Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 17
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Matulka, Paul Du, Xin and Walzel, Peter 2011. Particle motion and separation in a laminar tube flow with downstream enlargement. Chemical Engineering Science, Vol. 66, Issue. 23, p. 5930.

    Janssen, P. J. A. Baron, M. D. Anderson, P. D. Blawzdziewicz, J. Loewenberg, M. and Wajnryb, E. 2012. Collective dynamics of confined rigid spheres and deformable drops. Soft Matter, Vol. 8, Issue. 28, p. 7495.

    Navardi, Shahin and Bhattacharya, Sukalyan 2010. Effect of confining conduit on effective viscosity of dilute colloidal suspension. The Journal of Chemical Physics, Vol. 132, Issue. 11, p. 114114.

    Yeh, Hong Y. and Keh, Huan J. 2013. Axisymmetric creeping motion of a prolate particle in a cylindrical pore. European Journal of Mechanics - B/Fluids, Vol. 39, p. 52.

    Bhattacharya, S. 2016. Interfacial wave dynamics of a drop with an embedded bubble. Physical Review E, Vol. 93, Issue. 2,

    Navardi, Shahin and Bhattacharya, Sukalyan 2013. General methodology to evaluate two-particle hydrodynamic friction inside cylinder-bound viscous fluid. Computers & Fluids, Vol. 76, p. 149.

    Azese, Martin Ndi 2016. On the generalization of velocity slip in fluid flows using a steady-state series expansion of the wall shear stress: Case of simple Newtonian fluids. European Journal of Mechanics - B/Fluids, Vol. 57, p. 204.

    Imperio, A. Padding, J. T. and Briels, W. J. 2011. Diffusion of spherical particles in microcavities. The Journal of Chemical Physics, Vol. 134, Issue. 15, p. 154904.

    Bhattacharya, S. Gurung, D. K. and Navardi, S. 2013. Radial distribution and axial dispersion of suspended particles inside a narrow cylinder due to mildly inertial flow. Physics of Fluids, Vol. 25, Issue. 3, p. 033304.

    Navardi, Shahin and Bhattacharya, Sukalyan 2010. Axial pressure-difference between far-fields across a sphere in viscous flow bounded by a cylinder. Physics of Fluids, Vol. 22, Issue. 10, p. 103305.

    Kohale, Swapnil C. and Khare, Rajesh 2010. Molecular dynamics simulation study of friction force and torque on a rough spherical particle. The Journal of Chemical Physics, Vol. 132, Issue. 23, p. 234706.

    Navardi, Shahin Bhattacharya, Sukalyan and Wu, Hanyan 2015. Stokesian simulation of two unequal spheres in a pressure-driven creeping flow through a cylinder. Computers & Fluids, Vol. 121, p. 145.

    Dettmer, Simon L. Pagliara, Stefano Misiunas, Karolis and Keyser, Ulrich F. 2014. Anisotropic diffusion of spherical particles in closely confining microchannels. Physical Review E, Vol. 89, Issue. 6,

    Azese, Martin Ndi 2015. In an attempt to generalize wall slip in fluid flows using a series expansion of the wall shear stress: Case of non-Newtonian [Phan–Thien–Tanner fluid]. European Journal of Mechanics - B/Fluids, Vol. 52, p. 109.

    Bhattacharya, Sukalyan Gurung, Dil K. and Navardi, Shahin 2013. Radial lift on a suspended finite-sized sphere due to fluid inertia for low-Reynolds-number flow through a cylinder. Journal of Fluid Mechanics, Vol. 722, p. 159.

    O-tani, Hideyuki Akinaga, Takeshi and Sugihara-Seki, Masako 2011. Charge effects on hindrance factors for diffusion and convection of solute in pores I. Fluid Dynamics Research, Vol. 43, Issue. 6, p. 065505.

    Bławzdziewicz, J. Ekiel-Jeżewska, M. L. and Wajnryb, E. 2010. Hydrodynamic coupling of spherical particles to a planar fluid-fluid interface: Theoretical analysis. The Journal of Chemical Physics, Vol. 133, Issue. 11, p. 114703.

  • Journal of Fluid Mechanics, Volume 642
  • January 2010, pp. 295-328

Analysis of general creeping motion of a sphere inside a cylinder

  • DOI:
  • Published online: 07 December 2009

In this paper, we develop an efficient procedure to solve for the Stokesian fields around a spherical particle in viscous fluid bounded by a cylindrical confinement. We use our method to comprehensively simulate the general creeping flow involving the particle-conduit system. The calculations are based on the expansion of a vector field in terms of basis functions with separable form. The separable form can be applied to obtain general reflection relations for a vector field at simple surfaces. Such reflection relations enable us to solve the flow equation with specified conditions at different disconnected bodies like the sphere and the cylinder. The main focus of this article is to provide a complete description of the dynamics of a spherical particle in a cylindrical vessel. For this purpose, we consider the motion of a sphere in both quiescent fluid and pressure-driven parabolic flow. Firstly, we determine the force and torque on a translating-rotating particle in quiescent fluid in terms of general friction coefficients. Then we assume an impending parabolic flow, and calculate the force and torque on a fixed sphere as well as the linear and angular velocities of a freely moving particle. The results are presented for different radial positions of the particle and different ratios between the sphere and the cylinder radius. Because of the generality of the procedure, there is no restriction in relative dimensions, particle positions and directions of motion. For the limiting cases of geometric parameters, our results agree with the ones obtained by past researchers using different asymptotic methods.

Corresponding author
Email address for correspondence:
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.

S. Bhattacharya 2008 aCooperative motion of spheres arranged in periodic grids between two parallel walls. J. Chem. Phys. 128, 074709.

S. Bhattacharya 2008 bHistory force on an asymmetrically rotating body in Poiseuille flow inducing particle-migration across a slit-pore. Phys. Fluids 20, 093301.

S. Bhattacharya & J. Bławzdziewicz 2002 Image system for Stokes-flow singularity between two parallel planar walls. J. Math. Phys. 43, 57205731.

S. Bhattacharya , J. Bławzdziewicz & E. Wajnryb 2005 bMany-particle hydrodynamic interactions in parallel-wall geometry: Cartesian-representation method. Physica A 356, 294340.

S. Bhattacharya , J. Bławzdziewicz & E. Wajnryb 2006 aFar-field approximation for hydrodynamic interactions in parallel-wall geometry. J. Comput. Phys. 212, 718738.

S. Bhattacharya , J. Bławzdziewicz & E. Wajnryb 2006 bHydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls. Phys. Fluids 18 (5).

P. M. Bungay & H. Brenner 1973 bThe motion of a closely-fitting sphere in a fluid-filled tube. Intl J. Multiph. Flow 1, 2556.

J. J. Chiu , D. L. Wang , S. Chien , R. Skalak & S. Usami 1998 Effects of disturbed flow on endothelial cells. J. Biomech. Engng – Trans. ASME 120, 28.

B. Cichocki & R. B. Jones 1998 Image representation of a spherical particle near a hard wall. Physica A 258, 273302.

B. Cichocki , R. B. Jones , R. Kutteh & E. Wajnryb 2000 Friction and mobility for colloidal spheres in Stokes flow near a boundary: the multipole method and applications. J. Chem. Phys. 112, 2548–61.

R. G. Cox & S. G. Mason 1971 Suspended particles in fluid flow through tubes. Annu. Rev. Fluid Mech. 3, 291316.

G. Drazer , B. Khusid , J. Koplik & A. Acrivos 2005 Wetting and particle adsorption in nanoflows. Phys. Fluids 17, ARTN:017102.

B. U. Felderhof & R. B. Jones 1989 Displacement theorems for spherical solutions of the linear Navier–Stokes equations. J. Math. Phys. 30, 339–42.

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

T. Greenstein & J. Happel 1970 Viscosity of dilute uniform suspensions of sphere spheres. Phys. Fluids 13, 1821.

A. J. C. Ladd 1988 Hydrodynamic interactions in suspensions of spherical particles. J. Chem. Phys. 88, 5051.

W. J. Lunsmann , L. Genieser , R. C. Armstrong & R. A. Brown 1993 Finite-element analysis of steady viscoelastic flow around a sphere in a tube-calculations with constant viscosity models. J. Non-Newton. Fluid Mech. 48, 6399.

J. F. Morris & J. F. Brady 1998 Pressure-driven flow of a suspension: buoyancy effects. Intl J. Multiph. Flow 24, 105–30.

C. Pozrikidis 2005 Numerical simulation of cell motion in tube flow. Ann. Biomed. Engng 33, 165178.

C. Queguiner & D. BarthesBiesel 1997 Axisymmetric motion of capsules through cylindrical channels. J. Fluid Mech. 348, 349376.

M. SugiharaSeki & R. Skalak 1997 Asymmetric flows of spherical particles in a cylindrical tube. Biorheology 34, 155169.

N. Sushko & M. Cieplak 2001 Motion of grains, droplets, and bubbles in fluid-filled nanopores. Phys. Rev. E 64.

H. Tozeren 1982 Torque on eccentric spheres flowing in tubes. J. Appl. Mech. Trans. ASME 49, 279283.

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? *