Elastic collision dynamics kinetic energy

When the gas-solid flow in a multiphase system is dominated by the interparticle collisions, the stresses and other dynamic properties of the solid phase can be postulated to be analogous to those of gas molecules. Thus, the kinetic theory of gases is adopted in the modeling of dense gas-solid flows. In this model, it is assumed that collision among particles is the only mechanism for the transport of mass, momentum, and energy of the particles. The energy dissipation due to inelastic collisions is included in the model despite the elastic collision condition dictated by the theory. 

The dynamics of the two-particle problem can be separated into center-of-mass motion and relative motion with the reduced mass /i = morn s/(rnp + me), of the two particles. The kinetic energy of the relative motion is a conserved quantity. The outcome of the elastic collision is described by the deflection angle of the trajectory, and this is the main quantity to be determined in the following. The deflection angle, X, gives the deviation from the incident straight line trajectory due to attractive and repulsive forces. Thus, x is the angle between the final and initial directions of the relative velocity vector for the two particles. 

After an energetic ion strikes a surface, it will decelerate as its kinetic energy is dissipated via elastic (nuclear collision) and inelastic processes. A small fraction of the ions may reflect from the surface the majority are implanted beneath the surface. The average distance an ion travels before it is stopped within a solid increases with collision energy. Figure 12 shows the mean depth of penetration achieved by He+ incident on a silicon surface. Molecular dynamics simulations reveal that within the first picosecond after a keV ion impacts a solid, a local hot spot develops at the... 

Kinetic descriptions of high energy recoil reactions have also been developed. While the results obtained are not directly relevant to conventional thermal kinetics, they do provide considerable insight into high-energy collision dynamics. The recoil process itself consists of an irreversible dispersion of energy via elastic and inelastic collisions, and... 

The temperature instability of a two-dimensional reactive fluid of N hard disks bounded by heat conducting walls has been studied by molecular dynamics simulation. The collision of two hard disks is either elastic or inelastic (exothermic reaction), depending on whether the relative kinetic energy at impact exceeds a prescribed activation barrier. Heat removal is accomplished by using a wall boundary condition involving diffuse and specular reflection of the incident particles. Critical conditions for ignition have been obtained and the observations compared with continuum theory results. Other quantities which can be studied include temperature profiles, ignition times, and the effects of local fluctuations. 

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