scholarly journals Stress in a dilute suspension of spheres in a dilute polymer solution subject to simple shear flow at finite Deborah numbers

2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Donald L. Koch ◽  
Eric F. Lee ◽  
Ibrahim Mustafa
Keyword(s):  
Shear Flow ◽  
Polymer Solution ◽  
Simple Shear ◽  
Dilute Polymer Solution ◽  
Simple Shear Flow ◽  
Dilute Suspension

scholarly journals Viscoelasticity and nonlinear simple shear flow behavior of an entangled asymmetric exact comb polymer solution

2016 ◽  
Vol 60 (3) ◽  
pp. 451-463 ◽  
Author(s):  
F. Snijkers ◽  
K. M. Kirkwood ◽  
D. Vlassopoulos ◽  
L. G. Leal ◽  
A. Nikopoulou ◽  
...  
Keyword(s):  
Shear Flow ◽  
Polymer Solution ◽  
Simple Shear ◽  
Flow Behavior ◽  
Simple Shear Flow ◽  
Comb Polymer

The rheology of a semi-dilute suspension of swimming model micro-organisms

2007 ◽  
Vol 588 ◽  
pp. 399-435 ◽  
Author(s):  
TAKUJI ISHIKAWA ◽  
T. J. PEDLEY
Keyword(s):  
Shear Flow ◽  
Flow Field ◽  
Simple Shear ◽  
Apparent Viscosity ◽  
The Other ◽  
Surface Velocity ◽  
Simple Shear Flow ◽  
Other Hand ◽  
Dilute Suspension ◽  
Micro Organisms

The rheological properties of a cell suspension may play an important role in the flow field generated by populations of swimming micro-organisms (e.g. in bioconvection). In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). Effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The three-dimensional movement of 64 identical squirmers in a simple shear flow field, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The computation utilizes a database of pairwise interactions that has been constructed by the boundary element method. The restriction to pairwise additivity of forces is expected to be justified if the suspension is semi-dilute. The results for non-bottom-heavy squirmers show that the squirming does not have a direct influence on the apparent viscosity. However, it does change the probability density in configuration space, and thereby causes a slight decrease in the apparent viscosity atO(c2), wherecis the volume fraction of spheres. In the case of bottom-heavy squirmers, on the other hand, the stresslet generated by the squirming motion directly contributes to the bulk stress atO(c), and the suspension shows strong non-Newtonian properties. When the background simple shear flow is directed vertically, the apparent viscosity of the semi-dilute suspension of bottom-heavy squirmers becomes smaller than that of inert spheres. When the shear flow is horizontal and varies with the vertical coordinate, on the other hand, the apparent viscosity becomes larger than that of inert spheres. In addition, significant normal stress differences appear for all relative orientations of gravity and the shear flow, in the case of bottom-heavy squirmers.

An orientational order transition in a sheared suspension of anisotropic particles

2016 ◽  
Vol 811 ◽  
Author(s):  
Navaneeth K. Marath ◽  
Ruchir Dwivedi ◽  
Ganesh Subramanian
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Orientational Order ◽  
Thermal Fluctuations ◽  
Simple Shear Flow ◽  
Two Phase ◽  
Physics Literature ◽  
Dilute Suspension ◽  
Neutrally Buoyant

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.

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