Coulomb powders

The particulate phase in the annular zone of a spouted bed can be described as an isotropic, incompressible, rigid plastic, non-cohesive Coulomb powder. Assuming that this material is in a quasi-static critical condition, the stress field can be described by equations developed for a static material element. 

Mohr-Coulomb Failure Criterion and Coulomb Powders... 

A rigid-plastic powder which has a linear yield locus is called a Coulomb powder. Most powders have linear yield loci, although, in some cases, nonlinearity appears at low compressive stresses. A relation between the principal stresses in a Coulomb powder at failure can be found from the Mohr circle in Fig. 8.4 as... 

An important application of this equation is to distinguish between two extreme failure conditions, known as the active and passive failures. First, the active and passive states of stress may be explained as follows Consider a cohesionless Coulomb powder. If the powder is assembled in a large container in successive horizontal layers without disturbance, there will be no shear stresses along the horizontal and vertical planes inside the powder because of the symmetry of the problem. Thus, at any point, the horizontal and vertical normal stresses are the principal stresses at that point. In this case, if the major principal stress is the horizontal stress, passive state of stress. On the other hand, if the major principal stress is the vertical stress, active state of stress. Thus, Eq. (8.9) can be written for each state as... 

To close the problem, constitutive relations of powders must be introduced for the internal connections of components of the stress tensor of solids and the linkage between the stresses and velocities of solids. It is assumed that the bulk solid material behaves as a Coulomb powder so that the isotropy condition and the Mohr-Coulomb yield condition may be used. In addition, og has to be formulated with respect to the other stress components. 

Powder Mechanics Measurements As opposed to fluids, powders may withstand applied shear stress similar to a bulk solid due to interparticle friction. As the applied shear stress is increased, the powder will reach a maximum sustainable shear stress T, at which point it yields or flows. This limit of shear stress T increases with increasing applied normal load O, with the functional relationship being referred to as a yield locus. A well-known example is the Mohr-Coulomb yield locus, or... 

Zinc is electrodeposited from the sodium zincate electrolyte during charge. As in the zinc/bromine battery, two separate electrolytes loops ("posilyte" and "nega-lyte") are required. The only difference is the quality of the separator The zinc/ bromine system works with a microporous foil made from sintered polymer powder, but the zinc/ferricyanide battery needs a cation exchange membrane in order to obtain acceptable coulombic efficiencies. The occasional transfer of solid sodium ferrocya-nide from the negative to the positive tank, to correct for the slow transport of complex cyanide through the membrane, is proposed [54],... 

Catbon Determination in Small Amounts of Ceramic Powder by Coulombic Titration, J. Am. Ceram. Soc. 1995, 78, 2834.] The solid electrode material can be used for 02 filtration, 02 generation, or 02 removal. [S. P. S. Badwal and... 

So far, we understand that the flowability of powders depends on their failure stresses from the Mohr-Coulomb failure criterion. Therefore, analyses of powder flows... 

Remarkably uniform MgO smoke was prepared by Coulomb and Vilches (1984) by burning magnesium ribbons in dry OjAi mixtures. The MgO particles were collected in die form of a coating on a clean aluminium surface and were subjected to heat treatment (at c. 950°C and pressures < 10 6 mbar). The specific surface area of the final MgO(l 0 0) powder was c. 8 m2 g-1 so that it was not difficult to undertake accurate physisorption measurements and also neutron scattering experiments. 

FIGURE 12J3S The Mohr stress circle (a) is a representatioii of a two-dimensional state of stress in a powder compact (b). The Coulomb 3neld a-iterion is also plotted as a straight line in the Mohr stress circle. 

In soil mechanics, the pressures lie in a range up to and over 2 MPa, whereas in powder mechanics they are usually below 0.1 MPa. For this range of pressure, the Coulomb criterion is generally not applicable. Only cohesionless solids exhibit Coulomb yield behavior at low pressures. 

In general, this Ck)ulomb yield criterion can be used to determine what stress will be required to cause a ceramic powder to flow or deform. All that is needed are the two characteristics of the ceramic powder the angle of friction, 8, and the cohesion stress, c, for each particular void fraction. With these data, the effective yield locus can be determined, from which the force required to deform the powder to a particular void fraction (or density) can be determined. This Coulomb yield criterion, however, gives no information on how fast the deformation will take place. To determine the velocity that occurs durii flow or deformation of a dry ceramic powder, we need to solve the equation of motion. The equation of motion requires a constitutive equation for the powder. The constitutive equation gives the shear and normal states of stress in terms of the time derivative of the displacement of the material. This information is unavailable for ceramic powders, and the measurements are particularly difficult [76, p. 93]. 

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