Creeping motion of a sphere in tubes filled with a Bingham plastic material

Abstract Numerical simulations have been undertaken for the creeping flow of a Bingham plastic past a sphere contained in a cylindrical tube. Different diameter ratios have been studied ranging from 2:1 to 50:1. The Bingham constitutive equation is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. The emphasis is on determining the extent and shape of unyielded/yielded regions along with the drag coefficient for the whole range of Bingham numbers. The present results extend previous simulations for creeping flow of a sphere in an infinite medium and provide calculations of the Stokes drag coefficient in the case of wall effects.

[1]  O. Hassager,et al.  Flow of viscoplastic fluids in eccentric annular geometries , 1992 .

[2]  M. Crochet,et al.  Numerical simulation of the motion of a sphere in a boger fluid , 1994 .

[3]  Roger I. Tanner,et al.  Numerical analysis of three-dimensional Bingham plastic flow , 1992 .

[4]  Morton M. Denn,et al.  Flow of bingham fluids in complex geometries , 1984 .

[5]  N. Phan-Thien,et al.  The flow past a sphere in a cylindrical tube: effects of intertia, shear-thinning and elasticity , 1991 .

[6]  Evan Mitsoulis,et al.  Entry and exit flows of Bingham fluids , 1992 .

[7]  T. N. Smith,et al.  Motion of spherical particles in a Bingham plastic , 1967 .

[8]  O. Harlen.  High-Deborah-number flow of a dilute polymer solution past a sphere falling along the axis of a cylindrical tube , 1990 .

[9]  S. H. Bittleston,et al.  The axial flow of a Bingham plastic in a narrow eccentric annulus , 1991, Journal of Fluid Mechanics.

[10]  R. Byron Bird,et al.  The Rheology and Flow of Viscoplastic Materials , 1983 .

[11]  R. Chhabra,et al.  Wall effect for spheres falling at small reynolds number in a viscoplastic medium , 1990 .

[12]  John Tsamopoulos,et al.  Creeping motion of a sphere through a Bingham plastic , 1985, Journal of Fluid Mechanics.

[13]  Raja R. Huilgol,et al.  On the determination of the plug flow region in Bingham fluids through the application of variational inequalities , 1995 .

[14]  Two-dimensional planar flow of a viscoelastic plastic medium , 1993 .

[15]  R. P. Chhabra,et al.  Creeping sphere motion in Herschel-Bulkley fluids: flow field and drag , 1995 .

[16]  T. Papanastasiou.  Flows of Materials with Yield , 1987 .

[17]  David K. Gartling,et al.  A numerical simulation of a plastic fluid in a parallel-plate plastometer , 1984 .

[18]  C. R. Beverly,et al.  Numerical analysis of extrudate swell in viscoelastic materials with yield stress , 1989 .

[19]  R. Armstrong,et al.  Finite element analysis of steady viscoelastic flow around a sphere in a tube: calculations with constant viscosity models , 1993 .

[20]  J. O. Wilkes,et al.  Laminar jets of Bingham-plastic liquids , 1990 .

[21]  D. V. Boger,et al.  Direct Yield Stress Measurement with the Vane Method , 1985 .

[22]  E. Mitsoulis,et al.  Flow simulation of herschel‐bulkley fluids through extrusion dies , 1993 .

[23]  Roger I. Tanner,et al.  Numerical study of the Bingham squeeze film problem , 1984 .

[24]  N. Yoshioka,et al.  On Creeping Flow of a Visco-Plastic Fluid past a Sphere , 1971 .

[25]  O. Wünsch.  Oscillating sedimentation of spheres in viscoplastic fluids , 1994 .

[26]  Naoya Yoshioka,et al.  On creeping flow of a visco-plastic fluid past a circular cylinder , 1973 .

[27]  Evan Mitsoulis,et al.  Entry and exit flows of casson fluids , 1994 .

[28]  E. Mitsoulis,et al.  Numerical Flow Simulation of Viscoplastic Slurries and Design Criteria for a Tape Casting Unit , 1994 .

[29]  Marcel Crochet,et al.  The consistent streamline-upwind/Petrov-Galerkin method for viscoelastic flow revisited , 1992 .

[30]  J. Piau,et al.  Shear rheometry of fluids with a yield stress , 1987 .

[31]  E. Toorman.  An analytical solution for the velocity and shear rate distribution of non-ideal Bingham fluids in concentric cylinder viscometers , 1994 .

[32]  A. Magnin,et al.  Cone-and-plate rheometry of yield stress fluids. Study of an aqueous gel , 1990 .