Sedimenting sphere

Sedimenting spheres. What is the dependence of the sedimentation coefficient S of a spherical protein on its mass How much more rapidly does an 80-kd protein sediment than does a 40-kd protein ... 

Ladd, A. C. J. 1993 Dynamical simulations of sedimenting spheres. Physics of Eluids A 5, 299-310. 

Physicochemical reactions within the sea-sediment sphere tend to reach equilibrium. Those reactions that are so rapid that they occur prior to burial in the bottom sediments are referred to as "halmyrolysis" (e.g. formation of clay aggregates), while those that take place in the upper part of the sediment are termed "early diagenesis". The diagenetic processes include cementation, compaction, diffusion, redox reactions, transformation of organic and inorganic material, and ion exchange phenomena. A short... 

Piazza R, Bellini T and Degiorgio V 1993 Equilibrium sedimentation profiles of screened charged colloids a test of the hard-sphere equation of state Rhys. Rev. Lett. 71 4267-70... 

We shall see in Sec. 9.10 that sedimentation and diffusion data yield experimental friction factors which may also be described-by the ratio of the experimental f to fQ, the friction factor of a sphere of the same mass-as contours in solvation-ellipticity plots. The two different kinds of contours differ in detailed shape, as illustrated in Fig. 9.4b, so the location at which they cross provides the desired characterization. For the hypothetical system shown in Fig. 9.4b, the axial ratio is about 2.5 and the protein is hydrated to the extent of about 1.0 g water (g polymer)". ... 

The particle can be assumed to be spherical, in which case M/N can be replaced by (4/3)ttR P2, and f by 671770R- In this case the radius can be evaluated from the sedimentation coefficient s = 2R (p2 - p)/9t7o. Then, working in reverse, we can evaluate M and f from R. These quantities are called, respectively, the mass, friction factor, and radius of an equivalent sphere, a hypothetical spherical particle which settles at the same rate as the actual molecule. 

Particle Shape. Whereas the Stokes particle is assumed to be a sphere, very few real soHds are actually spherical. Flat and elongated particles sediment slower than spheres. For maximum sedimentation rate, the particle should be as spherical as possible. 

The particle size deterrnined by sedimentation techniques is an equivalent spherical diameter, also known as the equivalent settling diameter, defined as the diameter of a sphere of the same density as the irregularly shaped particle that exhibits an identical free-fall velocity. Thus it is an appropriate diameter upon which to base particle behavior in other fluid-flow situations. Variations in the particle size distribution can occur for nonspherical particles (43,44). The upper size limit for sedimentation methods is estabHshed by the value of the particle Reynolds number, given by equation 11 ... 

Hindered Settling When particle concentration increases, particle settling velocities decrease oecause of hydrodynamic interaction between particles and the upward motion of displaced liquid. The suspension viscosity increases. Hindered setthng is normally encountered in sedimentation and transport of concentrated slurries. Below 0.1 percent volumetric particle concentration, there is less than a 1 percent reduction in settling velocity. Several expressions have been given to estimate the effect of particle volume fraction on settling velocity. Maude and Whitmore Br. J. Appl. Fhys., 9, 477—482 [1958]) give, for uniformly sized spheres,... 

Stokes diameter is defined as the diameter of a sphere having the same density and the same velocity as the particle in a fluid of the same density and viscosity settling under laminar flow conditions. Correction for deviation from Stokes law may be necessary at the large end of the size range. Sedimentation methods are limited to sizes above a [Lm due to the onset of thermal diffusion (Brownian motion) at smaller sizes. 

Therefore, the inertia forces have an insignificant influence on the sedimentation process in this regime. Theoretically, their influence is equal to zero. In contrast, the forces of viscous friction are at a maximum. Evaluating the coefficient B in equation 55 for a = 1 results in a value of 24. Hence, we have derived the expression for the drag coefficient of a sphere, = 24/Re. 

Free-falling diameter Also known as sedimentation or Stokes diameter, the diameter of a sphere with the same terminal settling velocity and density as a nonspherical or irregular particle. 

Khan, A.R and Richardson, J.F., 1990. Pressure gradient and friction factor for sedimentation and fluidisation of uniform spheres in liquids. Chemical Engineering Science, 45, 255-265. 

The sedimentation coefficient provides a useful indicator of polysaccharide conformation and flexibility in solution, particiflarly if the dependence of on Mw is known [62]. There are two levels of approach (i) a general level in which we are delineating between overall conformation types (coil, rod, sphere) (ii) a more detailed representation where we are trying to specify particle aspect ratios in the case of rigid structures or persistence lengths for linear, flexible structures. 

The simplest indicator of conformation comes not from but the sedimentation concentration dependence coefficient, ks. Wales and Van Holde [106] were the first to show that the ratio of fcs to the intrinsic viscosity, [/ ] was a measure of particle conformation. It was shown empirically by Creeth and Knight [107] that this has a value of 1.6 for compact spheres and non-draining coils, and adopted lower values for more extended structures. Rowe [36,37] subsequently provided a derivation for rigid particles, a derivation later supported by Lavrenko and coworkers [10]. The Rowe theory assumed there were no free-draining effects and also that the solvent had suf-... 

Hermans, JJ, Sedimentation and Electrophoresis of Porous Spheres, Journal of Polymer Science 18, 527, 1955. 

This is Stokes Law for sedimentation where we have added a, a shape factor, just in case we do not have spherical particles. For spheres, a = 1. It is fractioncd otherwise. 

The size of a spherical particle is readily expressed in terms of its diameter. With asymmetrical particles, an equivalent spherical diameter is used to relate the size of the particle to the diameter of a perfect sphere having the same surface area (surface diameter, ds), the same volume (volume diameter, dv), or the same observed area in its most stable plane (projected diameter, dp) [46], The size may also be expressed using the Stokes diameter, dst, which describes an equivalent sphere undergoing sedimentation at the same rate as the sample particle. Obviously, the type of diameter reflects the method and equipment employed in determining the particle size. Since any collection of particles is usually polydisperse (as opposed to a monodisperse sample in which particles are fairly uniform in size), it is necessary to know not only the mean size of the particles, but also the particle size distribution. 

Jefri, M.A., Nichols, K.L., and Jayaraman, K. "Sedimentation of Two Contacting Spheres in Dilute Polymer Solutions," Proc. Svmp. Recent Dev. Struct. Continua.. 1985, 21-5. 

To determine the settling characteristics of a sediment, you drop a sample of the material into a column of water. You measure the time it takes for the solids to fall a distance of 2 ft and find that it ranges from 1 to 20 s. If the solid SG = 2.5, what is the range of particle sizes in the sediment, in terms of the diameters of equivalent spheres ... 

Eljarrat E, Labandeira A, Marsh G, Raldua D, Barcelo D (2007) Decabrominated diphenyl ether in river fish and sediment samples collected downstream an industrial park. Chemo-sphere 69 1278-1286... 

Data from Bush, B., L.A. Shane, and M. Wahlen. 1987. Sedimentation of 74 PCB congeners in the upper Hudson River. Chemo-sphere 16 733-744. 

Da (Dl IDA)m is the Stokes diameter, equal to the diameter of sphere, which in a laminar region (low Reynolds number Re < 0.2), sediments with the same velocity as the considered particle. 

Surface spectroscopic techniques must be separated carefully into those which require dehydration for sample presentation and those which do not. Among the former are electron microscopy and microprobe analysis, X-ray photoelectron spectroscopy, and infrared spectroscopy. These methods have been applied fruitfully to show the existence of either inner-sphere surface complexes or surface precipitates on minerals found in soils and sediments (13b,30,31-37), but the applicability of the results to natural systems is not without some ambiguity because of the dessication pretreatment involved. If independent experimental evidence for inner-sphere complexation or surface precipitation exists, these methods provide a powerful means of corroboration. 

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