Viscous drag coefficient

Dislocation motion in the clear region between obstacles is determined by the viscous drag coefficient B [2]. The relationship between the applied shear stress and dislocation velocity is... 

Intrinsic resistance to dislocation motion can be measured in either of two ways direct measurements of individual dislocation velocities (Vreeland and Jassby, 1973) or by measurements of internal friction (Granato, 1968). In both cases, for pure simple metals there is little or no static barrier to motion. As a result of viscosity there is dynamic resistance, but the viscous drag coefficient is very small (10" to 10" Poise). This is only 0.1 to 1 percent of the viscosity of water (at STP) and about 1 percent of the viscosity of liquid metals at their... 

The terms on the right side are the solvent, viscous, and elastic terms, ff", and in that order. The coefficient str is a viscous drag coefficient, which for long, slender fibers is given by (Batchelor 1970)... 

Here, v is the number concentration of fiber (volume fraction (j) = V7rd L/4) and is the viscous drag coefficient. The stress contribution by fiber (c ) is determined by and tensor parameter (). is dependent upon... 

The friction coefficient determines the strength of the viscous drag felt by atoms as they move through the medium its magnitude is related to the diffusion coefficient, D, through the relation Y= kgT/mD. Because the value of y is related to the rate of decay of velocity correlations in the medium, its numerical value determines the relative importance of the systematic dynamic and stochastic elements of the Langevin equation. At low values of the friction coefficient, the dynamical aspects dominate and Newtonian mechanics is recovered as y —> 0. At high values of y, the random collisions dominate and the motion is diffusion-like. 

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. 

If the relative velocity is sufficiently low, the fluid streamlines can follow the contour of the body almost completely all the way around (this is called creeping flow). For this case, the microscopic momentum balance equations in spherical coordinates for the two-dimensional flow [vr(r, 0), v0(r, 0)] of a Newtonian fluid were solved by Stokes for the distribution of pressure and the local stress components. These equations can then be integrated over the surface of the sphere to determine the total drag acting on the sphere, two-thirds of which results from viscous drag and one-third from the non-uniform pressure distribution (refered to as form drag). The result can be expressed in dimensionless form as a theoretical expression for the drag coefficient ... 

With regard to the drag on a sphere moving in a Bingham plastic medium, the drag coefficient (CD) must be a function of the Reynolds number as well as of either the Hedstrom number or the Bingham number (7V Si = /Vne//VRe = t0d/fi V). One approach is to reconsider the Reynolds number from the perspective of the ratio of inertial to viscous momentum flux. For a Newtonian fluid in a tube, this is equivalent to... 

Glicksman (1984) showed that the list of controlling dimensionless parameters could be reduced if the fluid-particle drag is primarily viscous or primarily inertial. The standard viscous and inertial limits for the drag coefficient apply. This gives approximately... 

For viscous dominated flows, it can be assumed that the gas inertia and the gas gravitational forces are negligible. By dropping the gas inertia and gravity time from the gas momentum equation and simplifying the dimensionless drag coefficient to the linear viscous term, the set of dimensionless equations does not include gas-to-solid density ratio as a parameter. 

From dimensional considerations, the drag coefficient is a function of the Reynolds number for the flow relative to the particle, the exponent, nm, and the so-called Bingham number Bi which is proportional to the ratio of the yield stress to the viscous stress attributable to the settling of the sphere. Thus ... 

The average DNA helix diameter used in modeling applications such as the ones described here includes the diameter of the atomic-scale B-DNA structure and— approximately—the thickness of the hydration shell and ion layer closest to the double helix [18]. Both for the calculation of the electrostatic potential and the hydrodynamic properties of DNA (i.e., the friction coefficient of the helix for viscous drag) a helix diameter of 2.4 nm describes the chain best [19-22]. The choice of this parameter was supported by the results of chain knotting [23] or catenation [24], as well as light scattering [25] and neutron scattering [26] experiments. 

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