Minimum distance approach

Table VIII. Values of Slope, /3 (Eq. 31), the Anionic Contribution to Minimum Distance of Approach (r ) and the Minimum Distance Approach (r) for a Number of Acids (25°C)°...

If separate blast sources are located close to one another, they may be initiated almost simultaneously. Coincidence of their blasts in the far field cannot be raled out, and their respective blasts should be superposed. The safe and most conservative approach to this issue is to assume a maximum initial blast strength of 10 and to sum the combustion energy from each source in question. Further definition of this important issue, for instance the determination of a minimum distance between potential blast sources so that their individual blasts may be considered separately, is a factor in present research. 

The angle at which the minimum distance of approach occurs, 6m (see Fig. 1-2), is thus ... 

The angle of deflection for the collision of rigid elastic spheres may be obtained from Fig. 1-3. The minimum distance of approach is... 

The Smoluchowski-Levich approach discounts the effect of the hydrodynamic interactions and the London-van der Waals forces. This was done under the pretense that the increase in hydrodynamic drag when a particle approaches a surface, is exactly balanced by the attractive dispersion forces. Smoluchowski also assumed that particles are irreversibly captured when they approach the collector sufficiently close (the primary minimum distance 5m). This assumption leads to the perfect sink boundary condition at the collector surface i.e. cp 0 at h Sm. In the perfect sink model, the surface immobilizing reaction is assumed infinitely fast, and the primary minimum potential well is infinitely deep. 

Particles attract whenever they approach to within a minimum distance. Whatever the magnitude of the interparticle attraction, energetic molecules will separate and continue moving after their encounter but, conversely, molecules of lower energy do not separate after the collision because the attraction force is enough to overwhelm the momentum that would cause the particles to bounce apart. The process of coalescence has begun. 

Solvent-separated ion pairs, in which the first solvation shells of both ions remain intact on pairing may be distingnished from solvent-shared ion pairs, where only one solvent molecule separates the cation and the anion, and contact ion pairs, where no solvent separates them (Fig. 2.6). The parameter a reflects the minimum distance by which the oppositely charged ions can approach each other. This eqnals the sum of the radii of the bare cation and anion pins 2, 1, and 0 diameters of the solvent, respectively, for the three categories of ion pairs. Since a appears in Eq. (2.49), and hence, also in Q(b), it affects the value of the equilibrium constant, K s- The other important variable that affects K ss is the product T and, at a given temperature, the value of the relative permittivity, e. The lower it is, the larger b is and, hence, also K s-... 

Bartell8> proposed a set of one angle radii, r0, which represent the minimum distance of approach of two atoms X and Y bonded to a central atom, M. These radii are... 

For a molecule in the excited state, the effective cross-section for coil os can be much greater than those for kinetic collision. The optical collisions nay be defined as the minimum distance of approach over which the excited mole-cule can interact with another molecule to bring about a physical or chemical change. 

A) A distance matrix was constructed from the inferred amino acid sequences using a Poisson correction for multiple hits and the tree constructed using the minimum evolution approach. Five hundred bootstrap resamplings were carried out. Branches with bootstrap support values less than 50% are indicated with an asterisk. 

In the microfluid dynamics approaches the continuity and Navier-Stokes equation coupled with methodologies for tracking the disperse/continuous interface are used to describe the droplet formation in quiescent and crossflow continuous conditions. Ohta et al. [54] used a computational fluid dynamics (CFD) approach to analyze the single-droplet-formation process at an orifice under pressure pulse conditions (pulsed sieve-plate column). Abrahamse et al. [55] simulated the process of the droplet break-up in crossflow membrane emulsification using an equal computational fluid dynamics procedure. They calculated the minimum distance between two membrane pores as a function of crossflow velocity and pore size. This minimum distance is important to optimize the space between two pores on the membrane... 

The atomic covalent radius (one half of the M-M distance) has been used for a long time for estimates of the nature of chemical bonds. Its magnitude correlates with the M—M bond energy. The notion of the van der Waals radius of an atom is ambiguous3. The sum of van der Waals radii of two atoms is defined in crystallography as the minimum distance at which they can approach each other. 

In the interaction force boundary layer approach the tangential velocity of the particles in the layer is neglected. Because the center of sufficiently large particles is far from the wall (even when the minimum distance h between wall and particle is small) this velocity may be appreciable. A second goal of the paper is to account for this effect. 

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