Rheological signatures in limit cycle behaviour of dilute, active, polar liquid crystalline polymers in steady shear

We consider the dilute regime of active suspensions of liquid crystalline polymers (LCPs), addressing issues motivated by our kinetic model and simulations in Forest et al. (Forest et al. 2013 Soft Matter 9, 5207–5222 (doi:10.1039/c3sm27736d)). In particular, we report unsteady two-dimensional heterogeneous flow-orientation attractors for pusher nanorod swimmers at dilute concentrations where passive LCP equilibria are isotropic. These numerical limit cycles are analogous to longwave (homogeneous) tumbling and kayaking limit cycles and two-dimensional heterogeneous unsteady attractors of passive LCPs in weak imposed shear, yet these states arise exclusively at semi-dilute concentrations where stable equilibria are nematic. The results in Forest et al. mentioned above compel two studies in the dilute regime that complement recent work of Saintillan & Shelley (Saintillan & Shelley 2013 C. R. Physique 14, 497–517 (doi:10.1016/j.crhy.2013.04.001)): linearized stability analysis of the isotropic state for nanorod pushers and pullers; and an analytical–numerical study of weakly and strongly sheared active polar nanorod suspensions to capture how particle-scale activation affects shear rheology. We find that weakly sheared dilute puller versus pusher suspensions exhibit steady versus unsteady responses, shear thickening versus thinning and positive versus negative first normal stress differences. These results further establish how sheared dilute nanorod pusher suspensions exhibit many of the characteristic features of sheared semi-dilute passive nanorod suspensions.

[1]  Leonid Berlyand,et al.  Three-dimensional model for the effective viscosity of bacterial suspensions. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Donald L. Koch,et al.  Collective Hydrodynamics of Swimming Microorganisms: Living Fluids , 2011 .

[3]  M. Marchetti,et al.  Hydrodynamics of polar liquid crystals. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  I. Aranson,et al.  Concentration dependence of the collective dynamics of swimming bacteria. , 2007, Physical review letters.

[5]  Salima Rafaï,et al.  Effective viscosity of microswimmer suspensions. , 2009, Physical review letters.

[6]  Frank Jülicher,et al.  The Taylor–Couette motor: spontaneous flows of active polar fluids between two coaxial cylinders , 2012 .

[7]  David Saintillan,et al.  The Dilute Rheology of Swimming Suspensions: A Simple Kinetic Model , 2010 .

[8]  Walter F Paxton,et al.  Motility of catalytic nanoparticles through self-generated forces. , 2005, Chemistry.

[9]  Sriram Ramaswamy,et al.  Rheology of active-particle suspensions. , 2003, Physical review letters.

[10]  M. Marchetti,et al.  Complex spontaneous flows and concentration banding in active polar films. , 2008, Physical review letters.

[11]  Alejandro D. Rey,et al.  Effect of long range order on sheared liquid crystalline materials Part 1: compatibility between tumbling behavior and fixed anchoring , 1997 .

[12]  M. Gregory Forest,et al.  The weak shear kinetic phase diagram for nematic polymers , 2004 .

[13]  Masao Doi,et al.  Constitutive Equation for Nematic Liquid Crystals under Weak Velocity Gradient Derived from a Molecular Kinetic Equation , 1983 .

[14]  Qi Wang,et al.  Dipole-induced, first-order phase transitions of nano-rod monolayers , 2008 .

[15]  M. Gregory Forest,et al.  NANO-ROD SUSPENSION FLOWS: A 2D SMOLUCHOWSKI-NAVIER-STOKES SOLVER , 2007 .

[16]  William M. Durham,et al.  Disruption of Vertical Motility by Shear Triggers Formation of Thin Phytoplankton Layers , 2009, Science.

[17]  Stephen J. Ebbens,et al.  In pursuit of propulsion at the nanoscale , 2010 .

[18]  Leonid Berlyand,et al.  Effective viscosity of dilute bacterial suspensions: a two-dimensional model , 2008, Physical biology.

[19]  T. Lubensky,et al.  Statistical mechanics and hydrodynamics of bacterial suspensions , 2009, Proceedings of the National Academy of Sciences.

[20]  L. Mahadevan,et al.  Excitable patterns in active nematics. , 2010, Physical review letters.

[21]  Andrey Sokolov,et al.  Reduction of viscosity in suspension of swimming bacteria. , 2009, Physical review letters.

[22]  M. Gregory Forest,et al.  The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates , 2004 .

[23]  I. Aranson,et al.  Viscosity of bacterial suspensions: hydrodynamic interactions and self-induced noise. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  M E Cates,et al.  Shearing active gels close to the isotropic-nematic transition. , 2008, Physical review letters.

[25]  Héctor D. Ceniceros,et al.  Computational studies of the shear flow behaviour of a model for nematic liquid crystalline polymers , 2005 .

[26]  M. Doi,et al.  Constitutive Equation for Nematic Liquid Crystals under Weak Velocity Gradient Derived from a Molecular Kinetic Equation. II. —Leslie Coefficients for Rodlike Polymers— , 1984 .

[27]  Geometry and dynamics of a nematic liquid crystal in a uniform shear flow , 2001 .

[28]  Qi Wang,et al.  The Weak Shear Phase Diagram for Nematic Polymers , 2004 .

[29]  Qi Wang,et al.  Scaling behavior of kinetic orientational distributions for dilute nematic polymers in weak shear , 2004 .

[30]  Explicit Flow-Aligned Orientational Distribution Functions for Dilute Nematic Polymers in Weak Shear , 2002 .

[31]  M. Shelley,et al.  Instabilities, pattern formation and mixing in active suspensions , 2008 .

[32]  Yanyan Cao,et al.  Catalytic nanomotors: autonomous movement of striped nanorods. , 2004, Journal of the American Chemical Society.

[33]  M Cristina Marchetti,et al.  Enhanced diffusion and ordering of self-propelled rods. , 2008, Physical review letters.

[34]  E. R. de Arantes e Oliveira,et al.  Two-Dimensional Model , 1975 .

[35]  A. A. Wheeler,et al.  Nonlinear dynamics of a nematic liquid crystal in the presence of a shear flow , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[36]  M. Shelley,et al.  Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. , 2008, Physical review letters.

[37]  Michael Shelley,et al.  Active suspensions and their nonlinear models , 2013 .

[38]  S. Ramaswamy,et al.  Hydrodynamics of soft active matter , 2013 .

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

[40]  Marcos,et al.  Resource Patch Formation and Exploitation throughout the Marine Microbial Food Web , 2008, The American Naturalist.

[41]  M. Parsek,et al.  Bacterial biofilms: an emerging link to disease pathogenesis. , 2003, Annual review of microbiology.

[42]  D. Saintillan.  Extensional rheology of active suspensions. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Siegfried Hess,et al.  Fokker-Planck-Equation Approach to Flow Alignment in Liquid Crystals , 1976 .

[44]  M. Gregory Forest,et al.  Kinetic theory and simulations of active polar liquid crystalline polymers , 2013 .

[45]  D. Saintillan.  Kinetic Models for Biologically Active Suspensions , 2012 .

[46]  Qi Wang,et al.  Kinetic Structure Simulations of Nematic Polymers in Plane Couette Cells. II: In-Plane Structure Transitions , 2005, Multiscale Model. Simul..

[47]  Luca Giomi,et al.  Polar patterns in active fluids , 2011, 1106.1624.

[48]  T. Ishikawa,et al.  Development of coherent structures in concentrated suspensions of swimming model micro-organisms , 2008, Journal of Fluid Mechanics.