Stokes centrifugal sedimentation

Stokes diameter by centrifugal sedimentation from various sources. 

Continuou.s Centrifugal Sedimentation Theory The Stokes settling velocity of a spherical particle under centrifugal field is given... 

Centrifugal Sedimentation Methods These methods extend sedimentation methods into the submicron size range. Sizes are calculated from a modified version of Stokes equation ... 

Sedimentation. The sedimentation method, described previously 5), is based on the relative sedimentation rates of swollen and unswollen latex particles. Starting with the Stokes expression for centrifugal sedimentation, an equation can be developed for the ratio of the sedimentation coefficient of a particle, S, to the sedimentation coefficient, S, of the same particle having a surface layer ... 

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). 

For (ncremenial, homogeneous, centrifugal sedimentation, the siiuation is considerably more complex. In general, the solution absorbance is monitored as a function of lime. The Stokes diameter is again inversely proporiional to the square root of the measurement lime. A radial dilution correction should be applied, The measured absorbance changes with time are then related matliemaiically to ihe particle size distribution. 

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. 

A useful method for determining relative aggregate sizes and distributions is by centrifugal sedimentation. For a sphere, the diameter can be derived from the sedimentation rates in the gravitational field according to Stokes equation. For the nonspherical particles such as carbon black aggregates, an equvalent Stokes... 

The so-caUed Sigma concept has been widely used in the field of centrifugal sedimentation ever since its first development by Ambler in 1952. It is a simplified relation between the machine performance in terms of X50, total volumetric flow rate Q and an index of the centrifuge size E. The cut size X50 is represented by its terminal settling velocity Vg in the given liquid under gravity so that from Stokes law (using equation 7.5b for the definition of K)... 

Gravitational settlement is allowed to proceed for 4 to 10 minutes, according to the particle-size range of the sample. The sedimentation tube is then centrifuged to reduce the time required for the smaller particles to reach the bottom. By measuring the volume of particles accumulated as a function of time, the equivalent spherical size distribution of the sample may be computed from formulae based upon Stokes law. In addition to the specially designed sedi-... 

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. 

The sedimentation of isometric particles, such as cubes and octa-hedra, deviates only slightly from the Stokes equation. Significantly anisometric particles that can be approximated by ellipsoids of revolution are amenable to rigorous sizing by centrifugation if the axial ratios q are known. If the major semi-axis is a and the minor semi-axis is c, the sedimentation velocity dx/dt can be written as... 

By accelerating deposition with a slowly rotating ultracentrifuge, Stokes law [Eq. (4.1)] is modified in uniform circular motion to an equilibrium distribution along the axis of rotation (0 to x), as a function of solute mass (mt). At higher centrifugal velocities, sedimentation succeeds the equilibrium distribution. Sedimentation equilibrium and sedimentation velocity provide a means to determine M. 

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