Albert Alexander

Spontaneous chaotic granular mixing

There are several types of instabilities in fluid mechanics that lead to spontaneous chaotic mixing and intricate patterns. Classical examples include the Kelvin–Helmholtz instability in shear layers, the instability of Taylor–Couette flow between rotating cylinders and the Rayleigh-Bénard instability in thermal convection. More recently, a variety of two- and three-dimensional chaotic mixing phenomena have been observed in other geometries. Mixing in granular flows, unlike that in stirred fluids, is thought to be diffusive—although periodic forcing has been used to enhance granular mixing, spontaneous chaotic granular mixing has not previously been reported. Here we report the observation of chaotic granular mixing patterns in simple cylindrical tumblers partially filled with fine grains. The patterns form spontaneously when sufficiently fine grains (≲300 µm diameter) are blended. We identify the mechanism by which the chaotic patterns are produced: a periodic stick–slip behaviour occurs in the shear layer separating static and flowing regions of grains. This causes weakly cohesive grains to mix at rates overwhelmingly exceeding those achievable for previously studied freely flowing grains.

Sampling and characterization of pharmaceutical powders and granular blends

We use a variety of experimental results to illustrate issues and challenges involved in the sampling and characterization of pharmaceutical mixtures. Accurate and reliable characterization of granular mixtures is hindered by both the complexity of granular systems and the lack of validated and reliable sampling technology and techniques. Both sampling tools and sampling protocols are critically important for accurate characterization. Using cohesive and free-flowing powders and four thief probe designs, we reveal a large potential for extremely misleading results as well as severe disturbance of the granular bed. We also discuss results from several experiments designed to test the validity of various sampling protocols by varying parameters such as sampling location and frequency of sampling. These experiments illustrate the importance of effective sampling procedures to achieve the best and most efficient results.

Scaling surface velocities in rotating cylinders as a function of vessel radius, rotation rate, and particle size

Abstract In industrial practice, scale-up of granular flows in tumbling devices has been largely attempted using one of two parameters, either the vessel tangential speed (ω) or the Froude (Fr) number. In this communication, we measure surface velocities of 1.6-mm particles in half-filled rotating cylinders and find that neither ω nor Fr accurately scales changes in particle velocity with changes in vessel rotation rate, diameter, or particle size. New non-dimensional scaling criteria using a simplified model produce agreement in both the magnitude and shape of the velocity profiles. A strong dependence on both rotation rate and vessel radius is found and a small but measurable effect of particle size is also demonstrated. We find that there are two different scaling regimes that depend on whether or not the cascading layer reaches a symmetric equilibrium state. At lower rotation rates, Ω, cascading particles can reach equilibrium, and granular surface speeds scale as Ω2/3; at higher rotation rates, particle velocities scale as Ω1/2. New effects of relative particle size with respect to the cylinder diameter are also reported.

Granular segregation in the double-cone blender: Transitions and mechanisms

We investigate granular segregation in one of the most common industrial devices used in granular processing: the double-cone blender. We report several new and spontaneously occurring segregation patterns, including stripes, bands, and a symmetry-breaking state in which one species vacates half the tumbler. By varying the tumbling speed along with particle size and size ratio, we find that the transitions between segregated patterns are extremely sharp: Changes in fill level or speed of under one percent are sufficient to produce a reproducible qualitative change in the observed pattern. We show that the several distinct segregation patterns observed experimentally can be reproduced from a simplified model in which outward rolling on the convective granular cascade competes against inertial motion of rapidly moving large particles. Finally, we identify a cutoff particle size ratio above which large particles become buried in the cascading flow, and segregation appears to cease.

Using flow perturbations to enhance mixing of dry powders in V-blenders

Experiments were conducted to compare mixing performance in a conventional V-blender and in a V-blender that incorporates perturbations of the particle flow by rocking the mixing vessel during rotation. Mixing was investigated using glass beads with sizes from 40 to 800 μm in vessels of approximately one liter volume. Mixture uniformity was assessed qualitatively using two different methods. One method used a transparent mixing vessel to visualize particle flow patterns and assess the state of homogeneity at the mixtures surface during the entire experiment. The second method involved solidification of the mixture by infiltration with a binder inside disposable aluminum mixing vessels. Using this method, it was possible to assess the state of the entire mixture, including its interior structure, by slicing the solidified structure after completion of each experiment. Mixture uniformity was also assessed quantitatively using image analysis to determine the composition of the solidified samples. In all cases, mixing was greatly enhanced in the rocking V-blender compared to the conventional V-blender.

Segregation patterns in V-blenders

Abstract We report several segregation patterns in V-blenders partially filled with mixtures of glass beads differing in size. Three dominant patterns are found, including one in which larger and smaller particles migrate to opposite halves of the blender. Changes in the rotation rate by as little as 3% can cause a change of pattern. Analysis of particle pathlines suggests that segregation in this vessel may be dominated by ‘trajectory segregation’, i.e. the inability of larger, more inertial, particles to navigate sharp bends in pathlines.

V-blender segregation patterns for free-flowing materials: effects of blender capacity and fill level.

Stable segregation patterns are shown to form in V-blenders over a wide range of vessel capacities, fill levels, and rotation rates. Slight changes in either rotation rate or fill level induce changes in pattern formation. Trajectory segregation in two regions of the flow, accumulating over many flow periods, drives segregation pattern formation. Scaling criteria derived to relate particle velocities to vessel size and rotation rate in rotating cylinders successfully predict the rotation rate for the transition between patterns across V-blenders of 0.8-26.5 quart total capacity. This agreement suggests that pattern formation is governed by the magnitude of particle velocities. Regardless of vessel size, when particle velocities at specific regions of the blender are below a certain value, one particular pattern appears, and when they increase beyond that speed (i.e. by changing the rotation rate or the vessel size), a different pattern emerges. A scaling relation between segregation pattern formation and blender fill level was not identified because the complex flow patterns in the V-blender (the length of the flowing layer and the mixture center of mass relative to the blender are constantly oscillating) preclude the determination of a relationship between blender fill level and particle velocities.

Chaotic granular mixing.

Several models for convective mixing of coarse, freely flowing in granular tumblers have been proposed over the past decade. Powders of practical interest, by contrast, are frequently fine and cohesive, and cannot be analyzed with these models. Moreover, even in the freely flowing regime, mixing transverse to the dominant, convective, direction is typically slow and inefficient. In this paper, we examine two chaotic mixing mechanisms, the first of which can be intentionally applied to increase transverse mixing rates severalfold, with new prospects for further improvements in three-dimensional mixing through judicious process design. The second mechanism occurs spontaneously in fine grains, resulting in mixing rates overwhelmingly exceeding what would be possible in freely flowing grains. Finally, we show that the same chaotic mixing mechanisms seen in simple drum mixers are also found to be at work in more complex blender configurations widely used in batch industrial operations. (c) 1999 American Institute of Physics.