Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-18T00:56:39.768Z Has data issue: false hasContentIssue false
  • English
  • Français

Cavitation structures formed during the collision of a sphere with an ultra-viscous wetted surface

Published online by Cambridge University Press:  05 May 2016

M. M. Mansoor ,
J. O. Marston ,
J. Uddin ,
G. Christopher ,
Z. Zhang  and
S. T. Thoroddsen
M. M. Mansoor
Affiliation:
Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
J. O. Marston*
Affiliation:
Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409-3121, USA
J. Uddin
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston B15 2TT, UK
G. Christopher
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409-1021, USA
Z. Zhang
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409-1021, USA
S. T. Thoroddsen
Affiliation:
Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
*
†Email address for correspondence: jeremy.marston@ttu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the inception of cavitation and resulting structures when a sphere collides with a solid surface covered with a layer of non-Newtonian liquid having a kinematic viscosity of up to ${\it\nu}_{0}=20\,000\,000$ cSt. We show the existence of shear-stress-induced cavitation during sphere approach towards the base wall (i.e. the pressurization stage) in ultra-viscous films using a synchronized dual-view high-speed imaging system. For the experimental parameters employed, liquids having viscoelastic properties of $De\geqslant O(1)$ are shown to enable sphere rebound without any prior contact with the solid wall. Cavitation by depressurization (i.e. during rebound) in such non-contact cases is observed to onset after a noticeable delay from when the minimum gap distance is reached. Also, the cavities created originate from remnant bubbles, being the remains of the primary bubble entrapment formed by the lubrication pressure of the air during film entry. Cases where physical contact occurs (contact cases) in 10 000 cSt ${\leqslant}{\it\nu}_{0}\leqslant 1000\,000$ cSt films produce cavities attached to the base wall, which extend into an hourglass shape. In contrast, strikingly different structures occur in the most viscous liquids due to the disproportionality in radial expansion and longitudinal extension along the cavity length. Horizontal shear rates calculated using particle image velocimetry (PIV) measurements show the apparent fluid viscosity to vary substantially as the sphere approaches and rebounds away from the base wall. A theoretical model based on the lubrication assumption is solved for the squeeze flow in the regime identified for shear-induced cavity events, to investigate the criterion for cavity inception in further detail.

JFM classification

Drops and Bubbles: Cavitation Drops and Bubbles: Drops and Bubbles Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 796 , 10 June 2016 , pp. 473 - 515
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.)

References

Ardekani, A. M., Joseph, D. D., Dunn-Rankin, D. & Rangel, R. H. 2009 Particle-wall collision in a viscoelastic fluid. J. Fluid Mech. 633, 475–483.Google Scholar
Ardekani, A. M., Rangel, R. H. & Joseph, D. D. 2007 Motion of a sphere normal to a wall in a second-order fluid. J. Fluid Mech. 587, 163–172.Google Scholar
Barnocky, G. & Davis, R. H. 1988a The effect of Maxwell slip on the aerodynamic collision and rebound of spherical particles. J. Colloid Interface Sci. 121 (1), 226–239.Google Scholar
Barnocky, G. & Davis, R. H. 1988b Elastohydrodynamic collision and rebound of spheres: Experimental verification. Phys. Fluids 31, 1324–1329.Google Scholar
Barnocky, G. & Davis, R. H. 1989 The influence of pressure-dependent density and viscosity on the elastohydrodynamic collision and rebound of two spheres. J. Fluid Mech. 209, 501–519.Google Scholar
Bhamidipati, K., Didari, S. & Harris, T. A. L. 2012 Experimental study on air entrainment in slot die coating of high-viscosity, shear-thinning fluids. Chem. Engng Sci. 80, 195–204.CrossRefGoogle Scholar
Blair, S. & Winer, W. O. 1987 The influence of ambient pressure on the apparent shear thinning of liquid lubricants. Inst. Mech. Engng C109‐87, 395–398.Google Scholar
Blair, S. & Winer, W. O. 1992 The high pressure high shear stress rheology of liquid lubricants. J. Tribol. 114 (1), 1–9.Google Scholar
Blake, T. D. & Ruschak, K. J. 1979 A maximum speed of wetting. Nature 282, 489–491.Google Scholar
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.Google Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16, 242–251.Google Scholar
Chen, Y. L. & Israelachvili, J. 1991 New mechanism of cavitation damage. Science 252, 1157–1160.Google Scholar
Dabiri, S., Sirignano, W. A. & Joseph, D. D. 2010 Interaction between a cavitation bubble and shear flow. J. Fluid Mech. 651, 93–116.CrossRefGoogle Scholar
Dahneke, B. 1972 The influence of flattening on the adhesion of particles. J. Colloid Interface Sci. 40 (1), 1–13.Google Scholar
Davis, R. H. 1987 Elastohydrodynamic collisions of particles. Physico-Chem. Hydrodyn. 9, 41–52.Google Scholar
Davis, R. H., Rager, D. A. & Good, B. T. 2002 Elastohydrodynamic rebound of spheres from coated surfaces. J. Fluid Mech. 468, 107–119.CrossRefGoogle Scholar
Davis, R. H., Serayssol, J.-M. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479–497.Google Scholar
Donahue, C. M., Hrenya, C. M., Davis, R. H., Nakagawa, K. J., Zelinskaya, A. P. & Joseph, G. G. 2010 Stokes cradle: normal three-body collisions between wetted particles. J. Fluid Mech. 650, 479–504.Google Scholar
Engmann, J., Servais, C. & Burbidge, A. S. 2005 Squeeze flow theory and applications to rheometry: A review. J. Non-Newtonian Fluid Mech. 132, 1–27.CrossRefGoogle Scholar
Gondret, P., Hallouin, E., Lance, M. & Petit, L. 1999 Experiments on the motion of a solid sphere toward a wall: from viscous dissipation to elastohydrodynamic bouncing. Phys. Fluids 11, 2803–2805.CrossRefGoogle Scholar
Guala, M. & Stocchino, A. 2007 Large-scale flow structures in particle-wall collision at low Deborah numbers. Eur. J. Mech. (B/Fluids) 26, 511–530.CrossRefGoogle Scholar
Johnson, K. L. 1985 Contact Mechanics. Cambridge University Press.CrossRefGoogle Scholar
Joseph, D. D. 1998 Cavitation and the state of stress in a flowing liquid. J. Fluid Mech. 366, 367–378.CrossRefGoogle Scholar
Kantak, A. A. & Davis, R. H. 2004 Oblique collisions and rebound of spheres from a wetted surface. J. Fluid Mech. 509, 63–81.CrossRefGoogle Scholar
Kantak, A. A. & Davis, R. H. 2006 Elastohydrodynamic theory for wet oblique collisions. Powder Technol. 168, 42–52.Google Scholar
Knapp, R., Daily, J. W. & Hammit, F. 1970 Cavitation. McGraw-Hill.Google Scholar
Kuhl, T., Ruths, M., Chen, Y. L. & Israelachvili, J. 1994 Direct visualization of cavitation and damage in ultrathin liquid films. J. Heart Valve Disease 3, 117–127.Google ScholarPubMed
Landau, L. D. & Lifshitz, E. M. 1959 Theory of Elasticity, 1st English edn. Pergamon.Google Scholar
Lian, G., Xu, Y., Huang, W. & Adams, M. J. 2001 On the squeeze flow of a power-law fluid between rigid spheres. J. Non-Newtonian Fluid Mech. 100, 151–164.Google Scholar
Löffler, F. 1980 Problems and recent advances in aerosol filtration. Sep. Sci. Technol. 15, 297–315.CrossRefGoogle Scholar
Love, A. E. H. 1927 A Treatise on the Mathematical Theory of Elasticity, 4th edn. Dover.Google Scholar
Lundberg, J. & Shen, H. H. 1992 Collisional restitution dependence on viscosity. J. Engng Mech. 118, 979–989.Google Scholar
Mansoor, M. M., Uddin, J., Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2014 The onset of cavitation during the collision of a sphere with a wetted surface. Exp. Fluids 55, 1648.CrossRefGoogle Scholar
Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2011a Bubble entrapment during sphere impact onto quiescent liquid surfaces. J. Fluid Mech. 680, 660–670.Google Scholar
Marston, J. O., Yong, W., Ng, W. K., Tan, R. B. H. & Thoroddsen, S. T. 2011b Cavitation structures formed during the rebound of a sphere from a wetted surface. Exp. Fluids 50, 729–746.CrossRefGoogle Scholar
Marston, J. O., Yong, W. & Thoroddsen, S. T. 2010 Direct verification of the lubrication force on a sphere travelling through a viscous film upon approach to a solid wall. J. Fluid Mech. 655, 515–526.CrossRefGoogle Scholar
Plesset, M.(1969) Tensile strength of liquids. Office of Naval Res. Rep. 85-4.Google Scholar
Seddon, J. R. T., Kok, M. P., Linnartz, E. C. & Lohse, D. 2012 Bubble puzzles in liquid squeeze: cavitation during compression. Europhys. Lett. 97, 24004.Google Scholar
Serayssol, J.-M. & Davis, R. H. 1986 The influence of surface interactions on the elastohydrodynamic collision of two spheres. J. Colloid Interface Sci. 114 (1), 54–66.Google Scholar
Severtson, Y. C. & Aidun, C. H. 1996 Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems. J. Fluid Mech. 312, 173–200.Google Scholar
Stocchino, A. & Guala, M. 2005 Particle-wall collision in shear thinning fluids. Exp. Fluids 38, 476–484.CrossRefGoogle Scholar
Uddin, J., Marston, J. O. & Thoroddsen, S. T. 2012 Squeeze flow of a Carreau fluid during sphere impact. Phys. Fluids 24, 073104.Google Scholar
Zener, C. 1941 The intrinsic inelasticity of large plates. Phys. Rev. 59, 669–673.Google Scholar

Mansoor et al. supplementary movie

Side (left) and bottom (right) views of the impact and rebound of a tungsten sphere in a 5 mm-thick layer of 100,000 cSt oil. The impact speeds are (a) 2.78 m/s and (b) 3.42 m/s giving St = 0.94 and 1.16 and De = 1.59 and 1.95, respectively.

Download Mansoor et al. supplementary movie(Video)
Video 2.2 MB

Mansoor et al. supplementary movie

Side-views of cavity structures forming during the rebound of a sphere from a 5 mm=thick layers of 20,000,000 cSt oil. The impact speeds are 5.51, 5.59 and 5.77 m/s respectively, giving St = O(10-2) and De = O(400).

Download Mansoor et al. supplementary movie(Video)
Video 1.6 MB

Mansoor et al. supplementary movie

Side-view of the cavity formation during the rebound of a sphere from a 4 mm-thick layer of 1,000,000 cSt oil. The oil is seeded with particles used for PIV measurements. The impact speed is 3.56 m/s giving St = 0.12 and De = 27.9.

Download Mansoor et al. supplementary movie(Video)
Video 1.5 MB

Mansoor et al. supplementary movie

Side-view of the cavity formation during the rebound of a sphere from a 4 mm-thick layer of 20,000,000 cSt oil. The oil is seeded with particles used for PIV measurements. The impact speed is 5.23 m/s giving St = 8.84 x 10-3 and De = 363.

Download Mansoor et al. supplementary movie(Video)
Video 1.8 MB