Compressible powders, particle density

For ideal mixtures there is a simple relationship between the measurable ultrasonic parameters and the concentration of the component phases. Thus ultrasound can be used to determine their composition once the properties of the component phases are known. Mixtures of triglyceride oils behave approximately as ideal mixtures and their ultrasonic properties can be modeled by the above equations [19]. Emulsions and suspensions where scattering is not appreciable can also be described using this approach [20]. In these systems the adiabatic compressibility of particles suspended in a liquid can be determined by measuring the ultrasonic velocity and the density. This is particularly useful for materials where it is difficult to determine the adiabatic compressibility directly, e.g., powders, biopolymer or granular materials. Deviations from equations 11 - 13 in non-ideal mixtures can be used to provide information about the non-ideality of a system. 

Yan et al. (2001), studied how bulk density of instant nonfat milk, spray-dried coffee, and freeze-dried coffee was affected by HHP processing times, particle size, and water activity. The experimental curves for each powder in Figure 10 show that the powder bulk density increased as the pressure increased but remained constant after the pressure reached a critical value of 207 MPa for spray-dried coffee and 276 MPa for freeze-dried coffee at different water activities. The final compressed densities were not significantly different. When the pressure is higher than the critical value, there are no void spaces between the agglomerates or primary particles even the primary particles are crushed, leaving no open or closed pores within. Bear in mind, it is assumed that the compression mechanisms are the same as those in the confined uniaxial compression tests. 

In some cases, the natural logarithm has been used for the compressibility characterization of food powders. Equation 14 shows the natural semi-log expression for compressibility determination, where density fraction T(a) is expressed as a function of porosity e between porosity and the solid density ps of particles (Equation 13). 

Flow problems are mainly dependent on interparticle/intraparticle forces, powder particle size and shape, and moisture and fat content. Conditioners (or anticaking agents) enhance powder flow by reducing interparticle force cohesiveness and compressibility while increasing bulk density (Peleg and Manheim, 1973). Peleg et al. (1973) showed that as concentrations of stearate or silicate (added to sucrose) were increased from 1% to 3%, there was no reduction in cohesiveness at agent concentrations of 1-2%, but cohesiveness decreased as more flow conditioner was added. 

Table 6.2 summarizes the low pressure intercept of observed shock-velocity versus particle-velocity relations for a number of powder samples as a function of initial relative density. The characteristic response of an unusually low wavespeed is universally observed, and is in agreement with considerations of Herrmann s P-a model [69H02] for compression of porous solids. Fits to data of porous iron are shown in Fig. 6.4. The first order features of wave-speed are controlled by density, not material. This material-independent, density-dependent behavior is an extremely important feature of highly porous materials. 

The bulk density of a powder is calculated by dividing its mass by the volume occupied by the powder (Abdullah Geldart, 1999). Tapped bulk density, or simply tapped density, is the maximum packing density of a powder achieved under the influence of well-defined, externally applied forces (Oliveira et al., 2010). Because the volume includes the spaces between particles as well as the envelope volumes of the particles themselves, the bulk and tapped density of a powder are highly dependent on how the particles are packed. This fact is related to the morphology of its particles and such parameters are able to predict the powder flow properties and its compressibility. 

For most ceramic pressing, a CR < 2.0 is desired since it rednces both the punch displacement and the compressed air in the compact. As indicated in Eq. (7.15), a high fill density leads to a low CR. For comparison, the CR in metal powder pressing is typically much greater than 2.0 dne to the dnctility of the particles. 

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