Axial dispersion of granular material in horizontal rotating cylinders

Third, J. R.; Scott, D. M.; Scott, Stuart A.

doi:10.1016/j.powtec.2010.06.017

Cited by 37 publications

(47 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 but is consistent with the fractional diffusion equation governing a subdiffusive process with hðΔzÞ 2 i 1∕2 ∝ t 0.3 (12). Subsequent numerical simulations of the axial diffusion of granular materials through particle dynamics using the discrete element method (DEM) (32)(33)(34) found that the mean squared displacement of individual particles grows (asymptotically) linearly with time, consistent with normal (Fickian) diffusion; i.e., hðΔzÞ 2 i ∝ t. X-ray measurements of individual particle trajectories in the most recent experiments (23) are in agreement with the simulations. Thus, there is a clear paradox between the microscopic and macroscopic theories of axial diffusion of granular materials.…”

supporting

confidence: 56%

Resolving a paradox of anomalous scalings in the diffusion of granular materials

Christov

Stone

2012

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Granular materials do not perform Brownian motion, yet diffusion can be observed in such systems when agitation causes inelastic collisions between particles. It has been suggested that axial diffusion of granular matter in a rotating drum might be “anomalous” in the sense that the mean squared displacement of particles follows a power law in time with exponent less than unity. Further numerical and experimental studies have been unable to definitively confirm or disprove this observation. We show two possible resolutions to this apparent paradox without the need to appeal to anomalous diffusion. First, we consider the evolution of arbitrary (non-point-source) initial data towards the self-similar intermediate asymptotics of diffusion by deriving an analytical expression for the instantaneous collapse exponent of the macroscopic concentration profiles. Second, we account for the concentration-dependent diffusivity in bidisperse mixtures, and we give an asymptotic argument for the self-similar behavior of such a diffusion process, for which an exact self-similar analytical solution does not exist. The theoretical arguments are verified through numerical simulations of the governing partial differential equations, showing that concentration-dependent diffusivity leads to two intermediate asymptotic regimes: one with an anomalous scaling that matches the experimental observations for naturally polydisperse granular materials, and another with a “normal” diffusive scaling (consistent with a “normal” random walk) at even longer times.

show abstract

supporting

confidence: 56%

Resolving a paradox of anomalous scalings in the diffusion of granular materials

Christov

Stone

2012

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…However, neither Parker et al [9] nor Third et al [10] were able to provide an explanation of why D ax is independent of D. Furthermore, for large values of D the particle motion within the bed will move from the rolling regime observed at low Fr to the cataracting or centrifuging regimes. Therefore, although it has never been reported, it is expected that there is an upper limit for D above which the observation that D ax is independent of D will fail.…”

Section: Introductionmentioning

confidence: 95%

“…Both Parker et al [9] and Third et al [10] found the rate of axial dispersion to be independent of the drum diameter (D) for sufficiently large values of D. This result is particularly intriguing since it implies that the rotational Froude number (Fr = 2 D/2g), which is often used to characterize particle motion within rotating cylinders [11,12], does not govern axial * jthird@ethz.ch dispersion within these systems. However, neither Parker et al [9] nor Third et al [10] were able to provide an explanation of why D ax is independent of D. Furthermore, for large values of D the particle motion within the bed will move from the rolling regime observed at low Fr to the cataracting or centrifuging regimes.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Is axial dispersion within rotating cylinders governed by the Froude number?

Third

Müller

2012

Phys. Rev. E

View full text Add to dashboard Cite

Axial dispersion rates of particles within horizontal rotating cylinders have been calculated for a decade of cylinder diameters. Throughout the range studied the rate of axial dispersion was found to be independent of the cylinder diameter. This phenomenon has been investigated further by spatially resolving the local contribution to the axial dispersion coefficient. This analysis demonstrates that, although the highest rates of axial dispersion occur at the free surface of the bed, there is a significant contribution to axial dispersion throughout the flowing region of the bed. Finally, based on an analogy with a Galton board, a linear relationship is proposed between the local rate of axial dispersion within a horizontal rotating cylinder and the product of the local particle concentration and the local shear rate in a plane perpendicular to the cylinder axis.

show abstract

“…An appropriate environment for microbial growth includes sufficient dissolved oxygen, rapid carbon dioxide discharge [3], and low or suitable intensity of shear force [4]. Rotating-drum equipment is commonly used in the process industry for drying and mixing of solid particles and materials [5][6][7][8]. Due to the mild shear force it can provide, the application of a rotating-drum bioreactor (RDB) has been explored in shear-sensitive bioprocesses, e.g., plant cell culture [9,10], solid substrate fermentation [11][12][13], composting [14], bioremediation [6,15,16], and bioleaching processes [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Power Consumption of Liquid and Liquid/Solid Systems in a Rotating‐Drum Bioreactor

et al. 2013

View full text Add to dashboard Cite

Rotating-drum bioreactors combine the advantage of quiescent environment with mild shear stress for microbial growth. Power consumption is a vital parameter to evaluate the performance of reactors. To provide primary information for design and optimization of the rotating-drum bioreactor, the effects of lifter arrangement conditions including number of lifters, lifter width and mounted angles, and operation conditions such as rotational speed, aeration rate, and solid volume fraction on power consumption were tested. Based on the experimental data, correlations for the power consumption of liquid and liquid/solid systems were proposed.

show abstract

Axial dispersion of granular material in horizontal rotating cylinders

Cited by 37 publications

References 10 publications

Resolving a paradox of anomalous scalings in the diffusion of granular materials

Resolving a paradox of anomalous scalings in the diffusion of granular materials

Is axial dispersion within rotating cylinders governed by the Froude number?

Power Consumption of Liquid and Liquid/Solid Systems in a Rotating‐Drum Bioreactor

Contact Info

Product

Resources

About