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A cloud of rigid fibres sedimenting in a viscous fluid



Experiments and numerical simulations have been performed to investigate the deformation and break-up of a cloud of rigid fibres falling under gravity through a viscous fluid in the absence of inertia and interfacial tension. The cloud of fibres is observed to evolve into a torus that subsequently becomes unstable and breaks up into secondary droplets which themselves deform into tori in a repeating cascade. This behaviour is similar to that of clouds of spherical particles, though the evolution of the cloud of fibres occurs more rapidly. The simulations, which use two different levels of approximation of the far-field hydrodynamic interactions, capture the evolution of the cloud and demonstrate that the coupling between the self-motion and hydrodynamically induced fluctuations are responsible for the faster break-up time of the cloud. The dynamics of the cloud are controlled by a single parameter which is related to the self-motion of the anisotropic particles. The experiments confirm these findings.


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Adachi, K., Kiriyama, S. & Koshioka, N. 1978 The behaviour of a swarm of particles moving in a viscous fluid. Chem. Engng Sci. 33, 115121.
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419440.
Bosse, T., Kleiser, L., Härtel, C. & Meiburg, E. 2005 Numerical simulation of finite Reynolds number suspension drops settling under gravity. Phys. Fluids 17, 037101.
Butler, J. E. & Shaqfeh, E. S. G. 2002 Dynamic simulations of the inhomogeneous sedimentation of rigid fibres. J. Fluid Mech. 468, 205237.
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 791810.
Ekiel-Jeżewska, M. L., Metzger, B. & Guazzelli, É. 2006 Spherical cloud of point particles falling in a viscous fluid. Phys. Fluids 18, 038104.
Harlen, O. G., Sundararajakumar, R. R. & Koch, D. L. 1999 Numerical simulation of a sphere settling through a suspension of neutrally buoyant fibres. J. Fluid Mech. 388, 355388.
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317328.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161179.
Machu, G., Meile, W., Nitsche, L. C. & Schaflinger, U. 2001 Coalescence, torus formation and breakup of sedimenting drops: Experiments and computer simulations. J. Fluid Mech. 447, 299336.
Mackaplow, M. B. & Shaqfeh, E. S. G. 1998 A numerical study of the sedimentation of fibre suspensions. J. Fluid Mech. 376, 149182.
Metzger, B., Nicolas, M. & Guazzelli, É. 2007 Falling clouds of particles in viscous fluids. J. Fluid Mech. 580, 283301.
Moran, J. P. 1963 Line source distributions and slender-body theory. J. Fluid Mech. 17, 285304.
Nitsche, J. M. & Batchelor, G. K. 1997 Breakup of a falling drop containing dispersed particles. J. Fluid Mech. 340, 161175.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1994 Numerical Recipes in Fortran, The Art of Scientific Computing. 2nd edn., pp. 719725. Cambridge University Press.
Saintillan, D., Shaqfeh, E. S. G. & Darve, E. 2006 The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation. J. Fluid Mech. 553, 347388.
Schaflinger, U. & Machu, G. 1999 Interfacial phenomena in suspensions. Chem. Engng Technol. 22, 617619.
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