Hopper and Standpipe Flow Theories

In this section, we introduce the theories of moving bed flows in hoppers and general standpipes. The hopper flow theory may be extended to the cases of moving bed flows through a discharge valve. A unique hopper-standpipe-discharger flow system is then discussed as an example of the application of these theories. Multiplicity of steady flows in a standpipe system is also illustrated. 

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The research of Roy Jackson combines theory and experiment in a distinctive fashion. First, the theory incorporates, in a simple manner, inertial collisions through relations based on kinetic theory, contact friction via the classical treatment of Coulomb, and, in some cases, momentum exchange with the gas. The critical feature is a conservation equation for the pseudo-thermal temperature, the microscopic variable characterizing the state of the particle phase. Second, each of the basic flows relevant to processes or laboratory tests, such as plane shear, chutes, standpipes, hoppers, and transport lines, is addressed and the flow regimes and multiple steady states arising from the nonlinearities (Fig. 6) are explored in detail. Third, the experiments are scaled to explore appropriate ranges of parameter space and observe the multiple steady states (Fig. 7). One of the more striking results is the... 

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