Particle Collision in Viscoelastic Fluids - Purdue University
Motion of a spherical particle towards a wall Re=850, edc=0. Comparison of present numerical results and experimental ones by Eames & Dalziel 7.
Interaction between beads and cells in the rimming flow inside a partially filled annular chamber is used for cell lysis. (Jitae Kim et al.6)
Particle-particle and particle-wall collision occurs in many natural and industrial applications such as sedimentation, crystal growth, suspension rheology, and microfluidic devices such as those used in mechanical cell lysis. To accurately predict the behavior of particulate flows, fundamental knowledge of the mechanisms of single collision is required. Whereas several experimental studies have been conducted on the influence of the Newtonian fluid on the collision process1-3, few numerical studies address this issue and the effect of viscoelasticity of the liquid yet to be discovered. In this work, particle-wall collision in Newtonian and viscoelastic fluids is numerically and experimentally studied. The effect of Stokes number, surface roughness, and Deborah number on the rebound velocity of a colliding spherical particle on a wall is considered. The experimental study of particle-wall collision in poly(ethyleneoxide) mixed with water shows that the results for the coefficient of restitution in polymeric liquids can be collapsed together with the Newtonian fluid behavior if one defines the Stokes number based on the local strain rate. Our theoretical analysis for a sphere moving normal to a wall in a second-order fluid shows that the contribution of the second-order fluid to the overall force applied to the particle is an attraction force towards the wall4,5.
Abstract
Particle Collision in Viscoelastic Fluids
Coefficient of restitution normalized by that for dry collision as a function of St where roughness height is 0.7 µm. The present numerical results are compared with the experimental results by Gondret et al.1
Lubrication theory (−) Davis et al.
Nylon (⃟)
Glass (Ο)
Derlin (∆)
Tungsten carbide (⊳)
Polyurethane (∇)
Teflon (⃞)
Steel (⃟)
Present results ( )
∙
Collision of a sphere onto a wall. Vorticity contours are shown. Reynolds number is 865 and roughness height is 9.8 µm.
Interaction of two circular particles in a Newtonian fluid at Re 470. Left) vorticity contours and stream lines Right) normal force8,9
1. P. Gondret, M. Lance, L. Petit, “Bouncing motion of spherical particles in fluids.” Physics of Fluids, Volume 14, 2002. 2. G.G. Joseph, R. Zenit, M.L. Hunt, A.M. Rosenwinkel, “Particle-wall collisions in a viscous fluid,” Journal of Fluid Mechanics, Volume 433, 329–346, 2001. 3. R.H. Davis, J.M. Serayssol, E.J. Hinch, “The elastohydrodynamic collision of two spheres,” Journal of Fluid Mechanics, Volume 163, 479, 1986. 4. A.M. Ardekani, R.H. Rangel, D.D. Joseph, “Motion of a sphere normal to a wall in second-order fluid,” Journal of Fluid Mechanics, Volume 587, 163-172, 2007. 5. A.M. Ardekani, R.H. Rangel, D.D. Joseph, “Two spheres in a free stream of a secondorder fluid,” Physics of Fluids, Volume 20, 2008. 6. J. Kim, S.H, Jang, G.Y. Jia, J.V. Zoval, N.A. Da Silva, M.J. Madou, “Cell lysis on a microfluidic CD,” Lab on a Chip, Volume 4, 516-522, 2004. 7. I. Eames, S.B. Dalziel, “Dust resuspension by the flow around an impacting sphere,” Journal of Fluid Mechanics, Volume 403, 305, 2000. 8. A.M. Ardekani, R.H. Rangel, “Numerical investigation of particle-particle and particlewall collisions in a viscous fluid,” Journal of Fluid Mechanics, Volume 596, 437-466, 2008. 9. A.M. Ardekani, S. Dabiri, R.H. Rangel, “Collision of multi-particle and general shape objects in a viscous fluid,” Journal of Computational Physics, Volume 227, 1009410107, 2008. 10. A.M. Ardekani, D.D. Joseph, D. Dunn-Rankin, R.H. Rangel, “Particle-wall collision in a viscoelastic fluid,” Journal of Fluid Mechanics, Volume 633, 475-483, 2009.
References
Collision of a sphere onto a wall in poly(ethylene-oxide). Coefficient of restitution normalized by that for dry collision as a function of St where roughness height is 0.5 µm. Left) shear rate is defined using the particle impact velocity and diameter. Right) using local shear rate10
Schematic of the experiment. Collision of a spherical particle onto a wall in 1% poly(ethylene-oxide)
Advisors: Roger H. Rangel & Daniel D. Joseph Mechanical and Aerospace Engineering, University of California, Irvine
Arezoo M. Ardekani
Interaction between beads and cells in the rimming flow inside a partially filled annular chamber is used for cell lysis. (Jitae Kim et al.6)
Particle-particle and particle-wall collision occurs in many natural and industrial applications such as sedimentation, crystal growth, suspension rheology, and microfluidic devices such as those used in mechanical cell lysis. To accurately predict the behavior of particulate flows, fundamental knowledge of the mechanisms of single collision is required. Whereas several experimental studies have been conducted on the influence of the Newtonian fluid on the collision process1-3, few numerical studies address this issue and the effect of viscoelasticity of the liquid yet to be discovered. In this work, particle-wall collision in Newtonian and viscoelastic fluids is numerically and experimentally studied. The effect of Stokes number, surface roughness, and Deborah number on the rebound velocity of a colliding spherical particle on a wall is considered. The experimental study of particle-wall collision in poly(ethyleneoxide) mixed with water shows that the results for the coefficient of restitution in polymeric liquids can be collapsed together with the Newtonian fluid behavior if one defines the Stokes number based on the local strain rate. Our theoretical analysis for a sphere moving normal to a wall in a second-order fluid shows that the contribution of the second-order fluid to the overall force applied to the particle is an attraction force towards the wall4,5.
Abstract
Particle Collision in Viscoelastic Fluids
Coefficient of restitution normalized by that for dry collision as a function of St where roughness height is 0.7 µm. The present numerical results are compared with the experimental results by Gondret et al.1
Lubrication theory (−) Davis et al.
Nylon (⃟)
Glass (Ο)
Derlin (∆)
Tungsten carbide (⊳)
Polyurethane (∇)
Teflon (⃞)
Steel (⃟)
Present results ( )
∙
Collision of a sphere onto a wall. Vorticity contours are shown. Reynolds number is 865 and roughness height is 9.8 µm.
Interaction of two circular particles in a Newtonian fluid at Re 470. Left) vorticity contours and stream lines Right) normal force8,9
1. P. Gondret, M. Lance, L. Petit, “Bouncing motion of spherical particles in fluids.” Physics of Fluids, Volume 14, 2002. 2. G.G. Joseph, R. Zenit, M.L. Hunt, A.M. Rosenwinkel, “Particle-wall collisions in a viscous fluid,” Journal of Fluid Mechanics, Volume 433, 329–346, 2001. 3. R.H. Davis, J.M. Serayssol, E.J. Hinch, “The elastohydrodynamic collision of two spheres,” Journal of Fluid Mechanics, Volume 163, 479, 1986. 4. A.M. Ardekani, R.H. Rangel, D.D. Joseph, “Motion of a sphere normal to a wall in second-order fluid,” Journal of Fluid Mechanics, Volume 587, 163-172, 2007. 5. A.M. Ardekani, R.H. Rangel, D.D. Joseph, “Two spheres in a free stream of a secondorder fluid,” Physics of Fluids, Volume 20, 2008. 6. J. Kim, S.H, Jang, G.Y. Jia, J.V. Zoval, N.A. Da Silva, M.J. Madou, “Cell lysis on a microfluidic CD,” Lab on a Chip, Volume 4, 516-522, 2004. 7. I. Eames, S.B. Dalziel, “Dust resuspension by the flow around an impacting sphere,” Journal of Fluid Mechanics, Volume 403, 305, 2000. 8. A.M. Ardekani, R.H. Rangel, “Numerical investigation of particle-particle and particlewall collisions in a viscous fluid,” Journal of Fluid Mechanics, Volume 596, 437-466, 2008. 9. A.M. Ardekani, S. Dabiri, R.H. Rangel, “Collision of multi-particle and general shape objects in a viscous fluid,” Journal of Computational Physics, Volume 227, 1009410107, 2008. 10. A.M. Ardekani, D.D. Joseph, D. Dunn-Rankin, R.H. Rangel, “Particle-wall collision in a viscoelastic fluid,” Journal of Fluid Mechanics, Volume 633, 475-483, 2009.
References
Collision of a sphere onto a wall in poly(ethylene-oxide). Coefficient of restitution normalized by that for dry collision as a function of St where roughness height is 0.5 µm. Left) shear rate is defined using the particle impact velocity and diameter. Right) using local shear rate10
Schematic of the experiment. Collision of a spherical particle onto a wall in 1% poly(ethylene-oxide)
Advisors: Roger H. Rangel & Daniel D. Joseph Mechanical and Aerospace Engineering, University of California, Irvine
Arezoo M. Ardekani
