Pattern formation in oscillatory granular flows

J. Jaimes¹, G. G. Joseph¹, E. Geffroy & B. Mena¹, J. R. Herrera-Velarde²

¹ Instituto de Investigaciones en Materiales, UNAM, Apdo. Post. 70-360, Circuito Exterior, Ciudad Universitaria, 04510 México, D.F., México.

² Instituto Tecnológico de Zacatepec, Av. Instituto Tecnológico #27, 67980 Zacatepec, Morelos, México.

Abstract

An experimental device has been used to examine the behavior of granular materials under vertical, horizontal and combined bi-axial vibrations. Containers with square, rectangular and circular cross sections geometries were used, with glass spheres, millet and lentil as granular media. The oscillating frequencies varied from 0 to 35 Hz, with amplitudes between 0 and 5.5 mm. Flow visualization was made possible with high-speed video cameras providing frontal and lateral views of the granular motion. Four different phenomena: heaping, arching, small amplitude surface waves and large amplitude surface waves were found. The onset of these phenomena depends basically on two dimensionless parameters; one involving the amplitude and frequency of oscillations coupled with gravity and the second one representing the amount of material in the vibrating container. In the case of vertical vibrations, results agreed well with those of Wassgren et al. (1996), although some discrepancies were found. For horizontal vibrations, convective cycles appeared rotating in opposite directions as well as lateral waves with one half the frequency of excitation. For the case of combined vibrations, a superposition of effects between those of horizontal and vertical vibrations was found and analyzed. Finally, comparison was made between experiments and numerical predictions based on molecular dynamics. The numerical solution agreed extremely well with experimental observations, particularly for the new results of combined vibrations.

Keywords: Granular dynamics; granular flow; granular materials.

Resumen

Se examina experimentalmente el comportamiento de materiales granulares sujetos a vibraciones horizontales, verticales y combinaciones de ambas. Se utilizaron geometrías de sección cuadrada, rectangular y circular, con esferas de vidrio, mijo y lentejas como medios granulados. Las frecuencias de oscilación cubrieron el intervalo entre 0 y 35 Hz y las amplitudes se variaron entre 0 y 5.5 mm. Cámaras de video de alta velocidad localizadas frontal y lateralmente permitieron analizar los patrones de flujo. Cuatro distintos fenomenos fueron observados: apilamiento, arqueo, ondas superficiales de pequeña amplitud y ondas superficiales de gran amplitud. La aparición de dichos patrones depende básicamente de dos parámetros adimensionales: el primero involucra la amplitud, la frecuencia de oscilación y la aceleración gravitacional, mientras que el segundo es representativo de la cantidad de material granular en el contenedor experimental. Para vibraciones verticales, los resultados concuerdan con los reportados por Wassgren, et al. (1996), aunque con ciertas discrepancias. En el caso de vibraciones horizontales se presentaron ciclos convectivos que giraban en direcciones opuestas y ondas laterales a una frecuencia equivalente a la mitad de la frecuencia de excitación. Para el caso de vibraciones combinadas, una superposición de efectos entre los de vibración horizontal y vertical apareció y fue analizada. Finalmente, se compararon los resultados experimentales con predicciones numéricas basadas en dinámica molecular con resultados aceptables.

Descriptores: Dinámica granular; flujo granular; materiales granulares.

PACS: 46.40.f; 62.40.+i; 81.05.Rm; 83.85.-c

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Acknowledgements

The authors wish to acknowledge the assistance of the machine shop of the I.I.M. and in particular J. Camacho and M. Serrano, for the construction of the experimental device. G. F. Guevara provided assistance with the computer images. Support from grants IN302392 and IN503494 from PAPIIT, UNAM are also gratefully acknowledged. Many fruitful conversations with M. Hunt and C. Brennen and their groups at Caltech are also acknowledged.

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