Centrifugal Sedimentation 5 Diffusion

Collection of particles is based on filtration, gravitational and centrifugal sedimentation, inertial impaction and impingement, diffusion, interception, or electrostatic or thermal precipitation (e.g., see Spurny, 1986, Chapter 3). The choice of method depends on a number of parameters such as the composition and size of the particles, the purpose of the sample, and acceptable sampling rates. Table 11.10 summarizes some of the commonly used methods and the size ranges over which they are effective. 

It is our objective in this chapter to outline the basic concepts that are behind sedimentation and diffusion. As we see in this chapter, gravitational and centrifugal sedimentation are frequently used for particle-size analysis as well as for obtaining measures of solvation and shapes of particles. Diffusion plays a much more prevalent role in numerous aspects of colloid science and is also used in particle-size analysis, as we see in Chapter 5 when we discuss dynamic light scattering. The equilibrium between centrifugation and diffusion is particularly important in analytical and preparative ultracentrifuges. 

Field flow fractionation (FFF) can also be used for microbial cell separation. In the FFF technique, a field (may be gravitational, centrifugal, thermal-gradient, electrical, magnetic, etc.) is applied perpendicular to the fluid flow, causing particles to migrate with different velocities. Fields of sedimentation, diffusion, and electrical diffusion are manipulated to optimize the separations of microbes. Separation of Pseudomonas putida and E. coli has been achieved by hyperlayer FFF. Fractions of the whole cells were collected after the separation at different time intervals, dif-... 

Thermodynamic data from the ultracentrifuge experiment ean be obtained either from flie sedimentation velocity (sedimentation coefficient) or from the sedimentation-diffusion equilibrium since the centrifugal forces are balanced by the activity gradient. The determination of sedimentation and diffusion coefficients yields the virial coefficients by ... 

If a sedimentation experiment is carried out long enough, a state of equilibrium is eventually reached between sedimentation and diffusion. Under these conditions material will pass through a cross section perpendicular to the radius in both directions at equal rates downward owing to the centrifugal field, and upward owing to the concentration gradient. It is easy to write expressions for the two fluxes which describe this situation ... 

The specific polysaccharide of the dominant O somatic antigen of Shigella dysenteriae has been shown to be electrophoretically and ultra-centrifugally homogeneous, and to possess a molecular weight of 26,000 from sedimentation and diffusion measurements.2601... 

In sedimentation velocity experiments, a dilute solution in high centrifugal field gets separated into a clear pure solvent layer and a solution. The initial clear boundary between the two then spreads because of diffusion. The rate of movement of boundary can be measured by suitable methods. Sedimentation constants is given by... 

Finally, we consider the behavior of a solute in a solution in the cell subjected to the centrifugal field. At a suitable angular velocity, the tendency of the solute to sediment toward the bottom of the cell is countered by its tendency to diffuse backward toward the meniscus, because the concentration increases with increasing r, as indicated in Figure 2. 2 b). At some time, a sedimentation equilibrium is attained. A typical equilibrium concentration distribution is depicted in Figure 2. 2 b). Our aim is to find a quantitative analytical expression for this curve. 

The sedimentation velocity determination is dynamic and can be completed in a short period of time. The sedimentation equilibrium method gives quantitative results, but long periods of time are required for centrifugation at relatively low velocities to establish equilibrium between sedimentation and diffusion. 

In a centrifugal field, dissolved molecules or suspended particles either sediment (if their density exceeds that of the pure solvent), or flotate for the opposite case (negative or inverse sedimentation). Under otherwise identical experimental conditions, the velocity of the molecules or particles depends on the viscosity of the solution or suspension and - very importantly - on the mass and shape of the dissolved species. Sedimentation and flotation are antagonized by the diffusion. Depending on the rotor speed and the molar mass of the dissolved/dis-... 

D=mass diffumsion coefficient Z)T=fiiermal diffusion coefficient /=friction coefficient G=(oh (centrifugal acceleration) / =Boltzniann constant meff=particle effective mass r=radius of centrifuge basket s=sedimentation coefficient T = absolute temperature =geometric volume of die channel w=channel thickness y=diermal expansion coefficient p=electrophoretic... 

The equilibrium between gravitational or centrifugal force and diffusion is routinely taken advantage of in colloid science, as illustrated in Vignette II. Our objective in this chapter is to examine the effects of sedimentation and diffusion, first taken separately and then combined, on particles in the colloidal size range. 

Equations (33) and (34) show that diffusion studies combined with sedimentation studies, either under the force of gravity or in a centrifuge, yield information about particle masses with no assumptions about the shape of the particle. 

We have already noted that sedimentation and diffusion are opposing processes, the first tending to collect and the second to scatter. Let us now consider the circumstances under which these two tendencies equal each other. Once this condition is reached, of course, there will be no further macroscopic changes the system is at equilibrium. In order to formulate this problem, consider the unit cross section shown in Figure 2.15, in which the x direction is in the direction of either a gravitational or a centrifugal field. Suppose this field tends to pull... 

Colloids (casein micelles) of two different particle sizes are isolated from skim milk by centrifugation under different conditions. The sedimentation and diffusion coefficients of the two preparations are as follows ... 

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