The effect of undulations on the particle stress in dilute suspensions of rod-like particles
Keywords:
Rheology, active suspension, suspension, rod suspension, self-propulsion, active particleAbstract
We compared a dilute suspension of undulating rod-like particles (active suspension) with a similar one consisting of rigid rods (passive suspension) under shear flow. For the active suspension, a synchronised group of swimmers propel themselves forward by passing a travelling wave through their bodies while at the same time rotate due to planar background shear flow. Using a high resolution immersed body numerical simulations, we have shown that an active particle can exhibit complex dynamics, which is fundamentally different from a similar passive one. The orientation of the active particle consists of two separate oscillations: a low-frequency oscillation similar to the passive particle (determined by shear rate) and a high-frequency oscillation due to the body undulations. Nevertheless, different dynamics did not result in a major difference in rheological behaviour of the suspension.Wefound that the effective viscosity of the active suspension is equal to that of a passive one, i.e. self-propulsion did not change the viscosity of the suspension probably because of the high shear rate and inertia of our simulations.
Downloads
References
Aidun, C. K., & Clausen, J. R. (2010). Lattice-boltzmann method for complex flows. Annual
Review of Fluid Mechanics, 42, 439–472.
Asgharzadeh, H., & Borazjani, I. (2016). A newton–krylov method with an approximate
analytical jacobian for implicit solution of navier–stokes equations on staggered oversetcurvilinear
grids with immersed boundaries. Journal of Computational Physics. 331, 227–
doi: 10.1016/j.jcp.2016.11.033
Asgharzadeh, H., & Borazjani, I. (2016). Effects of reynolds and womersley numbers on the
hemodynamics of intracranial aneurysms. Computational and Mathematical Methods in
Medicine, 2016, 7412926. doi: 10.1155/2016/7412926
Balasubramanian, S., Kagan, D., Jack Hu, C.-M., Campuzano, S., Lobo-Casta non, M. J.,
Lim, N., ... Wang, J. (2011). Micromachine-enabled capture and isolation of cancer cells in
complex media. Angewandte Chemie International Edition, 50, 4161–4164.
Balay, S., Buschelman, K., Gropp, W. D., Kaushik, D., Knepley, M. G., McInnes, L. C., &
Zhang, H. (2001). PETScWeb page. http://www.mcs.anl.gov/petsc.
Baraff, D. (2001). An introduction to physically based modeling: Rigid body simulation I –
Unconstrained rigid body dynamics. SIGGRAPH Course Notes, 2, G1–68. Retrieved from
http://graphics.cs.cmu.edu/courses/15-869-F08/lec/14/notesg.pdf
Batchelor, G. K. (1970). The stress system in a suspension of force-free particles. Journal of
Fluid Mechanics, 41, 545–570.
Becker, A. D., Masoud, H., Newbolt, J. W., Shelley, M., & Ristroph, L. (2015). Hydrodynamic
schooling of flapping swimmers. Nature Communications, 6.
Borazjani, I., Ge, L., & Sotiropoulos, F. (2008). Curvilinear immersed boundary method
for simulating fluid structure interaction with complex 3d rigid bodies. Journal of
Computational Physics, 227, 7587–7620.
Brennen, C., & Winet, H. (1977). Fluid mechanics of propulsion by cilia and flagella. Annual
Review of Fluid Mechanics, 9, 339–398.
Daghooghi, M., & Borazjani, I. (2014, August 17–20). Parallel implementation of periodic
boundary conditions for a curvilinear immersed boundary method. In ASME 2014
International Design Engineering Technical Conferences and Computers and Information
in Engineering Conference, Volume 1A: 34th Computers and Information in Engineering
Conference. (pp. V01AT02A019–V01AT02A019), New York, USA. American Society of
Mechanical Engineers.
Daghooghi, M., & Borazjani, I. (2015). The influence of inertia on the rheology of a periodic
suspension of neutrally buoyant rigid ellipsoids. Journal of Fluid Mechanics, 781, 506–549.
Daghooghi, M., & Borazjani, I. (2015). The hydrodynamic advantages of synchronized
swimming in a rectangular pattern. Bioinspiration & Biomimetics, 10, 056018.
Daghooghi, M., & Borazjani, I. (2016). Self-propelled swimming simulations of bio-inspired
smart structures. Bioinspiration & Biomimetics, 11, 056001.
Elgeti, J., Winkler, R. G., & Gompper, G. (2015). Physics of microswimmers – Single particle
motion and collective behavior: A review. Reports on Progress in Physics, 78, 056601.
Gazzola, M., Tchieu, A. A., Alexeev, D., de Brauer, A., & Koumoutsakos, P. (2016). Learning
to school in the presence of hydrodynamic interactions. Journal of Fluid Mechanics, 789,
–749.
Ge, L., & Sotiropoulos, F. (2007). A numerical method for solving the 3d unsteady
incompressible navier-stokes equations in curvilinear domains with complex immersed
boundaries. Journal of Computational Physics, 225, 1782–1809.
Gilmanov, A., & Sotiropoulos, F. (2005). A hybrid cartesian/immersed boundary method for
simulating flows with 3d, geometrically complex, moving bodies. Journal of Computational
Physics, 207, 457–492.
Gyrya, V., Lipnikov, K., Aranson, I. S., & Berlyand, L. (2011). Effective shear viscosity and
dynamics of suspensions of micro-swimmers from small to moderate concentrations.
Journal of Mathematical Biology, 62, 707–740.
Haddadi, H., & Morris, J. (2014). Microstructure and rheology of finite inertia neutrally
buoyant suspensions. Journal of Fluid Mechanics, 749, 431–459. doi:10.1017/jfm.2014.238
Haines, B. M., Sokolov, A., Aranson, I. S., Berlyand, L., & Karpeev, D. A. (2009). Threedimensional
model for the effective viscosity of bacterial suspensions. Physical Review E,
, 041922.
Hatwalne, Y., Ramaswamy, S., Rao, M., & Simha, R. A. (2004). Rheology of active-particle
suspensions. Physical Review Letters, 92, 118101.
Jeffery, G. B. (1922). The motion of ellipsoidal particles immersed in a viscous fluid.
Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering
Sciences, 102, 161–179.
Jeffrey, D. J., & Acrivos, A. (1976). The rheological properties of suspensions of rigid particles.
AIChE Journal, 22, 417–432.
Lauga, E., & Powers, T. R. (2009). The hydrodynamics of swimming microorganisms. Reports
on Progress in Physics, 72, 096601.
Leal, L. G., & Hinch, E. J. (1971). The effect of weak brownian rotations on particles in shear
flow. Journal of Fluid Mechanics, 46, 685–703.
Li, G.,Müller, U. K., van Leeuwen, J. L., & Liu, H. (2012). Body dynamics and hydrodynamics
of swimming fish larvae: A computational study. Journal of Experimental Biology, 215,
–4033.
Mueller, S., Llewellin, E. W., & Mader, H. M. (2010). The rheology of suspensions of solid
particles. Proceedings of the Royal SocietyA:Mathematical, Physical and Engineering Science,
, 1201–1228.
Ozin, G. A., Manners, I., Fournier-Bidoz, S., & Arsenault, A. (2005). Dream nanomachines.
Advanced Materials, 17, 3011–3018.
Rosén, T., Do-Quang,M., Aidun, C. K.,&Lundell, F. (2015). The dynamical states of a prolate
spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia.
Journal of Fluid Mechanics, 771, 115–158.
Saintillan, D., & Shelley, M. J. (2007). Orientational order and instabilities in suspensions of
self-locomoting rods. Physical Review Letters, 99, 058102.
Saintillan, D., & Shelley, M. J. (2015). Theory of active suspensions. In S. E. Spagnolie (Ed.),
Complex fluids in biological systems (pp. 319–355). New York, NY: Springer.
Sokolov, A., & Aranson, I. S. (2009). Reduction of viscosity in suspension of swimming
bacteria. Physical Review Letters, 103, 148101.
Sokolov, A.,Aranson, I. S., Kessler, J.O.,&Goldstein, R. E. (2007). Concentration dependence
of the collective dynamics of swimming bacteria. Physical Review Letters, 98, 158102.
Tao, Y.-G., den Otter,W. K., & Briels, W. J. (2005). Kayaking and wagging of rods in shear
flow. Physical Review Letters, 95, 237802.
Toner, J., Tu, Y., & Ramaswamy, S. (2005). Hydrodynamics and phases of flocks. Annals of
Physics, 318, 170–244.
Wensink, H. H., & Löwen, H., (2012). Emergent states in dense systems of active rods: From
swarming to turbulence. Journal of Physics: Condensed Matter, 24, 464130.
Willert, C. E., & Gharib, M. (1991). Digital particle image velocimetry. Experiments in Fluids,
, 181–193.
Yang, Y., Marceau, V., & Gompper, G. (2010). Swarm behavior of self-propelled rods and
swimming flagella. Physical Review E, 82, 031904.