Studying the porosity of powders under pressure compaction in deaeration mixers

Mathematical Model of the Deaeration of Finely Dispersed Solid Media in a Spherical Matrix of a Roller-Type Apparatus

“…Hemispherical shaft and belt surfaces are used to obtain deaerated portions of powder (Figure 1) with radius r. The Cartesian coordinate system Oxy and the "inverted" motion method (Kapranova et al, 2000;Kapranova et al, 2015) are used when the horizontal tape appears to be stationary. The planar motion of the surfaces of the shaft forms is assumed when decomposed into translational motion together with the K i pole (Figure 1).…”

“…where α 2 is the porosity of the powder, and λ, μ are the Lame coefficients. Additionally, the condition of limiting equilibrium is assumed (Kapranova and Zaitzev, 2011;Kapranova et al, 2015). According to Kapranova and Zaitzev (2011), neglecting the deformations of the dispersed medium along the z coordinate, the following representations are used for the equation of porosity change and the relation for shear stresses, respectively.…”

“…In this case, the constants c 0 , C 1 , c 2 , C 3 , a n , h n are set by the values of the coordinates of the points K i , D i from Equations (1-3) and the characteristics of the physical and mechanical properties of the compacted material, including the angle of friction of the dispersed medium ρ (Kapranova and Zaitzev, 2011;Kapranova et al, 2015) and the adhesion coefficient of the material H k s ρ (Kapranova and Zaitzev, 2011;Kapranova et al, 2015), where k s is the parameter of caking (adhesion).…”

“…The design of roller devices for the deaeration of dispersed media is associated with the formation of theoretical foundations (Kapranova et al, 2000;Kapranova, 2010;Kapranova et al, 2015) for the engineering calculation of the parameters of these devices (Kapranova et al, 2001;Kapranova et al, 2006a;Kapranova et al, 2006b). For example, this is relevant in the manufacture of granules (Zaitsev et al, 2010) from bitumen (Santos et al, 2014;Fingas and Fieldhouse, 2009) and mineral powder (Renner et al, 2007).…”

“…For these purposes, as a rule, the mechanics of heterogeneous systems are used (Nigmatulin, 1978;Generalov, 2002). The analytical results (Kapranova et al, 2000;Kapranova, 2010;Kapranova et al, 2015) when describing the behavior of the system solid particles-gas have some advantages over numerical solutions, (Pizette et al, 2010;Bayle et al, 2016;Seong et al, 2020) for example, when choosing rational ranges for changing the main parameters of the compaction process or when evaluating their optimal values (Kapranova et al, 2001;Kapranova et al, 2006a;Kapranova et al, 2006b). The importance of understanding the mechanism of the behavior of compacted materials is obvious for any type of modeling methods: analytical (Kapranova and Zaitzev, 2011;Kapranova et al, 2015;Udalov et al, 2019) or numerical (Khoei, 2005;Pizette et al, 2010;Bayle et al, 2016;Seong et al, 2020).…”