Stokes* formula

This is the Stokes formula, which permits us to find the elevation of the geoid at point p. Imagine that the z-axis of the spherical system of coordinates goes through the point p. Then for this point the angle lA plays the role of the azimuth 9 and... 

Figure 9b shows the friction constant as a function of a. For large a the friction coefficient varies linearly with ct in accord with the prediction of the Stokes formula. The figure also shows a plot of (slip boundary conditions) versus ct. It lies close to the simulation value for large ct but overestimates the friction for small ct. For small ct, microscopic contributions dominate the friction coefficient as can be seen in the plot of (m. The approximate expression 1 = + 071 interpolates between the two limiting forms. Cluster friction... 

If we know the friction coefficients a, we thus have an explicit formula for the conductivity coefficient. In particular, it is often assumed that a is determined by the well-known Stokes formula ... 

In the case of an immobile macromolecule in solution it is possible to estimate a value of the frictional force (F) developed between the solvent and polymer molecules by assuming the macromolecule to consist of a number (n) of solid spherical entities and applying the Stokes formula in a modified form (Eq. 5.8). 

Two growth mechanisms, becoming operative after the early stage, will be mentioned here. When the growth mechanism in later stages is governed by hydrodynamic interactions and the Stokes formula D kT/Lr for the diffusion coefficient may be applied then it follows that... 

Stokes formula for e Stokes-Einstein equation - Einsteins general... 

The definition of the coefficient of friction leads to a general form of Stokes formula, which enables us to use our expressions for the Frame area and the characteristic length instead of using the expression for spheres. 

Scheme 2. Since it is not easy to modify the evaluation software in commercially available PCS measuring instruments, one can always select the hydrodynamic or Stokes radius (equivalent spherical radius) rather than using the roundabout approach. It is possible to eliminate several parameters by setting both terms, Stokes formula and its new version, equal.

For small core radius (e -> 0), this formula tends to the Hadamard-Rybczynski formula (2.2.15) for a drop if the membrane is thin (e - 1), then we obtain the Stokes formula (2.2.5) for a solid sphere. 

Let us consider the term of the translation diffusion. The diffusion coefficient D expresses the abihty of a molecule to change its position in solution due to chaotic translation motion. Basic evaluation of the diffusion coefficient can be obtained from the Stokes formula for a sphere in a fluid ... 

The proportionality constant D is called the diffusion coefficient and quantifies the chaotic translation motion of the molecules in solution. Its basic evaluation is given by the Stokes formula (Eq. 33). The diffusion coefficient decreases as the size of the molecule increases. For typical biomolecules in aqueous medium, D is usually between 10 cm s and 10 cm s Temperature dependence of the diffusion coefficient follows T/rj, where T is absolute temperature and t] viscosity of the solvent, unless the temperature change does not alter the molecular shape. 

Any mobility of the surface decreases the velocity difference and the viscous stresses. The result is that the hydrodynamic resistance becomes smaller and the floating velocity of a bubble according to (8.6) increases by a factor of 3/2 as compared to Stokes Eq. (8.5). In early experiments, under the condition of Re < 1, it was found (Lebedev 1916) that small bubbles of a diameters less than 0.01 cm behave like rigid spheres since their velocity is described by Stokes formula (8.5). At the same time. Bond (1927) has found that drops of a sufficiently large size fall at velocities described by Eq. (8.6). To overcome contradictions with the Hadamard-Rybczynski theory, Boussinesq (1913) considered the hypothetical influence of the surfaee viscosity and derived the following relation. 

This relation coincides with the boundary condition for a viscous flow around solid spheres. In this approximation the velocity distribution at Re l is expressed by Stokes formula. From Stokes velocity distribution v(z,0) it is easy to calculate the viscous stresses acting on the surface of the sphere and the equilibrating surface tension gradient... 

In order to define this accessibility curve clearly it is necessary to use a number of solute molecules which range in size over the whole range of pore sizes anticipated in the swollen structure. We have found the most suitable solutes to be the dextrans marketed by Pharmacia (Uppsala) Ltd. supplemented by a few low molecular weight sugars. Grotte (7) has reviewed evidence to show that these dextrans behave in solution as hydro-dynamic spheres, and that the diameters of these molecules in solution may be calculated from their diffusion coefficients according to the Einstein-Stokes formula ... 

Stokes formula for a Stokes-Einstein equation - Einsteins general laminar flow of spheres the basis of dynamic light formula for difFusion scattering particle sisdng... 

Investigations of the perturbation equations for the rotating sphere have been carried out more or less independently by a number of individuals. The first of these appears to be due to Bickley (B5), who obtained a solution correct to the first order in R. His solution indicates an inflow of fluid towards the poles and a corresponding outflow around the equator. Rather interestingly, to this order in R the torque itself is unaffected and continues to be given by the Stokes formula... 

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