Inhomogeneous Distribution of a Rigid Fibre undergoing Rectilinear Flow between Parallel Walls at High Peclet Numbers


We use slender-body theory to simulate a rigid fibre within simple shear flow and parabolic flow at zero Reynolds number and high Péclet numbers (weak Brownian motion). Hydrodynamic interactions of bulk fibres with the bounding walls are included using previously developed methods (Harlen, Sundararajakumar & Koch, J. Fluid Mech., vol. 388, 1999, pp. 355-388; Butler & Shaqfeh, J. Fluid Mech., vol. 468, 2002, pp. 205-237). We also extend a previous analytic theory (Park, Bricker & Butler, Phys. Rev. E, vol. 76, 2007, 04081) predicting the centre-of-mass distribution of rigid fibre suspensions undergoing rectilinear flow near a wall to compare the steady and transient distributions. The distributions obtained by the simulation and theory are in good agreement at sufficiently high shear rates, validating approximations made in the theory which predicts a net migration of the rigid fibres away from the walls due to a hydrodynamic lift force. The effect of the inhomogeneous distribution on the effective stress is also investigated.


Chemical and Biochemical Engineering


National Science Foundation (U.S.)


This work was supported by the National Science Foundation through a CAREER Award (CTS-0348205).

Keywords and Phrases

Analytic Theory; Brownian Motion; Centre of Mass; Effective Stress; High Shear Rate; Hydrodynamic Interaction; Hydrodynamic Lift Forces; Inhomogeneous Distribution; Rectilinear Flow; Simple Shear Flow; Slender-Body Theory; Steady and Transient; Brownian Movement; Fluid Dynamics; Hydrodynamics; Reynolds Number; Shear Deformation; Suspensions (Fluids); Fibers; Computer Simulation; Prediction; Shear Flow; Theoretical Study; Transient Flow

International Standard Serial Number (ISSN)

0022-1120; 1469-7645

Document Type

Article - Journal

Document Version


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