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.
J. Park and J. E. Butler, "Inhomogeneous Distribution of a Rigid Fibre undergoing Rectilinear Flow between Parallel Walls at High Peclet Numbers," Journal of Fluid Mechanics, vol. 630, pp. 267-298, Cambridge University Press, Jul 2009.
The definitive version is available at https://doi.org/10.1017/S0022112009006545
Chemical and Biochemical Engineering
National Science Foundation (U.S.)
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)
Article - Journal
© 2009 Cambridge University Press, All rights reserved.
01 Jul 2009