Theory of batchwise centrifugal filtration

Abstract

In centrifugal filtration, centrifugal forces serve as the driving force in the production of cakes. Centrifugal sedimentation leads to formation of a clear supernatant followed by a slurry and a cake that grows and compacts simultaneously. The slurry concentration is independent of radius but decreases everywhere within the suspension at the same rate with respect to time. The theoretical analysis of centrifugal filtration presented here takes cake compressibility and variable permeability into account. Experiments were carried out under low driving forces with a centrifuge having a diameter of 150 rnrn and speeds of 1,000-2,000 RPM. With centrifugal accelerations of 75-300 g and pressure differentials under 1 atm, the sedimentation process was relatively slow and could be observed experimentally with ease.Masao Sambuichi, Hideo Nakakura, Kunihisa OsasaYarnaguchi University Ube, Japan 755 F.M. TillerUniversity of Houston Houston, TX 77004 Centrifugal Filtration and SedimentationCentrifugal sedimentation and centrifugal filtration are carried out in solid-bowl, Figure 1, and perforated-bowl, Figure 2, centrifuges. In batch centrifugal sedimentation, three interfaces are produced. The first involves gas and liquid, the second supernatant clear liquid and the slurry surface, while the third appears as the interface between slurry and cake. As the solids sediment out of the slurry, they form a network of interconnected particles capable of sustaining compressive and shear forces. In the suspension, particles are not in contact and cannot transmit internal forces from one to another. Once a structure is formed in the cake zone, it undergoes a compression process in which liquid is squeezed out of the sediment until the structure is sufficiently consolidated to carry the forces produced by the centrifuge.The thickness of the sediment for centrifugal sedimentation is less than for a gravitational process because the increased acceleration produces larger compressive forces. In centrifugal filtration, liquid passes through the cake and the supporting medium, which may be paper, cloth, metal screen, or any porous material. In contrast to centrifugal sedimentation, a density difference between liquid and solid is not necessary for operation.In Figure 3a gravity and centrifugal sedimentation are compared. In gravity sedimentation, the upper interface initially falls at a constant rate along H A . Simultaneously, sediment forms at the bottom of the container and the settling velocity decreases. The slurry begins to concentrate at successively greater distances from the bottom, and ultimately when the upper interface reaches A it begins to fall at a slower pace. At B the rising sediment meets the upper interface and the slurry disappears, leaving all of the solids in the sediment or cake. Further consolidation results from disruption of the particulate structure in a squeezing process. The velocity and flux of particles is generally assumed to be a unique function of concentration up to point B, or point B' in centrifugal...

Theory of batchwise centrifugal casting

“…18 will be zero and Eq. 18 simplifies to (Fujita, 1962;Bowen and Rowe, 1970;Sambuichi et al, 1987;Probstein, 1989):…”

“…9 and 16 into Eq. 17 results in the following differential equation: Sambuichi et al (1987) showed that when the initial concentration & is uniform, 4 remains independent of r for the suspension phase. Thus the second term on the righthand side of Eq.…”

“…Because of particle stabilization in suspension, a dense and noncompressible cast develops (Lange and Miller, 1987). Therefore it is not necessary to solve momentum balances over the cast as has been done by Sambuichi et al (1987Sambuichi et al ( , 1991 and Tiller and Hsyung (1993) to describe cast formation from a flocculated suspension.…”

Comparison of batchwise centrifugal and constant-pressure filtration.

“…A force balance over a differential element in centrifugal cake yields6'11} dPL ,dps tM uxps -+^-+(l -fc0)- (6) whereps is the solid compressive pressure and /?L is the hydraulic pressure at radius r in the cake, and where it is assumed that the lateral stress is proportional to the normal stress on the particles and that the momentum changes are negligible.…”

“…The basic flow equation can be written for a differential element at radius r as dpL= -prco2à"dr-jLi(xpp(\ -e)-ur'dr (7) by assuming the momentumchange of liquid to be negligible. In Eq.…”