ALBERT

Description: In this paper, we discuss experimental evidence for radial particle segregation in a parallel-plate geometry. The motion of coloured tracer particles of a size different from the bulk suspension is followed as a function of time. The tracer particles are seen to experience a constant drift velocity independent of their radial position. This is in addition to the random-walk motion arising from their interactions with other particles in the suspension. These observations are found to be consistent with the shear-induced migration model of Leighton & Acrivos (1987 a,b) as well as the tracer diffusivity measurements of Phan & Leighton (1996). In the experiments of Abbott et al. (1991), it was observed that larger particles migrated radially outward to regions of lower shear stress in a wide-gap Couette device. In our experiments large tracers were also observed to migrate radially outward. In this case, however, the radial migration resulted in migration to regions of higher shear stress, contrary to expectations. This apparent discrepancy is explained in terms of a model that incorporates both the stress-induced migration of earlier studies and a curvature-induced migration flux (which in turn is shear-induced) as an opposing effect.

Description: It was first demonstrated experimentally by H. Giesekus in 1965 that the second normal stress difference in polymers can induce a secondary flow within the cross-section of a non-axisymmetric conduit. In this paper, we show through simulations that the same may be true for suspensions of rigid non-colloidal particles that are known to exhibit a strong negative second normal stress difference. Typically, the magnitudes of the transverse velocity components are small compared to the average axial velocity of the suspension; but the ratio of this transverse convective velocity to the shear-induced migration velocity is characterized by the shear-induced migration Péclet number χ which scales as B2/a2, B being the characteristic length scale of the cross-section and a being the particle radius. Since this Péclet number is kept high in suspension experiments (typically 100 to 2500), the influence of the weak circulation currents on the concentration profile can be very strong, a result that has not been appreciated in previous work. The principal effect of secondary flows on the concentration distribution as determined from simulations using the suspension balance model of Nott & Brady (J. Fluid Mech. vol. 275, 1994, p. 157) and the constitutive equations of Zarraga et al. (J. Rheol. vol. 44, 2000, p. 185) is three-fold. First, the steady-state particle concentration distribution is no longer independent of particle size; rather, it depends on the aspect ratio B/a. Secondly, the direction of the secondary flow is such that particles are swept out of regions of high streamsurface curvature, e.g. particle concentrations in corners reach a minimum rather than the local maximum predicted in the absence of such flows. Finally, the second normal stress differences lead to instabilities even in such simple geometries as plane-Poiseuille flow. © 2008 Cambridge University Press.

Description: The pair distribution function of 3.18 mm diameter particles was measured in the plane of shear of a simple shear flow at concentrations of 5%, 10% and 15% by volume. A new direct flow-visualization procedure and a new pattern recognition algorithm were used in the investigation. The measurements show a depletion of bound pairs of particles in the direction of flow. A simple model which includes the effect of particle surface roughness on the particle interactions and the pair distribution function is presented. An important effect of surface roughness is that the particles in a suspension can experience irreversible interactions in the presence of an externally imposed simple shear flow. The model shows that such irreversibilities eliminate all bound pairs of particles in the plane of shear by displacing particles out of the closed orbit trajectory region. Surface roughness is found to induce significant asymmetry in the fore and aft region of a two-particle interaction. The measurements and predictions are in qualitative agreement with these conclusions.