Collision angles

Figure 32. Scattering intensity / ( normalized to I as function of light-incidence angle 0 for the e + Na(3/>)—>Na(3.s) + e process at incident energy of IN= 10 eV for various collision angles dcol.

After entering the collision chamber, the cyano radical beam collides with the molecules of the second pulsed beam with a collision angle of 90°. The unsaturated hydrocarbon beams were produced by expanding the pure gas or vapor at room temperature through a pulsed valve. For the experiments described here the typical collision energies are in the range 13.0—35.0kJ/mol. The reaction products are detected at different laboratory angles by the QMS which is preceded by an electron impact ionizer the velocity distributions... 

Note that this assumption simply transforms the problem of modeling the pair correlation function into the new problem of modeling o-The usual model for go assumes that the radial distribution function depends neither explicitly on the collision angle (i.e. on X12) nor explicitly on x. The former amounts to assuming that the particle with velocity V2 has no preferential spatial direction relative to the particle with velocity vi. The radial distribution function can then be modeled as a function of the disperse-phase volume fraction. For example, a typical model is (Carnahan Starling, 1969)... 

The reader should not confuse the spherical angles (0i and 0i) (which parameterize v ) with the collision angles (0 and 0) (which parameterize X12). Indeed, the integrals over the collision angles are done with fixed values of the spherical angles (i.e. fixed values of v ). 

We would now like to evaluate explicitly the integrals in the collision terms appearing in Eq. (6.23). We will do this separately for each term involving the collision angles, and then reconstruct the final result at the end. The term V iACv) can be written in the collision frame of reference using xu = L xj2... 

Considering the first integral in Eq. (6.23) and using the result in Eq. (6.30), after a change of reference into the collision frame, the two integrals over the collision angles are... 

The terms on the right-hand side of this expression involve three new collision-angle integrals ... 

Using the analytical expressions for the integrals over the collision angles, we can now rewrite the collision source term in Eq. (6.21) as the sum of two contributions. 

The reader will recognize that the coefficients are related to the integrals over the collision angles discussed in Section 6.1.4. The exact definitions are... 

FIGURE 4.2 Schematic classification of oblique collisions according to the collision angle a represented in the real space (a) 2a < nil oblique acute collision, (b) 2a nil neutral colhsion, (c) la > nJl Mach-Russell oblique collision. 

Fig. 10.13. Diagram of grazing trajectories of particles taking into account inertia forces and SHRI (near hydrodynamic interaction) 1 - grazing trajectory in terms of Sutherland 2 - liquid stream-line coinciding with grazing trajectory 2 - trajectory branching out from stream-line 2 under the effect of inertia force 2" - trajectory branching out from trajectory 2 under the effect of SHRI 0( collision angle 6 - angle characterising the boundary of the part of trajectory controlled by SHRI.

The collision angle (Fig. 10.14) characterises the position of the point of tangency of the grazing trajectory and results from the following equation,... 

An integration (i.e., averaging) of all collision angles results in the relation (Smith 1965)... 

Planer collisions] Let us collide H+ with LiH with no impact parameter but different relative angles other than 180° (collinear collision). LiH is placed on the x-coordinate (Li at left and H at right). The collision angle 6 is measured by an angle between the x-coordinate and the line connecting H+ and the centroid of LiH [(LiHH) is 0 = 0°, while for (HLiH) 0 = 180°]. Three configurations, 0 = 30°, 60°, and 90° are examined. In... 

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