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

  • M. M. Mansoor (a1), J. O. Marston (a2), J. Uddin (a3), G. Christopher (a4), Z. Zhang (a4) and S. T. Thoroddsen (a1)...
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.

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Corresponding author
Email address for correspondence: jeremy.marston@ttu.edu
References
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Ardekani A. M., Joseph D. D., Dunn-Rankin D. & Rangel R. H. 2009 Particle-wall collision in a viscoelastic fluid. J. Fluid Mech. 633, 475483.
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, 163172.
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), 226239.
Barnocky G. & Davis R. H. 1988b Elastohydrodynamic collision and rebound of spheres: Experimental verification. Phys. Fluids 31, 13241329.
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, 501519.
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, 195204.
Blair S. & Winer W. O. 1987 The influence of ambient pressure on the apparent shear thinning of liquid lubricants. Inst. Mech. Engng C109‐87, 395398.
Blair S. & Winer W. O. 1992 The high pressure high shear stress rheology of liquid lubricants. J. Tribol. 114 (1), 19.
Blake T. D. & Ruschak K. J. 1979 A maximum speed of wetting. Nature 282, 489491.
Brennen C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.
Brenner H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16, 242251.
Chen Y. L. & Israelachvili J. 1991 New mechanism of cavitation damage. Science 252, 11571160.
Dabiri S., Sirignano W. A. & Joseph D. D. 2010 Interaction between a cavitation bubble and shear flow. J. Fluid Mech. 651, 93116.
Dahneke B. 1972 The influence of flattening on the adhesion of particles. J. Colloid Interface Sci. 40 (1), 113.
Davis R. H. 1987 Elastohydrodynamic collisions of particles. Physico-Chem. Hydrodyn. 9, 4152.
Davis R. H., Rager D. A. & Good B. T. 2002 Elastohydrodynamic rebound of spheres from coated surfaces. J. Fluid Mech. 468, 107119.
Davis R. H., Serayssol J.-M. & Hinch E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479497.
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, 479504.
Engmann J., Servais C. & Burbidge A. S. 2005 Squeeze flow theory and applications to rheometry: A review. J. Non-Newtonian Fluid Mech. 132, 127.
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, 28032805.
Guala M. & Stocchino A. 2007 Large-scale flow structures in particle-wall collision at low Deborah numbers. Eur. J. Mech. (B/Fluids) 26, 511530.
Johnson K. L. 1985 Contact Mechanics. Cambridge University Press.
Joseph D. D. 1998 Cavitation and the state of stress in a flowing liquid. J. Fluid Mech. 366, 367378.
Kantak A. A. & Davis R. H. 2004 Oblique collisions and rebound of spheres from a wetted surface. J. Fluid Mech. 509, 6381.
Kantak A. A. & Davis R. H. 2006 Elastohydrodynamic theory for wet oblique collisions. Powder Technol. 168, 4252.
Knapp R., Daily J. W. & Hammit F. 1970 Cavitation. McGraw-Hill.
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, 117127.
Landau L. D. & Lifshitz E. M. 1959 Theory of Elasticity, 1st English edn. Pergamon.
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, 151164.
Löffler F. 1980 Problems and recent advances in aerosol filtration. Sep. Sci. Technol. 15, 297315.
Love A. E. H. 1927 A Treatise on the Mathematical Theory of Elasticity, 4th edn. Dover.
Lundberg J. & Shen H. H. 1992 Collisional restitution dependence on viscosity. J. Engng Mech. 118, 979989.
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.
Marston J. O., Vakarelski I. U. & Thoroddsen S. T. 2011a Bubble entrapment during sphere impact onto quiescent liquid surfaces. J. Fluid Mech. 680, 660670.
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, 729746.
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, 515526.
Plesset M.(1969) Tensile strength of liquids. Office of Naval Res. Rep. 85-4.
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.
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), 5466.
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, 173200.
Stocchino A. & Guala M. 2005 Particle-wall collision in shear thinning fluids. Exp. Fluids 38, 476484.
Uddin J., Marston J. O. & Thoroddsen S. T. 2012 Squeeze flow of a Carreau fluid during sphere impact. Phys. Fluids 24, 073104.
Zener C. 1941 The intrinsic inelasticity of large plates. Phys. Rev. 59, 669673.
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Journal of Fluid Mechanics
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Type Description Title
VIDEO
Movies

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.

 Video (1.8 MB)
1.8 MB
VIDEO
Movies

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).

 Video (1.6 MB)
1.6 MB
VIDEO
Movies

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.

 Video (2.2 MB)
2.2 MB
VIDEO
Movies

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.

 Video (1.5 MB)
1.5 MB

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