Effect of flexibility on the growth of concentration fluctuations in a suspension of sedimenting fibers: Particle simulations

Three-dimensional numerical simulations are performed to study the stability of a sedimenting suspension of weakly flexible fibers. It is well known that a suspension of rigid rods sedimenting under gravity at low Reynolds number is unstable to concentration fluctuations owing to hydrodynamic interactions. Flexible fibers, however, reorient while settling and even weak flexibility can alter their collective dynamics. In our recent work [Manikantan et al., “The instability of a sedimenting suspension of weakly flexible fibres,” J. Fluid Mech. 756, 935–964 (2014)], we developed a mean-field theory to predict the linear stability of such a system. Here, we verify these predictions using accurate and efficient particle simulations based on a slender-body model. We also demonstrate the mechanisms by which flexibility-induced reorientation alters suspension microstructure, and through it, its stability. Specifically, we first show that the anisotropy of the base state in the case of a suspension of flexible fib...

[1]  H. Hasimoto On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres , 1959, Journal of Fluid Mechanics.

[2]  D. Koch,et al.  Numerical simulations of a sphere settling through a suspension of neutrally buoyant fibres , 1999, Journal of Fluid Mechanics.

[3]  John Hinch,et al.  Fluctuations and Instability in Sedimentation , 2011 .

[4]  D. Saintillan,et al.  Subdiffusive transport of fluctuating elastic filaments in cellular flows , 2013 .

[5]  E. Lauga Floppy swimming: viscous locomotion of actuated elastica. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  David Saintillan,et al.  The instability of a sedimenting suspension of weakly flexible fibres , 2014, Journal of Fluid Mechanics.

[7]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[8]  Ali Nadim,et al.  DEFORMATION AND ORIENTATION OF AN ELASTIC SLENDER BODY SEDIMENTING IN A VISCOUS LIQUID , 1994 .

[9]  Sangtae Kim,et al.  Microhydrodynamics: Principles and Selected Applications , 1991 .

[10]  P. Gönczy,et al.  Mechanisms of nuclear positioning. , 1998, Journal of cell science.

[11]  É. Guazzelli,et al.  Experimental Investigation of the Sedimentation of a Dilute Fiber Suspension. , 1996, Physical review letters.

[12]  Elisabeth Guazzelli,et al.  Experimental investigation of the instability of a sedimenting suspension of fibres , 2007, Journal of Fluid Mechanics.

[13]  T. Powers,et al.  The hydrodynamics of swimming microorganisms , 2008, 0812.2887.

[14]  Eric S. G. Shaqfeh,et al.  The instability of a dispersion of sedimenting spheroids , 1989, Journal of Fluid Mechanics.

[15]  M. Shelley,et al.  Buckled in translation , 2009, 1003.5832.

[16]  E. Gaffney,et al.  Mammalian Sperm Motility: Observation and Theory , 2011 .

[17]  Eric F Darve,et al.  Hydrodynamic interactions in the induced-charge electrophoresis of colloidal rod dispersions , 2005, Journal of Fluid Mechanics.

[18]  Eric Darve,et al.  The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation , 2006, Journal of Fluid Mechanics.

[19]  G. Batchelor,et al.  Slender-body theory for particles of arbitrary cross-section in Stokes flow , 1970, Journal of Fluid Mechanics.

[20]  Eric S. G. Shaqfeh,et al.  Dynamic simulations of the inhomogeneous sedimentation of rigid fibres , 2002, Journal of Fluid Mechanics.

[21]  A. Dahlkild Finite wavelength selection for the linear instability of a suspension of settling spheroids , 2011, Journal of Fluid Mechanics.

[22]  John F. Brady,et al.  Accelerated Stokesian dynamics: Brownian motion , 2003 .

[23]  Anna-Karin Tornberg,et al.  Gravity induced sedimentation of slender fibers , 2009 .

[24]  Michael Shelley,et al.  Simulating the dynamics and interactions of flexible fibers in Stokes flows , 2004 .

[25]  M. Fixman Construction of Langevin forces in the simulation of hydrodynamic interaction , 1986 .

[26]  M. Fixman,et al.  Simulation of polymer dynamics. I. General theory , 1978 .

[27]  Eric F Darve,et al.  A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers , 2005 .

[28]  J. Happel,et al.  Low Reynolds number hydrodynamics , 1965 .

[29]  Paul Grassia,et al.  Computer simulations of Brownian motion of complex systems , 1995, Journal of Fluid Mechanics.

[30]  David Saintillan,et al.  The sedimentation of flexible filaments , 2013, Journal of Fluid Mechanics.

[31]  E. Shaqfeh,et al.  The effect of Brownian motion on the stability of sedimenting suspensions of polarizable rods in an electric field , 2009, Journal of Fluid Mechanics.