Geometric constant

Now let V be the voltage required to maintain the particle at the null point of the chamber when there is a steady upward flow with velocity U. Substituting Eq. (30) in Eq. (29) to eliminate the geometrical constants and the charge, there results... 

Since the presentation of this model new data have appeared which allow various tests and new conclusions. The diffusion coefficients of Karger (14), together with Equation 1 and the median jump time from the relaxation data at room temperature yield a jump distance of 2.7 A for the zeolitic water as compared with 2.2 A in bulk water (see Table III for a data summary). One might be tempted to explain the jump distance in terms of some geometrical constant of the zeolite structure such as the distance between Sn and Sm ionic sites (40), but with the cages full of... 

The unknown parameters in these equations are the three diffusion coefficients, Dx >y, and Dz, describing the diffusive rotation of the molecule about the three principal axes of the diffusion tensor (Fig. 4). The geometry of the molecule is reflected in several geometric constants, which are functions of the directional cosines of the angles formed between the C—H vectors and the three principal axes.45... 

Here DR and >, are the diffusion coefficients for the isotropic overall and free internal motions, respectively. Equation 31 assumes a diffusional process for the methyl group. If a jumping process between three equivalent positions separated by 120° is considered,47 the last term becomes C/(6DK + Z), ). Parameters A, B, and C are geometric constants similar to those in Eq. 27, but here the angle is that formed between the methyl C—H vectors and the axis of rotation. Assuming tetrahedral angles, for free internal motion ( >, ) ), 1/7 ,(CH3) is decreased to one-ninth of the value expected for a rigidly attached CH carbon. For slow internal rotation (D, — ) ), l/r1(CH3) becomes one-third of the value of a methine carbon in the same molecule, as predicted by Eq. 16. 

T geometric constant relating circumference and diameter of a circle, 3.14159 dimensionless... 

Oc is the geometric constant for the shape of the ceramic particles and [1 + (Lg/a f] is the volume fraction correction for the adsorbed layer on the ceramic particles. Again, this equation is only good for colloidally stable suspensions. Fleer et al. [19] verified this equation for cubic particles with polytvinyl alcohol) adsorbed at the surface. For polymer solution concentrations (i.e., p) that give essentially monolayer coverage of the particle surface, the value of [1 + (LJaf] is nearly constant for a wide range of ceramic powder concentrations (Le., d>c)-... 

A complex capacitance can be expressed as the product of the complex dielectric constant, e, and a geometrical constant, Cq, of the sample ... 

Here the density of the solid is p and a is another geometric constant. Geometric surface areas have often been used to estimate rates of weathering in held systems (White and Peterson, 1990). In addition, when volumetric rates of dissolution are estimated from rates of interface advance by Equation (10), these rates are implicitly normalized by geometric surface area (e.g., Brantley et al, 1993 Brantley and Chen, 1995). 

A correction of the length affects the geometric constant, which in turn influences the value of the modulus. Since the force and the displacement are the same with and without corrections, we obtain... 

A size-shape geometrical constant oq is derived from the radius of gyration as [Wilding and Rowley, 1986] ... 

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