Radius, sedimentation

From solubilized membrane proteins you can— without major equipment—determine MW, Stokes radius, sedimentation coefficient, proportion of bound detergent and phospholipid, isoelectric point, and the apparent frictional coefficient. Knowledge of Stokes radius, MW, and isoelectric point comes in handy during planning of a purification or drafting of a detection assay (the other measures are good for the library). 

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

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. 

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 ... 

Equivalent spherical radius Approximate size Sedimentation rate (time to settle 30 cm)... 

There are two essential consequences of this relation. Because larger droplets sediment or rise much faster (a 5-p.m drop rises 625 times faster than a 0.2-p.m droplet), the process is equal to shearing, leading to enhanced flocculation. The ratio between flocculation due to shear and to diffusion of droplets is proportional to the cube of the radius. Secondly, flocculation to droplet aggregates means an enhanced sedimentation rate. Sis drops ia an octahedral arrangement gives approximately four times the sedimentation rate. 

Consider the simple initial condition t = 0 where the sohd concentration (t),o is constant across the entire shiny domain ix < r < rb where / l and l b are, respectively, the radii of the shiny surface and the bowl. At a later time t > 0, three layers coexist the top clarified layer, a middle shiny layer, and a bottom sediment layer. The air-liquid interface remains stationaiy at radius / l, while the hqiiid-slurry interface with radius i expands radiaUy outward, with t with i given by ... 

The settling capacity for a given size of particles is a function of R, C and u, which itself is proportional to R. In general, for the sedimentation of heavy particles in a suspension it is sufficient that the radial component of Uf be less than at a radius greater than Rj. 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

TTiere are several particle sizing methods, all based upon sedimentation and Stokes Law. If a particle is suspended in a fluid (which may be gas, or any liquid), the force of resistance to movement by the particle will be proportional to the particle s velocity, v, and its radius, r, vis-... 

Increasing the radius of the suspended particles, Brownian motion becomes less important and sedimentation becomes more dominant. These larger particles therefore settle gradually under gravitational forces. The basic equation describing the sedimentation of spherical, monodisperse particles in a suspension is Stokes law. It states that the velocity of sedimentation, v, can be calculated as follows ... 

Sedimentation of particles follows the principle outlined above [Eq. (1)] in which particles in the Stokes regime of flow have attained terminal settling velocity. In the airways this phenomenon occurs under the influence of gravity. The angle of inclination, t /, of the tube of radius R, on which particles might impact, must be considered in any theoretical assessment of sedimentation [14,19]. Landahl s expression for the probability, S, of deposition by sedimentation took the form ... 

At radius r, the centrifugal sedimentation velocity of a particle, whose diameter is d is given by ... 

A third approach was developed by Aller (1980a, b) who studied solute fluxes in near-shore marine sediments showing seasonal variation. In this approach, the geometry of the burrow-sediment system is allowed for explicitly and transport in the sediment between the burrows is described with appropriate diffusion equations. It is assumed that the burrows are oriented normal to the sediment surface and distributed uniformly or randomly in the horizontal plane (Figure 2.11). Thereby a cylindrical zone of influence is ascribed to each burrow with a radius... 

Theory. The velocity (v) of particle sedimentation during centrifugation depends on the angular velocity co of the rotor, its effective radius (teff, the distance from the axis of rotation), and the particle s sedimentation properties. These properties are expressed as the sedimentation coef cient S (1 Svedberg, = 10 s). The sedimentation coef cient depends on the mass M of the particle, its shape (expressed as the coef cient of friction, f), and its density (expressed as the reciprocal density v, partial specific volume ). 

Wheeler [16] proposed that the mean radius, r, and length, L, of pores in a catalyst pellet (of, for that matter, a porous solid reactant) are determined in such a way that the sum of the surface areas of all the pores constituting the honeycomb of pores is equal to the BET (Brunauer, Emmett and Teller [17]) surface area and that the sum of the pore volume is equed to the experimental pore volume. If represents the external surface area of the porous particle (e.g. as determined for cracking catalysts be sedimentation [18]) and there are n pores per unit external area, the pore volume contained by nSx cylindrically shaped pores is nSx nr L. The total extent of the experimentally measured pore volume will be equal to the product of the pellet volume, Vp, the pellet density, Pp, and the specific pore volume, v. Equating the experimental pore volume to the pore volume of the model... 

Minerals were ground such that a size distribution ranging from sub-micron to millimetre particles were obtained. For the experiments described here, it is desirable to use monodisperse minerals. To this end, a sedimentation technique was used to obtain minerals in the particle size range (effective Stokes radius) (i) 10-20 jam and (ii) above 20 um. 

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