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43508-AC9
Instabilities in Granular Taylor-Couette Flow
As a critical technology for the petroleum industry, understanding of many aspects of particulate processing operations is surprisingly limited. A large number of petrochemical processes stand to benefit from improved understanding of granular flows. The processing of granular materials necessarily involves flow and the associated complexities of such flows. However, a fundamental understanding of granular flows is far from complete. Poor understanding and control of granular flows causes processing inefficiencies at best, and failures at worst. More globally speaking, there is an increasing need for engineers and scientists to develop technologies that increase process yields, reduce waste production, and improve protection of health, safety and the environment. In many cases, the success of future technologies hinge on improved fundamental understanding and control of granular flow and mixing.
In fluids, analysis of paradigmatic or model experiments, like Benard, Couette, Taylor-Couette, and Kelvin-Helmholtz, has served to uncover aspects of shear transmission that have led to a better understanding of flows of engineering importance. For granular flows, we believe improved understanding will hinge on analysis of analogous paradigmatic or model experiments. The focus of this work is Taylor-Couette flows which are one of the simplest model geometries encompassing both shear and boundary interactions – essential ingredients of practical flows.
The Taylor-Couette geometry provides an ideal geometry for examining the rheological responses of granular materials undergoing shear. The Taylor-Couette geometry also provides a means to control and study granular flow instabilities. Since most industrial or natural flows are not steady or uniform it is crucial to examine flow instabilities and the resulting spatio-temporal dynamics. The azimuthal symmetry of the Taylor-Couette experiment means that structures that are coherent in space and time can be studied in a compact experiment. While there is ongoing work examining rapid granular shear flows of spheres in small systems (to avoid instabilities and maintain nearly homogeneous flows) we have begun to examine larger systems in order to provoke instabilities.
During the past year, we have continued to make use of both physical and computational experiments in Couette and Taylor-Couette flows. We have also examined shear in cylindrical mixers. These share some of the features of Couette flows. We have shown that the segregation occurring in the flows we have studied can be understood in terms of a competition of three forces: a pressure diffusion force dependent on the gradient of the particle pressure, a thermal diffusion force dependent on the gradient of the granular temperature, and an ordinary diffusion force that is determined by the gradient of the particle number density. We have considered binary mixtures with different size but equal mass, different mass and equal size, and different size and mass but equal density. For the equal mass case (different size), the thermal diffusion force is equal to zero. The pressure diffusion force drives small particles to segregate to high density regions. For the equal size case (different mass), the direction of the pressure diffusion force is reversed with an increase in the thermal diffusion force, leading to heavy particles to segregate in high density regions. Segregation in the equal density case is due to the competition of the above two mechanisms.
One interesting observation that has come from this work is that the presence of the density waves means that shearing or stirring faster doesn't necessarily lead to better mixing. Intuitively we expect that stirring two different materials faster will lead to their mixing e.g. consider stirring milk into your coffee, or stirring sugar into flour. However, we have seen that stirring faster can lead to separation of ingredients that were thoroughly mixed.
Students involved in the research have received training in particle technology which has been recognized as an area of national need as it has traditionally been neglected in the U.S.
