Shape dynamics of interfacial front in rotating cylinders

Ristow, Gerald H.; Nakagawa, Masami

doi:10.1103/physreve.59.2044

Cited by 32 publications

(32 citation statements)

References 14 publications

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“…Previously, Ristow and Nakagawa (35) proposed that DðCÞ ¼ 1 AE ðC − 1∕2Þ so that ∫ 1 0 DðCÞdC ¼ 1 and there is no concentration dependence for a perfect mixture (i.e., Dð1∕2Þ ¼ 1). Neither experiments (35,36) nor DEM simulations (34, 37) provide sufficiently well resolved data to determine the functional form of DðCÞ with any certainty or whether to pick the "þ" or "−" sign in the proposed expression.…”

Section: Resultsmentioning

confidence: 99%

“…Neither experiments (35,36) nor DEM simulations (34, 37) provide sufficiently well resolved data to determine the functional form of DðCÞ with any certainty or whether to pick the "þ" or "−" sign in the proposed expression. Nevertheless, a concentration-dependent axial diffusivity with Dð0Þ ¼ 0 (as in refs.…”

Section: Resultsmentioning

confidence: 99%

“…8, the estimates in Table 1 and the numerical evidence for collapse under Eq. 3 with DðCÞ ¼ 1 þ ðC − 1∕2Þ because T Ã is valid for constant D only, and neither the experimental (35,36) nor the simulated (34,37) data is sufficiently well esolved to specify the form of DðCÞ used here.…”

Section: Resultsmentioning

confidence: 99%

“…Another set of experiments (35,36) and DEM simulations (37) have provided some evidence for a concentration-dependent diffusivity in bidisperse mixtures, i.e., granular materials consisting of two kinds of particles differing either in size, density, shape, roughness, etc. Specifically, it was found that that a band of larger particles diffuses anomalously in a background of smaller particles.…”

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

Christov

Stone

2012

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

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

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

Christov

Stone

2012

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

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“…In fact, heterogeneous mixtures commonly undergo segregation, a phenomenon of great interest for materials processing [6]. Segregation of binary mixtures also occurs in the laboratory, in vibrating bed [7,8] and rotating drum experiments [9][10][11][12][13][14][15][16][17][18][19][20][21][22], and upon pouring into a Hele-Shaw cell [23][24][25]. It can be caused by differences in particle size, shape, smoothness, or density.…”

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confidence: 99%

Segregation and stability of a binary granular heap

et al. 2009

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We measure stability of two-dimensional granular mixtures in a rotating drum and relate grain configurations to stability. We use two types of grains which differ in both size and shape, with the larger grains reaching a larger average angle before an avalanche. In our mixtures, the smaller grains cluster near the center of the drum, while the larger grains remain near the outer edge, a pattern suggesting that grain size rather than avalanche angle determines the segregation behavior. One consequence of the size segregation is that the smaller grains heavily influence the stability of the heap. We find that the maximum angle of stability is a non-linear function of composition, changing particularly rapidly when small grains are first added to a homogeneous pile of large grains. We conclude that the grain configuration within the central portion of the heap plays a prominent role in stability.

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