Flow and rheology of suspensions of two-dimensional cylindrical or anisotropic particles with Navier slip

Through boundary integral simulations, we investigate, in the creeping flow limit and in the absence of Brownian noise, the effects of Navier slip on the orientational dynamics and effective shear viscosity of a semidilute suspension of two-dimensional particles with either circular or elongated (platelike) shape, interacting only via hydrodynamic and contact forces. We have recently shown that it is theoretically possible for a dilute system of slip platelike particles to display an effective shear viscosity smaller than the viscosity of the suspending fluid. This large viscosity reduction is primarily due to the suppression of the tumbling motion predicted for a no-slip particle and the attainment of a stable orientation. In this paper, we show that the effect of particle-particle interaction at semidilute concentrations is to cause the particles to fluctuate about the stable orientation and, above a threshold solid fraction <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>c</a:mi><a:mtext>crt</a:mtext></a:msub></a:math>, to tumble. As a consequence, a sharp increase in the effective shear viscosity with solid fraction <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>c</b:mi></b:math> occurs for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>c</c:mi><c:mo>></c:mo><c:msub><c:mi>c</c:mi><c:mtext>crt</c:mtext></c:msub></c:mrow></c:math>. Our results suggest that, for a given particle aspect ratio, there is a value of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>c</d:mi></d:math> that maximizes the reduction in the effective shear viscosity of the suspension.