Mean collision time

Particles are moved along their current velocity vectors without undergoing interactions for a time At which is chosen smaller than the mean collision time. If a particle hits the domain boundary, its velocity vector is modified according to the corresponding boundary condition (for example specular or diffuse reflection if a particle hits a wall) ... 

For most carbonyl compounds, kp is approximately independent of vibrational excitation energy (Eypp,), whereas kfjR usually increases with Evpp,. Therefore, p becomes smaller and ip becomes shorter as Evpb increases. Typically, highly sensitive technique of fluorescence excitation spectroscopy permits measurement of Op over an extensive range of Evib- Hence the rates of radiative transitions as well as the rates of radiationless transitions of SVLs and SRVLs can be readily determined (135). For simple carbonyl compounds with small amounts of vibrational energy in the Sp state, collision-induced processes can become important at pressures above a few torr, since the lifetimes (tp) are comparable to the mean collision times (tu) at these pressures. Rate data reported for a number of aliphatic carbonyls are summarized in Table 2. 

Photoinduced reactions in the liquid phase are influenced much more by collisions than those in the gas phase. In order to study such reactions on a time scale below the mean collision time, femtosecond spectroscopy is needed. One example is the exploration of transition-state dynamics and rotational dynamics of the fragments in the photolysis of mercuric iodide Hgl2 in ethanol solution [1415, 1416]. 

The size of the timestep At should be estimated from the characteristic time scales for both rotational and translational motion. The mean collision time Tcoi defines the time scale for the translational motion, which is given by ... 

The relation between the means-square displacement (MSD) to the diffusion constant is valid in the physical limit of the observation time being larger compared with the mean-collision time (Haile 1991). We used Equation 10.6 to compute diffusivities through MD simulations. We computed diffusivity, D, along each direction using the projected Einstein equations ... 

Droplet coalescence, however, appears to be important and, therefore, it is taken into account [39, 45]. In the present work, the collision efficiency is computed following the procedure of O Rourke [46]. Usually, it is assumed [39] that binary droplet collisions lead either to coalescence or bouncing. Before, during and after the interaction, mass, and momentum are conserved [39], and it is assumed that the mean collision time is smaller than the inter-collision time. Details of the... 

We will use this equation rather than Eq. (9.8-13). The mean collision time Tcoh is given by the familiar relation time = distance/speed ... 

The mean molecular collision rate z is the reciprocal of the mean collision time ... 

Lise 10 s, which is three orders of magnitude less than convective timescale. The mean collision time of air at standard condition is the order of the 10 ° s. Hence, the DSMC step must run about 10 ° time steps for settling to a steady-state condition. 

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