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Julio M Ottino

Publications and source records attributed to Julio M Ottino.

12 recordsLinked to original sources
PubMed2006

Capturing patterns and symmetries in chaotic granular flow.

Segregation patterns formed by time-periodic flow of polydisperse granular material (varying in particle size) in quasi-two-dimensional (quasi-2D) tumblers capture the symmetries of Poincaré sections, stroboscopic maps of the underlying flow, derived from a continuum model which contains no information about particle properties. We study this phenomenon experimentally by varying the concentration of small particles in a bidisperse mixture in quasi-2D tumblers with square and pentagonal cross sections. By coupling experiments with an analysis of periodic points, we explain the connection between the segregation patterns and the dynamics of the underlying flow. Analysis of the eigenvectors and unstable manifolds of hyperbolic points shows that lobes of segregated small particles stretch from hyperbolic points toward corners of the tumbler, demonstrating the connection between regions of chaotic flow and the shape of the segregation patterns. Furthermore, unstable manifolds map the shape of lobes of segregated particles. The techniques developed here can also be applied to nonpolygonal tumblers such as elliptical tumblers, as well as to circular tumblers with time-periodic forcing.

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PubMed2006

Creeping granular motion under variable gravity levels.

In a rotating tumbler that is more than one-half filled with a granular material, a core of material forms that should ideally rotate with the tumbler. However, the core rotates slightly faster than the tumbler (precession) and decreases in size (erosion). The precession and erosion of the core provide a measure of the creeping granular motion that occurs beneath a continuously flowing flat surface layer. Since the effect of gravity on the subsurface flow has not been explored, experiments were performed in a 63% to 83% full granular tumbler mounted in a large centrifuge that can provide very high g-levels. Two colors of 0.5 mm glass beads were filled side by side to mark a vertical line in the 45 mm radius quasi-two-dimensional tumbler. The rotation of the core with respect to the tumbler (precession) and the decrease in the size of the core (erosion) were monitored over 250 tumbler revolutions at accelerations between 1g and 12g. The flowing layer thickness is essentially independent of the g-level for identical Froude numbers, and the shear rate in the flowing layer increases with increasing g-level. The degree of core precession increases with the g-level, while the core erosion is essentially independent of the g-level. Based on a theory for core precession and erosion, the increased precession is likely a consequence of the higher shear rate. Core erosion, on the other hand, is related to the creep region decay constant, which is connected with slow diffusion in the bed and unaffected by gravity.

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PubMed2006

End-wall effects in granular tumblers: From quasi-two-dimensional flow to three-dimensional flow.

The flow of granular material in rotating tumblers is confined to a thin flowing layer at the free surface in which the particle velocity is primarily streamwise, perpendicular to the axis of rotation, with minimal axial motion. Particle tracking velocimetry was used to measure the surface velocity for 1 and 2 mm glass particles and sand in cylindrical tumblers of various diameters, lengths, and rotation rates for a flat continuously flowing surface. End-wall friction slows the streamwise surface velocity adjacent to the walls, yet material just inward from the end wall flows faster than the material in the center of a long tumbler. An axial velocity occurs near the end walls both upstream and downstream of the midlength of the flowing layer. Increasing the tumbler diameter and corresponding flowing layer length causes the magnitude of the axial and streamwise velocity components, as well as the axial thickness of the end-wall region, to increase. An increase of end-wall friction slows particles directly adjacent to the end wall, further enhancing the axial flow near the end wall. Increasing the rotation rate, while still maintaining a flat continuously flowing surface, causes a corresponding increase in both the streamwise and axial velocities in the tumbler. The boundary flow effects are localized to end walls when the axial length of the tumbler (L) is greater than the diameter (D), so that the flow in the center region of the tumbler is independent of the end walls and hence similar to the conditions at the center of an infinitely long tumbler. Decreasing the axial length of the tumbler so that L/D<1 causes the axial velocity to decrease as the regions affected by the end walls merge. This also leads to a streamwise velocity in quasi-two-dimensional tumblers that can be more than twice that at the center of three-dimensional tumblers.

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PubMed2006

Dynamics of axial segregation in granular slurries: parallel experiments and influence of aspect ratio and periodic tilting.

An efficient technique for conducting rotating tumbler experiments in parallel is introduced and used to study the effect of tumbler length and periodic tilting of the tumbler on axial segregation. When rotated, bidisperse granular slurries segregate into what appear at the surface to be alternating bands of larger and smaller particles. The number of bands increases linearly with tumbler length while the fractional area occupied by each type of band is constant. Periodic tilting of the rotation axis induces a periodic axial flow of particles in the flowing layer. For the range of tilt angle amplitudes investigated (0 degrees -3.5 degrees), the number of bands decreases with increasing angle, but the rate of merging and the fractional area of bands rich in smaller particles are unaffected.

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PubMed2006

Surface roughness effects in granular matter: influence on angle of repose and the absence of segregation.

We investigate the effect of nanoscale variations in the surface roughness of individual particles on macroscale granular flow characteristics. Experiments were conducted in circular rotating tumblers with smooth and rough 2 and 3 mm steel particles. The smooth beads had a rms surface roughness of approximately 30 to 60 nm; rough beads had a surface roughness of approximately 240 to 350 nm. The dynamic angle of repose for rough particles increased by 10 degrees to 25 degrees over that of smooth particles over a wide range of rotation speeds. Even though surface roughness affects the angle of repose, we were unable to detect any segregation of bidisperse mixtures of rough and smooth particles in the radial direction in two-dimensional (2D) tumblers. Furthermore, no axial banding segregation occurred in 3D tumblers, both cylindrical and spherical. For mixtures of smooth and rough particles, the angle of repose increased monotonically with increasing concentration of rough particles. Particle dynamics simulations verified that the dependence of the angle of repose on the concentration of rough particles can be directly related to the coefficient of friction of the particles. Simulations over a broad range of friction parameters failed to induce segregation solely from differences in the angle of repose. These results indicate that nanoscale surface roughness can affect the flowability and angle of repose of granular matter without driving demixing of the bulk granular material.

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PubMed2005

Combined size and density segregation and mixing in noncircular tumblers.

Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). For noncircular tumblers the additional interaction between the segregation mechanisms and chaotic advection complicates the physics. Experiments are performed using a bi-disperse mixture of equal volumes of different sizes of steel and glass beads in a quasi-two-dimensional square tumbler. Mixing is observed instead of segregation when the denser beads are larger than the lighter beads so that the ratio of particle sizes is greater than the ratio of particle densities. This can be expressed in terms of the particle diameters and masses as d(heavy)/d(light) >(m(heavy)/m(light))(1/4) . Segregation patterns vary from a semicircular core when the fill level is below 50% to more complicated patterns including lobes and streaks for fill levels above 50%. Temporal evolution of segregated patterns is quantified in terms of a "segregation index" (based on the area of the segregated pattern) to capture both the rate and extent of segregation at different particle properties. The circular and noncircular tumblers have no significant difference in the segregation index, even though the segregation patterns differ significantly.

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PubMed2005

Creeping motion in granular flow.

The core of a quasi-two-dimensional rotating cylinder filled more than half full with glass beads rotates slightly faster than the cylinder itself and decreases in radius over time. Core precession depends linearly on the number of tumbler revolutions while core erosion varies logarithmically. Both processes serve to quantify the slow granular motion in the "fixed" bed and depend on the filling fraction and the tumbler rotation rate. A simple model, based on experimental observations of an exponential decrease in velocity parallel to the free surface, captures the primary features of the core dynamics.

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PubMed2005

Dynamics of granular band formation: Long-term behavior in slurries, parameter space, and tilted cylinders.

Band formation (axial segregation) and subsequent coarsening of bidisperse mixtures in long circular tumblers is well documented for the case where the cylinder is at a single fill level and the interstitial fluid is air. However, little information is available for a range of fill levels, nor is the effect of rotational speed on segregation clear. Moreover just a handful of studies have focused on slurry systems, where the interstitial fluid is a liquid. This is precisely the parameter space covered in this study. Experiments are conducted using a 2:1 mixture of 882 and 272 mum glass beads with water as the interstitial fluid. Several different phenomena are uncovered. Results indicate that bands are less likely to form at low rotational speeds and low fill levels. As the fill level and rotational speed increase, more bands form and they form more quickly. However, at fill levels near 50% and high rotational speeds the bands contain a mixture of particles rather than being relatively pure. Furthermore, the evolution of the core of small beads that forms deep in the bed depends on the fill level and the rotational speed. For certain fill levels and rotational speeds, the core remains prominent as bands form, while in other cases the core disappears entirely between bands. Finally, when the tumbler is tilted so that the fill level varies from 14% at one end to slightly more than half full at the other end, the bands and core that form locally qualitatively correspond with those that would form for the corresponding fill level in a horizontal cylinder.

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PubMed2004

Introduction: mixing in microfluidics.

In this paper we briefly review the main issues associated with mixing at the microscale and introduce the papers comprising the Theme Issue.

Complex Mixtures↗
PubMed2004

Foundations of chaotic mixing.

The simplest mixing problem corresponds to the mixing of a fluid with itself; this case provides a foundation on which the subject rests. The objective here is to study mixing independently of the mechanisms used to create the motion and review elements of theory focusing mostly on mathematical foundations and minimal models. The flows under consideration will be of two types: two-dimensional (2D) 'blinking flows', or three-dimensional (3D) duct flows. Given that mixing in continuous 3D duct flows depends critically on cross-sectional mixing, and that many microfluidic applications involve continuous flows, we focus on the essential aspects of mixing in 2D flows, as they provide a foundation from which to base our understanding of more complex cases. The baker's transformation is taken as the centrepiece for describing the dynamical systems framework. In particular, a hierarchy of characterizations of mixing exist, Bernoulli --> mixing --> ergodic, ordered according to the quality of mixing (the strongest first). Most importantly for the design process, we show how the so-called linked twist maps function as a minimal picture of mixing, provide a mathematical structure for understanding the type of 2D flows that arise in many micromixers already built, and give conditions guaranteeing the best quality mixing. Extensions of these concepts lead to first-principle-based designs without resorting to lengthy computations.

Complex Mixtures↗