Direct investigation of anisotropic suspension structure in pressure-driven flow.

Evidence is presented to show the microstructural anisotropy responsible for normal stress in sheared suspensions. Particle velocimetry is combined with three-dimensional particle locations obtained via confocal microscopy at rest. A range of volume fractions phi and local shear rates gamma are investigated in a weakly Brownian pressure-driven suspension. At high gamma, the pairwise distribution shows a strong probability along the axis of compression similar to observations from Stokesian dynamics simulation at phi=0.32. At the channel center where gamma-->0, the concentrated suspension at phi=0.56 behaves as a confined isotropic fluid.

Mixing and segregation of microspheres in microchannel flows of mono- and bidispersed suspensions.

We investigate the mixing and segregation of mono- and bidispersed microsphere suspensions in microchannel flows. These flows are common in biological microelectromechanical systems (BioMEMS) applications handling blood or suspensions of DNA. Suspension transport in pressure driven flows is significantly hindered by shear-induced migration, where particles migrate away from the walls and are focused in the center due to multibody hydrodynamic interactions. The microchannels used in this study have geometries that induce chaotic advection in Newtonian fluids. Our results show that mixing in straight, herringbone and staggered herringbone channels depends strongly on volume fraction. Due to this complex interplay of advection and shear-induced migration, a staggered herringbone channel that typically results in chaotic mixing is not always effective for dispersing particles. The maximum degree of segregation is observed in a straight channel once the maximum packing fraction is reached at channel center. We modify a one-dimensional suspension balance model [R. Miller and J. Morris, J. Non-Newtonian Fluid Mech. 135, 149 (2006)] to describe the behavior at the center of the straight channel. The degree of mixing is then calculated as a function of bulk volume fraction, predicting the volume fraction that results in the maximum degree of segregation. In bidispersed suspension flow, it is shown that mixing of the larger species is enhanced in straight and staggered herringbone channels while segregation is enhanced at moderate volume fractions in herringbone channels. This suggests mixing and separations can be tailored by adjusting both the suspension properties and the channel geometry.

Shear-induced particle migration in one-, two-, and three-dimensional flows.

We investigate the segregation resulting from the competition between advection and shear-induced migration of suspensions in steady open flows. Herringbone channels form a concentration profile deviating from the particle focusing found in straight channels. Transients can result from a buckling instability during the onset of migration when particle-depleted fluid is injected into particle-rich fluid. In chaotic flows, the better mixing found at low bulk volume fraction is not seen at higher bulk volume fraction. Thus, the ability of static mixers to reduce the effects of shear-induced migration is significantly limited.

Competition between chaos and order: mixing and segregation in a spherical tumbler.

We investigate the competition between granular mixing and segregation in a sphere rotating and rocking on two orthogonal axes. Operation corresponds to the continuous-flow regime and the flow within the sphere is three-dimensional and time-periodic. Experimental results are organized in a frequency/amplitude phase diagram showing modes of segregation (band formation/no axial bands); segregated bands are remarkably robust and survive rocking amplitudes as large as 60 degrees over a wide range of frequencies. Details differ, but the phenomenon occurs under both dry and slurry conditions, that is, when all air is replaced by a liquid. Experimental space-time plots of the stationary segregated patterns agree well with Poincaré maps obtained using a continuum model of the flow, suggesting that the final segregation patterns are relatively independent of materials tumbled.

Segregation-driven organization in chaotic granular flows.

An important industrial problem that provides fascinating puzzles in pattern formation is the tendency for granular mixtures to de-mix or segregate. Small differences in either size or density lead to flow-induced segregation. Similar to fluids, noncohesive granular materials can display chaotic advection; when this happens chaos and segregation compete with each other, giving rise to a wealth of experimental outcomes. Segregated structures, obtained experimentally, display organization in the presence of disorder and are captured by a continuum flow model incorporating collisional diffusion and density-driven segregation. Under certain conditions, structures never settle into a steady shape. This may be the simplest experimental example of a system displaying competition between chaos and order.

Chaotic mixing of granular materials in two-dimensional tumbling mixers.

We consider the mixing of similar, cohesionless granular materials in quasi-two-dimensional rotating containers by means of theory and experiment. A mathematical model is presented for the flow in containers of arbitrary shape but which are symmetric with respect to rotation by 180 degrees and half-filled with solids. The flow comprises a thin cascading layer at the flat free surface, and a fixed bed which rotates as a solid body. The layer thickness and length change slowly with mixer rotation, but the layer geometry remains similar at all orientations. Flow visualization experiments using glass beads in an elliptical mixer show good agreement with model predictions. Studies of mixing are presented for circular, elliptical, and square containers. The flow in circular containers is steady, and computations involving advection alone (no particle diffusion generated by interparticle collisions) show poor mixing. In contrast, the flow in elliptical and square mixers is time periodic and results in chaotic advection and rapid mixing. Computational evidence for chaos in noncircular mixers is presented in terms of Poincare sections and blob deformation. Poincare sections show regions of regular and chaotic motion, and blobs deform into homoclinic tendrils with an exponential growth of the perimeter length with time. In contrast, in circular mixers, the motion is regular everywhere and the perimeter length increases linearly with time. Including particle diffusion obliterates the typical chaotic structures formed on mixing; predictions of the mixing model including diffusion are in good qualitative and quantitative (in terms of the intensity of segregation variation with time) agreement with experimental results for mixing of an initially circular blob in elliptical and square mixers. Scaling analysis and computations show that mixing in noncircular mixers is faster than that in circular mixers, and the difference in mixing times increases with mixer size. (c) 1999 American Institute of Physics.