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An orientational order transition in a sheared suspension of anisotropic particles

Published online by Cambridge University Press:  12 December 2016

Navaneeth K. Marath ,
Ruchir Dwivedi  and
Ganesh Subramanian
Navaneeth K. Marath
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore, Karnataka 560 064, India
Ruchir Dwivedi
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore, Karnataka 560 064, India
Ganesh Subramanian*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore, Karnataka 560 064, India
*
†Email address for correspondence: sganesh@jncasr.ac.in
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Abstract

Under Stokesian conditions, a neutrally buoyant non-Brownian spheroid in simple shear flow rotates indefinitely in any of a one-parameter family of closed (Jeffery) orbits characterized by an orbit constant $C$. The limiting values, $C=0$ and $C=\infty$, correspond to spinning and tumbling modes respectively. Hydrodynamics alone does not determine the distribution of spheroid orientations across Jeffery orbits in the absence of interactions, and the rheology of a dilute suspension of spheroids remains indeterminate. A combination of inertia and stochastic orientation fluctuations eliminates the indeterminacy. The steady-state Jeffery-orbit distribution arising from a balance of inertia and thermal fluctuations is shown to be of the Boltzmann equilibrium form, with a potential that depends on $C$, the particle aspect ratio ($\unicode[STIX]{x1D705}$), and a dimensionless shear rate ($Re\,Pe_{r}$, $Re$ and $Pe_{r}$ being the Reynolds and rotary Péclet numbers), and therefore lends itself to a novel thermodynamic interpretation in $C{-}\unicode[STIX]{x1D705}{-}Re\,Pe_{r}$ space. In particular, the transition of the potential from a single to a double-well structure, below a critical $\unicode[STIX]{x1D705}$, has similarities to a thermodynamic phase transition, and the small-$C$ and large-$C$ minima are therefore identified with spinning and tumbling phases. The hysteretic dynamics within the two-phase tumbling–spinning envelope renders the rheology sensitively dependent on the precise shear rate history, the signature in simple shear flow being a multivalued viscosity at a given shear rate. The tumbling–spinning transition identified here is analogous to the coil–stretch transition in the polymer physics literature. It should persist under more general circumstances, and has implications for the suspension stress response in inhomogeneous shearing flows.

JFM classification

Non-Newtonian Flows: Polymers Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 811 , 25 January 2017 , R3
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Copyright
© 2016 Cambridge University Press 

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