Predicting Fluidization and Expansion of Filter Media

Blood, lead and spheres: A hindered settling equation for sedimentologists based on metadata analysis

“…Richardson and Zaki (1954a), Fouda and Capes (1977), Chong et al (1979), Chianese et al (1992) and Baldock et al (2004) showed convincingly that the m ‐values in Equation are lower for spherical particles than for non‐spherical particles, because the particle density, and therefore the settling velocity, is reduced by the capture of stagnant fluid in the angularities of the non‐spherical particles (Steinour, 1944b; Whitmore, 1956). Correction factors for particle shape were proposed by Steinour (1944b), Richardson and Zaki (1954a), Fouda and Capes (1977), Cleasby and Fan (1981) and Dharmarajah and Cleasby (1986), but these require laborious measurements of sphericity and angularity of individual particles. Di Felice (1995) found that the shape correction factor of Steinour (1944b) nearly always predicts an increase in particle volume by 20%–30%, which is equivalent to a 2.7%–3.1% increase in the diameter of spherical particles.…”

“…The settling velocity of individual non‐cohesive particles depends on the particle diameter, the particle density, the liquid density and the viscosity of the fluid. However, it is widely known that the settling velocity also depends on the particle shape and shape distribution (Baldock et al, 2004; Beňa et al, 1963; Camenen, 2007; Chianese et al, 1992; Chong et al, 1979; Cleasby & Fan, 1981; Di Felice, 1995; Dietrich, 1982; Ferguson & Church, 2004; Fouda & Capes, 1977; Komar & Reimers, 1978; Maude & Whitmore, 1958; Richardson & Zaki, 1954a; Steinour, 1944b), the presence of adjacent particles (Carey, 1987; Pal & Ghoshal, 2013; Richardson & Zaki, 1954a, 1954b) and the particle size distribution (Di Felice, 1995; Hoffman et al, 1960; Lockett & Al‐Habbooby, 1974; Maude & Whitmore, 1958; Mirza & Richardson, 1979; Richardson & Meikle, 1961; Scott & Mandersloot, 1979; Wilson, 1953).…”

Terminal fall velocity: the legacy of Stokes from the perspective of fluvial hydraulics

“…In fact, the hindered settling exponent ϑ has been found to be dependent on the particle Reynolds number R [67]. The ϑ(R) relationship obtained by Richardson & Zaki [67] was approximated as follows [72]: In figure 7b, the experimental data of the hindered settling exponent ϑ are plotted as a function of particle Reynolds number R [68][69][70][71]74,75]. In addition, the ϑ(R) relationships proposed by Richardson & Zaki [67] and Garside & Al-Dibouni [73] are shown.…”

Characterization of Granular Materials with Internal Pores for Hydraulic Calculations Involving Fixed and Fluidized Beds

“…For such materials, a representative equivalent diameter value is commonly determined by counting and weighing a large number (N) of particles. 1,4,5 If m p is the total mass of N particles, then the average volume of a single particle is given by (m p /ρ p )/N, and the diameter d eq of the equivalent volume sphere is calculated as follows:…”

“…26 In contrast, very few general correlations applicable to nonspherical particles are available. 4,6,9,11,27,28 A large number of measurements were carried out by Akgiray and Soyer 26 and Soyer and Akgiray 1 using several sieved fractions of crushed glass, silica sand, garnet sand, perlite, and several different sizes of plastic and glass balls to develop the following general equation applicable to both spherical and nonspherical media:…”