online by Cambridge University Press:  01 February 2016

Benedict C.-W. Tan ,
J. H. A. Vlaskamp ,
P. Denissenko  and
P. J. Thomas
Benedict C.-W. Tan
Affiliation:
Fluid Dynamics Research Centre, School of Engineering, University of Warwick, Coventry CV4 7AL, UK
J. H. A. Vlaskamp
Affiliation:
Fluid Dynamics Research Centre, School of Engineering, University of Warwick, Coventry CV4 7AL, UK
P. Denissenko
Affiliation:
Fluid Dynamics Research Centre, School of Engineering, University of Warwick, Coventry CV4 7AL, UK
P. J. Thomas*
Affiliation:
Fluid Dynamics Research Centre, School of Engineering, University of Warwick, Coventry CV4 7AL, UK
*
†Email address for correspondence: Peter.Thomas@warwick.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We experimentally study the cavities forming in the wake of rigid spheres when submerging into a stratified, two-layer system of immiscible, quiescent liquids comprising a thin layer of oil above a deep pool of water. The results obtained for our two-layer system are compared with data from the literature for the corresponding type of cavities formed when spheres enter a homogeneous liquid that is not covered by an oil layer. The discussion and the data analysis reveal that the oil coating acquired by the spheres while propagating through the thin oil layer, before entering the pool of water underneath, substantially affects qualitative and quantitative aspects of the dynamics associated with the cavity formation. In particular, we observe the formation of a ripple-like pattern on the cavity walls which is not known to exist when spheres enter a homogeneous liquid. The data analysis suggests that the ripple patterns form as a consequence of a two-dimensional instability arising due to the shear between the oil layer coating the spheres and the ambient water.

JFM classification

Drops and Bubbles: Drops and Bubbles Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Multiphase flow

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 790 , 10 March 2016 , pp. 33 - 56
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Aristoff, J. M. & Bush, J. W. M. 2009 Water entry of small hydrophobic spheres. J. Fluid Mech. 619, 45–78.Google Scholar
Bell, G. E. 1924 On the impact of a solid sphere with a liquid surface and the influence of surface tension, surface layers, and viscosity on the phenomenon. Phil. Mag. 6 48, 753–764.Google Scholar
Bergmann, R., van der Meer, D., Gekle, S., van der Bos, A. & Lohse, D. 2009 Controlled impact of a disk on a water surface: cavity dynamics. J. Fluid Mech. 633, 381–409.CrossRefGoogle Scholar
Brown, P. P. & Lawler, D. F. 2003 Sphere drag and settling velocity revisited. J. Environ. Engng 129, 222–231.Google Scholar
Duclaux, V., Caillé, F., Duez, C., Ybert, C., Bocquet, L. & Clanet, C. 2007 Dynamics of transient cavities. J. Fluid Mech. 591, 1–19.Google Scholar
Gekle, S., Gordillo, J. M., van der Meer, D. & Lohse, D. 2009 High-speed jet formation after solid object impact. Phys. Rev. Lett. 102, 034502.Google Scholar
Glasheen, J. W. & McMahon, T. A. 1996 Vertical water entry of disks at low Froude numbers. Phys. Fluids 8, 2078–2083.CrossRefGoogle Scholar
Grumstrup, T., Keller, J. B. & Belmonte, A. 2007 Cavity ripples observed during the impact of solid objects into liquids. Phys. Rev. Lett. 99, 114502.CrossRefGoogle ScholarPubMed
Le Goff, A., Quéré, D. & Clanet, C. 2013 Viscous cavities. Phys. Fluids 25, 043101.Google Scholar
Lucassen-Reynders, E. H. & Lucassen, J. 1970 Properties of capillary waves. Adv. Colloid Interface Sci. 2, 347–395.Google Scholar
Mallock, A. 1918 Sounds produced by drops falling on water. Proc. R. Soc. Lond. A 95, 138–143.Google Scholar
Mansoor, M. M., Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2014 Water entry without surface seal: extended cavity formation. J. Fluid Mech. 743, 295–326.Google Scholar
Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2012 Cavity formation by the impact of Leidenfrost spheres. J. Fluid Mech. 699, 465–488.Google Scholar
May, A. 1952 Vertical entry of missiles into water. J. Appl. Phys. 23, 1362–1372.Google Scholar
Sakamoto, S. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. Trans. ASME J. Fluids Engng 112, 386–392.Google Scholar
Thoroddsen, S. T., Etoh, T. G., Takehara, K. & Takano, Y. 2004 Impact jetting by a solid sphere. J. Fluid Mech. 499, 139–148.Google Scholar
Thoroddsen, S. T. 2012 The making of a splash. J. Fluid Mech. 690, 1–4.Google Scholar
Truscott, T. T. & Techet, A. H. 2006 Cavity formation in the wake of a spinning sphere impacting the free surface. Phys. Fluids 18, 091113.Google Scholar
Truscott, T. T. & Techet, A. H. 2009a Water entry of spinning spheres. J. Fluid Mech. 625, 135–165.Google Scholar
Truscott, T. T. & Techet, A. H. 2009b A spin on cavity formation during water entry of hydrophobic and hydrophilic spheres. Phys. Fluids 21, 121703.Google Scholar
Truscott, T. T., Epps, B. P. & Techet, A. H. 2012 Unsteady forces on spheres during free-surface water entry. J. Fluid Mech. 704, 173–210.Google Scholar
Truscott, T. T., Epps, B. P. & Belden, J. 2014 Water entry of projectiles. Annu. Rev. Fluid Mech. 46, 355–378.CrossRefGoogle Scholar
Worthington, A. M. 1908 A Study of Splashes. Longmans, Green.Google Scholar
Worthington, A. M. & Cole, R. S. 1897 Impact with a liquid surface, studied by the aid of instantaneous photography. Phil. Trans. R. Soc. Lond. A 189, 137–148.Google Scholar
Worthington, A. M. & Cole, R. S. 1900 Impact with a liquid surface, studied by the aid of instantaneous photography. Paper II. Phil. Trans. R. Soc. Lond. A 194, 175–199.Google Scholar

Tan Supplementary Movie

Tan Supplementary Movie

Download Tan Supplementary Movie(Video)
Video 3.6 MB