Granular flows, solids shear

The first term on the right-hand side represents momentum exchange between solid phases I and s and Kis is the solid-solid exchange coefficient. The last term represent additional shear stresses, which appear in granular flows (due to particle translation and collisions). Expressions for solids pressure, solids viscosity (shear and bulk) and solid-solid exchange coefficients are derived from the kinetic theory of granular flows. 

Several different expressions have been derived for solids pressure, solids shear viscosity and solids bulk viscosity, employing different approximations and assumptions while applying the kinetic theory of granular flows. Some of the commonly used equations are described below (see Gidaspow, 1994 and a review given by Peirano, 1998) Solids pressure ... 

Fig. 5.6. Flow and compression properties of feed solids for theoretical roll press design [15]. (a) Shear cell to measure internal friction of granular solid, (b) Cell to measure angle of friction between roll face and granular solid, (c) Pressure-density relationship of feed material.

Particle size. The soattering theory described above assumes that the particles are spherical in shape. Although emulsion droplets oan usually be assumed to be spherioal beoause of the effeots of surfaoe tension, they may beoome deformed under shear flow or in oonoentrated systems where they are closely paoked. Many solid particles are non-spherical (granular, crystalline, fibrous). Non-spherioity oan have a substantial effeot on ultrasonio measurements and a number of theories have been derived to consider suoh an effeot [58-60]. 

Fig. 2 Schematic of dilation mechanism that is a prerequisite for the flow of solids. (A) In undisturbed state, grains are interlocked and behave much like an ordinary solid. (B) A granular bed dilates in response to applied shear, and can then flow. (C) In the flowing state, the bed can form distinct crystalline, glassy, fluid-like and gas-like phases. The crystalline phase is regular and ordered, the glassy phase is disordered but static, the fluid-like state flows but exhibits enduring contacts, and the gas-like state is characterized by rapid and brief interparticle contacts.

Lenoble et al. (2005) studied a suspension of heavy particles at an initial solid fraction of ( ) = 0.59, a mixture they in fact termed a "wet granular material," in a simple shear flow configuration (between parallel plates) and found a sheared layer over a static layer. Granular avalanche flows under liquid have also been studied to determine the normal stress response, specifically through the pore pressure at the base of the flow (Cassar et al. 2005), and a model for the development of the steady state in such flows was presented by Pailha and Pouliquen (2009). 

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