Velocity sedimentation data

EXAMPLE 2.1 Analyzing Cumulative Sedimentation Data for Most Probable Settling Velocity. The following data show—as a function of time—the weight (as percentage of total) of suspended clay particles W, which has accumulated on a plate submerged 20 cm beneath the surface in a sedimentation experiment (Oden 1915). 

Most probable settling velocity from sedimentation data Particle-size determination from sedimentation equation Sedimentation in an ultracentrifuge Solvation and ellipticity from sedimentation data Diffusion and Gaussian distribution Temperature-dependence of diffusion coefficients... 

Diffusion coefficients can be related to molecular weight in three ways first by application of the Stokes-Einstein equation, second by combination with sedimentation data, and third by consideration of homologous polymer solutions. In the first method, an equivalent spherical size of the molecules is calculated from Dt, and an approximate molecular weight is found by combining these data with the appropriate density. In the second method, diffusion measurements are coupled with those of sedimentation velocity to give molecular weights, and in the third method, molecular weights may be determined directly from measurements of diffusion coefficients alone once a calibration has been... 

Velocity sedimentation experiments on both proteins at several concentrations were performed at 55,000 rpm in the same buffer at 20°C. The data were analyzed using the time derivative method of Stafford [8]. 

The elastic properties of hydrates are important to understanding the sonic and seismic velocity field data obtained from the natural hydrates-bearing sediments. Data on the mechanical properties of CO2 hydrates are hmited. Table 10.3 shows the elastic properties of ice, CH4 hydrates, and CO2 hydrates. It should be noted that these properties may vary for different guests and occupancies. For example, Kiefte et al. [21] measured the compressional velocity of methane, propane, and hydrogen sulfide hydrates as 3.3, 3.7, and 3.35 km/s, respectively. 

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 ... 

Determine the settling velocity of a particle (d = 4 x 10" m and Pp = 900 kg/m ) through water in a sedimentation centrifuge operating at 4,000 rpm. The particle velocity is a function of distance from the axis of rotation, as shown by the following data ... 

One can see the M procedure has a parallel to either g (s) vs. s or c(s) vs. s in sedimentation velocity where the data are transformed from radial displacement space [concentration, c(r) versus r] to sedimentation coefficient space [g s) or c(s) versus s]. Here we are transforming the data from concentration space [concentration relative to the meniscus j(r) versus r] to molecular weight space [M r) versus r]. 

Environmental Fate. It can be concluded from the transport characteristics that surface water sediment will be the repository for atmospheric and aquatic thorium. Normally, thorium compounds will not transport long distances in soil. They will persist in sediment and soil. There is a lack of data on the fate and transport of thorium and its compounds in air. Data regarding measured particulate size and deposition velocity (that determines gravitational settling rates), and knowledge of the chemical forms and the lifetime of the particles in air would be useful. 

Criticize or defend the following proposition The data give the time required for particles to fall 20 cm, making it easy to convert time to sedimentation velocity for each point. Equation (11) may then be used to convert the velocity into the radius of an equivalent sphere. The resulting graph of W versus radius is a cumulative distribution function similar to that shown in Figure 1.18b. 

The molecular weight of the calf duodenal adenosine aminohydrolase determined from sedimentation and diffusion data (91) and by comparative elution from Sephadex gels (93, 94) ranges from 31,000-35,000 (84,91, 93, 95). A molecular weight of 52,000 from sedimentation velocity and sedimentation equilibrium data has not been confirmed (93). 

Indirect methods for obtaining information on the kinetics of the associa-tion/dissociation equilibrium include sedimentation velocity and GPC experiments. The application of these techniques is based on comparison of sedimentation or GPC elution curves with model curves based on theories for separation of unimers and micelles during a sedimentation velocity (Gilbert 1955) or GPC (Ackers and Thompson 1965 Coll 1971 Prochazka et at. 1988, 1989) experiment. Experiments have been performed that demonstrate several of the qualitative model predictions (Prochazka et at. 1989). The main conclusions were that GPC curves with two well-separated peaks can only result from a slow dynamic molecule micelle equilibrium, and that no simple interpretation of elution curves in terms of relative concentrations of unimer and micelles is possible (Prochazka et at. 1989). Thus no quantitative information on the kinetics of the molecule micelle equilibrium can be obtained from sedimentation velocity or GPC data. 

It is evident from the above expressions that the appropriate diffusion coefficient must also be measured in order that molecular or particle masses may be determined from sedimentation velocity data. In this respect, a separate experiment is required, since the diffusion coefficient cannot be determined accurately in situ, because there is a certain self-sharpening of the peak due to the sedimentation coefficient increasing with decreasing concentration. 

As is well known, when the gravity and the drag force acting on the particle are numerically the same but in opposite directions, the relative velocity of the particle with respect to the gas flow will be kept constant such a relative velocity is called terminal velocity , denoted as u, = (u - p) and is numerically equal to the sedimentation velocity of the particle in a stationary gas. Setting dupldt = 0 and using Eqs. (2.33) to (2.35) and the data listed in Table 2.1, the terminal velocities for various flow regimes can be directly obtained from Eq. (2.32) as follows ... 

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