In this thesis the interaction of a normal gas dynamic shockwave with a gas containing a distribution of small solid sphericalparticles of two distinct radii, σ1 and σ2, is studied (1) to demonstratethat the methods of kinetic theory can be extended to treat solidparticle collision phenomena in multidimensional gas-particle flows;(2) to elucidate some of the essential physical characteristics associatedwith particle-particle collision processes; and (3) to give someindication regarding the importance of particle collisions in particle-ladengas flows. It is assumed that upstream of the shock waveparticles σ1 are uniformly distributed while particles σ2 are non-uniformlydistributed parallel to the shock face and in much smallernumbers than particles σ1. Under these conditions the gas-particleσ1 flow downstream of the shock wave is very nearly one-dimensionaland independent of the presence of particles σ2. The usual shockrelaxation zone is established by the interaction of particles σ andthe gas downstream of the shock wave. The collisional model pro-posed by Marble3 is then extended and used with a modified formof the mean free path method of kinetic theory to calculate the macroscopicdistribution and velocity of particles σ2 as determined by theparticle σ1- particle σ2 and particle σ2-gas interactions. Within thecondition that the random velocity imparted to a particle σ2 by acollision is damped by its viscous interaction with the gas before itsuffers another collision, the kinetic theory method established heremay be extended to include more general particle-particle and particle-gasinteraction laws than those used by Marble. However, thecollisional model employed is particularly important because thecriteria for its application are easy to establish and because itadmits a wide class of physically interesting situations.
Within the restrictions of this collision model, it is possibleto analyze the macroscopic motion of particles σ2 in three importantlimiting cases: (σ2/σ1)2 >> ⊥,(σ2/σ1)2 << ⊥and (σ2/σ1)2 ~ ⊥. It is found that when(σ2/σ1)2 >> ⊥ thereis essentially no redistribution of particles σ2 normal to the gas flow.The only effect of particle σ1 -particle σ2 encounters is a drag forceacting to slow down particles σ2. When (σ2/σ1)2 << ⊥ it is foundthat particles σ2. may have many collisions during their passagethrough the shock relaxation zone. As a consequence there may bea substantial redistribution of particles σ2 downstream of the shockwave. The physical features of this process are studied in detailtogether with the range of validity of this diffusion model. The case(σ2/σ1)2 ~ ⊥ is analyzed under the condition particles σ2 haveat most one collision during their passage through the shock relaxationzone. It is found that when the gas or particle σ1 density is low,the single collision effects may be important even when σ2/σ1 differssignificantly from unity and the particles are not very small.
Under most conditions of practical significance, because thereis invariably a distribution of particles sizes present in a dusty gas,the calculation of the particle distribution in the shock relaxation zoneshould account for the effects of particle-particle encounters. It issuggested that an experimental observation of particle size distributionin a shock relaxation zone can yield significant information on particle-particleand particle-gas interaction laws.
