Stokes centrifugal separation

Trybus et al., 1982 Trybus and Lowey, 1984 Craig etal., 1983). Centrifugation separates the soluble folded monomer from filaments, whereas gel filtration can be used to separate folded from extended monomers because of their difference in Stokes radius (Trybus and Lowey, 1984, 1988). 

In centrifugal separation, g in Stokes equation is replaced by centrifugal force, 03 R, where co is the centrifugal speed in radianss" (27t radians = 360°) and R is the distance (cm) of the particle from the axis of rotation. 

Because centrifuges are normally used for separating fine particles and droplets, it is necessary to consider only the Stokes law region in calculating the drag between the particle and the liquid. 

A centrifuge is fitted with a conical disc stack with an included angle of 29, and there are n flow passages between the discs. A suspension enters at radius r and leaves at radius r2. Obtain an expression for the separating power E of the centrifuge. It may be assumed that the resistance force acting on the particles is given by Stokes law. 

An Improved disc centrifuge photosedimentometer (DCP) was developed for use in the determination of the particle size and size distribution of latices, pigments and other particulates. Separation is based on Stokes Law for the sedimentation of particles in a centrifugal force field and does not rely on the use of particle size calibrants or standards. The DCP Instrument provides accurate stable particle size analyses over a wide range of conditions while at the same time is rugged enough for heavy use in both a research and quality control environment. A stand-alone data collection, analysis and management system was developed both for routine quality control operation and for research use of the instrument. 

At a specific radial distance the moving particles interrupt and attenuate a light beam, the intensity of which is measured by a photodetector. The particle size is related to the appearance time at the photodetector by means of Stokes Law for centrifugation. The concentration of particles is obtained from the photodetector response and the application of Mie scattering theory.(1) A very Important step in this operation is the formation of a density gradient within the spin fluid to allow a hydrodynamically stable separation of the suspended particles. An accepted method for forming this spin fluid density gradient within the disc cavity is the widely used and patented (2) Joyce-Loebl Buffered Line Start... 

Sedimentation Techniques. Other techniques that effect a physical separation include gravitational or centrifugal sedimentation, in which particles or emulsion droplets are separated on the basis of size and density. The separation that occurs can be quantified by monitoring X-ray or light absorbance as a function of position. Stokes law then can be used to determine the particle size distribution from the absorbance data as a function of the sedimentation time (73, 74). 

The value of Sp depends on several parameters, including the hydrodynamic properties of the channels, the centrifugal force (Sp increases to reach a maximum with the centrifugal force), the mobile-phase flow rate (Sp decreases linearly with the mobile-phase flow rate), the physical properties of the solvent system (such as viscosity, density, interfacial tension), the sample volume, the sample concentration, and the tensioactive properties of solutes to separate [2,3]. It is necessary to precisely monitor Sp because various chromatographic parameters depend on it, in particular the efficiency, the retention factor, and the resolution. Foucault proposed an explanation for the variation of Sp with the various parameters previously described. He modeled the mobile phase in a channel as a droplet and applied the Stokes law which relies on the density difference between the two phases, the viscosity of the stationary phase, and the centrifugal force. Then, he applied the Bond number, derived from the capillary wavelength which was formerly introduced for the hydrodynamic mode [4] and which relies on the density difference between the two phases the interfacial tension and the centrifugal force [3]. 

In a sedimenting centrifuge, a continuous liquid phase moves through the rotor. To accomplish a useful separation, the discontinuous phase, either the insoluble solids or the immiscible liquid drops (or both), must move in a direction different from the flow of the continuous liquid. Stokes law is usually applied to describe this relationship. The effective force accelerating the particle in a centrifugal field is then given as ... 

The cells harvested and separated from the medium with a centrifuge were rinsed with distilled water. Then the cells were suspended in an appropriate amount of distilled water such that the turbidity at 530 millimicrons showed the value of 0.5 in this preparation. Without any addition of a dispersing agent the suspension was found well-dispersed. Cells used were nearly spherical, average diameter, dp=3.2 microns, while the density, determined by measuring the rate of interfacial subsidence of the cell suspension under gravity and by applying the Stokes law was 1-09 cm at 20° C. 

Consider the motion of a drop of radius R in a centrifugal branch pipe. Since large drops have already been separated from the gas in the settling section of the separator, only relatively small drops move in the branch pipe. Therefore, resistance forces acting on the drops obey Stokes s law, and gravity can be neglected. These assumptions enable us to write the equations of drop motion as... 

Theory for cyclone separators. It is assumed that particles on entering a cyclone quickly reach their terminal settling velocities. Particle sizes are usually so small that Stokes law is considered valid. For centrifugal motion, the terminal radial velocity v,n is given by Eq. (14.4-8), with v,] being used for v,. 

Gravity and centrifugal sedimentation can be combined for the same sample in order to directly determine Stokes diameter for a wide range of particle sizes. In such a way conversion are avoided and a mass distributions, applicable to processes where gravimetric efficiencies are relevant, can be properly derived. Ortega-Rivas and Svarovsky (1994) determined particle sizes distributions of fines powders using a combined Andreasen Pipette-pipette centrifuge method. They derive relations useful to model hydrocyclone separations, which were later employed to describe apple juice clarification. 

As was stated in the introduction, Stokes diameter jcst is usually used to characterize particle size in those applications where it is the behaviour of particles in liquids that determines the separation efficiency and other operational characteristics of the separators (e.g. in sedimentation, centrifugation and hydrocyclones). Methods that measure Stokes diameter, such as sedimentation or fluid classification, have therefore been used extensively in this field. Although preference is naturally given to wet methods, air classification is also widely used. 

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