Calculations differential sedimentation distribution

An analysis of the kinetic curves of the pigments samples sedimentation has been done in accordance with the method [5]. Calculated differential curves of particles aggregates distribution per sizes in water and butyl acetate are represented on Fig. 4. 

For molecules of similar shape, this approach may be further refined by correcting for diffusional spreading. A differential sedimentation coefficient distribution that incorporates a relationship between s and D, termed c(s), is generated by a complex calculation. Exceptional sensitivity can be obtained in this manner. 

Another separation technique of particular application for proteins, high-molar-mass molecules, and particles is the general class known as field-flow fractionation (FFF) in its various forms (cross-flow, sedimentation, thermal, and electrical). Once again, MALS detection permits mass and size determinations in an absolute sense without calibration. For homogeneous particles of relatively simple structure, a concentration detector is not required to calculate size and differential size and mass fraction distributions. Capillary hydrodynamic fractionation (CHDF) is another particle separation technique that may be used successfully with MALS detection. 

Collision efficiency was calculated by the method proposed for the first time by Dukhin Derjaguin (1958). To calculate the integral in Eq. (10.25) it is necessary to know the distribution of the radial velocity of particles whose centre are located at a distance equal to their radius from the bubble surface. The latter is presented as superposition of the rate of particle sedimentation on a bubble surface and radial components of liquid velocity calculated for the position of particle centres. Such an approximation is possibly true for moderate Reynolds numbers until the boundary hydrodynamic layer arises. At a particle size commensurable with the hydrodynamic layer thickness, the differential of the radial liquid velocity at a distance equal to the particle diameter is a double liquid velocity which corresponds to the position of the particle centre. Such a situation radically differs from the situation at Reynolds numbers of the order of unity and less when the velocity in the hydrodynamic field of a bubble varies at a distance of the order ab ap. At a distance of the order of the particle diameter it varies by less than about 10%. Just for such conditions the identification of particle velocity and liquid local velocity was proposed and seems to be sufficiently exact. In situations of commensurability of the size of particle and hydrodynamic boundary layer thickness at strongly retarded surface such identification leads to an error and nothing is known about its magnitude. 

As in Section 11.1, we consider the reflection of a particle from a flat boundary at normal sedimentation. This assumption can be used for a bubble when we are interested in impacts close to the pole, at < ,. Thus, we can simplify the expression for the normal flow of liquid setting cosine to unity and assuming that over whole section of the surface at < j the length of recoil is characterized by a constant value. In dimensionless form, the equation for calculating the inertia path change due to the opposite motion of the liquid which has a velocity distribution expressed by a linear relationship (differs from a linear second-order differential equation with constant coefficients only due to a variation of Reynolds number for a retarded particle). It reads... 

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