Skip to main content
    • Aa
    • Aa

Motion of a sphere normal to a wall in a second-order fluid

  • A. M. ARDEKANI (a1), R. H. RANGEL (a1) and D. D. JOSEPH (a1) (a2)

The motion of a sphere normal to a wall is investigated. The normal stress at the surface of the sphere is calculated and the viscoelastic effects on the normal stress for different separation distances are analysed. For small separation distances, when the particle is moving away from the wall, a tensile normal stress exists at the trailing edge if the fluid is Newtonian, while for a second-order fluid a larger tensile stress is observed. When the particle is moving towards the wall, the stress is compressive at the leading edge for a Newtonian fluid whereas a large tensile stress is observed for a second-orderfluid. The contribution of the second-order fluid to the overall force applied to the particle is towards the wall in both situations. Results are obtained using Stokes equationswhen α12=0. In addition, a perturbation method has been utilized for a sphere very close to a wall and the effect of non-zero α12 is discussed. Finally, viscoelastic potential flow is used and the results are compared with the other methods.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

A. M. Ardekani & R. H. Rangel 2006 Unsteady motion of two solid spheres in Stokes flow. Phys. Fluids. 18, 103306.

A. M. Ardekani & R. H. Rangel 2007 Numerical investigation of particle–particle and particle–wall collisions in a viscous fluid. J. Fluid Mech. (submitted).

D. L. E. Becker , G. H. McKinley & H. A. Stone 1996 Sedimentation of a sphere near a plane wall: Weak non-Newtonian and inertial effects. J. Non-Newtonian Fluid Mech. 63, 4586.

R. Bird , R. Armstrong & O. Hassager 1987 Dynamics of Polymeric Liquids. John Wiley.

H. Brenner 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Eng. Sci. 16, 242.

G. Brindley , J. M. Davies & K. Walters 1976 Elastico-viscous squeeze films. Part I. J. Non-Newtonian Fluid Mech. 1, 1937.

P. Brunn 1977 Interaction of spheres in a viscoelastic fluid. Rheologica Acta. 16, 461475.

B. Coleman & W. Noll 1960 An approximation theorem for functionals, with applications in continum mechanics. Arch. Rat. Mech. Anal. 6, 355370.

R. H. Davis 1987 Elastohydrodynamic collisions of particles. PhysicoChem. Hydrodyn. 9, 4152.

J. Engmann , C. Servais & A. S. Burbidge 2005 Squeeze flow theory and applications to rheometry: A review. J. Non-Newtonian Fluid Mech. 132, 127.

A. J. Goldman , R. G. Cox & H. Brenner 1967 Slow viscous motion of a sphere parallel to a plane wall. I. Motion through quiescent fluid. Chem. Engng. Sci. 22, 637651.

B. P. Ho & L. G. Leal 1976 Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. J. Fluid Mech. 79, 783799.

D. J. Jeffrey 1973 Conduction through a random suspension of spheres. Proc. R. Soc. Lond. A 335, 355.

D. D. Joseph 1990 Dynamics of Viscoelastic Liquids. Springer.

D. D. Joseph 1992 Bernoulli equation and the competition of elastic and inertial pressure in the potential flow of a second-order fluid. J. Non-Newtonian Fluid Mech. 42, 358389.

D. D. Joseph & J. Feng 1996 A note on the forces that move particles in a second-order fluid. J. Non-Newtonian Fluid Mech. 64, 299302.

D. D. Joseph , T. Funada & J. Wang 2007 Potential Flows of Viscous and Viscoelastic Fluids. Cambridge University Press.

D. D. Joseph , Y. J. Liu , Poletto, & M. J. Feng 1994 Aggregation and dispersion of a spheres falling in viscoelastic liquids. J. Non-Newtonian Fluid Mech. 54, 4586.

G. G. Joseph , R. Zenit , M. L. Hunt & A. M. Rosenwinkel 2001 Particle-wall collisions in a viscous fluid. J. Fluid Mech. 433, 329346.

D. L. Koch & Subramanian 2006 The stress in a dilute suspension of spheres suspended in a second-order fluid subject to a linear velocity field. J. Non-Newtonian Fluid Mech. 138, 87.

H. Lamb 1945 Hydrodynamics. Dover.

A. D. Maude 1961 End effects in a falling-sphere viscometer. Br. J. Appl. Phys. 12, 293.

R. T. Mifflin 1985 Dissipation in a dilute suspension of spheres in a second-order fluid. J. Non-Newtonian Fluid Mech. 17, 267274.

L. Pasol , M. Chaoui , S Yahiaoui . & F. Feuillebois 2005 Analytic solution for a spherical particle near a wall in axisymmetrical polynomial creeping flows. Phys. Fluids. 17, 073602.

M. J. Riddle , C. Narvaez & R. B. Bird 1977 Interactions between two spheres falling along their line of centers in viscoelastic fluid. J. Non-Newtonian Fluid Mech. 2, 2325.

R. S. Rivlin & J. L. Ericksen 1955 Stress deformation relations for isotropic materials. J. Rat. Mech. Anal. 4, 323425.

G. Rodin 1995 Squeeze film between two spheres in a power-law fluid. J. Non-Newtonian Fluid Mech. 63, 141152.

P. Singh & D. D. Joseph 2000 Sedimentation of a sphere near a wall in Oldroyd-B fluid. J. Non-Newtonian Fluid Mech. 94, 179203.

K. Sun & K. Jayaraman 1984 Bulk rheology of dilute suspensions in viscoelastic liquids. Rheol. Acta. 23, 84.

S. Takagi , H. N. Oguz , Z. Zhang & A. Prosperetti 2003 A new method for particle simulation - part ii: Two-dimensional Navier-Stokes flow around cylinders. J. Comput. Phys. 187, 371390.

R. I. Tanner 1985 Engineering Rheology. Clarendon.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *