A kinetic-theory analogy in a two-phase particle-laden flow problem

A particle-laden jet experiment was created by flowing glass particles in a turbulent air pipe flow under low loading. Two batches of particles were used, with particle sizes distributed around 30 and 70-micron averages respectively; three lengths of tube were used, creating very different particle-laden jets as a result of the tube exit conditions of the high-inertia particles. Phase-Doppler anemometry was used to measure size-classified velocity within the jets. The velocity measured for the smallest particles may be attributed to the gas phase, while that of the larger particles may be compared to the gas in order to quantify the level of momentum equilibration between the two phases. The results show that for the large Stokes number particles the velocity field is barely affected by the gas flow and can be predicted by the initial condition at the tube exit. These tube exit conditions may in turn be predicted by a simple integration along the particle motion along the tube and therefore depends only on injector tube length. Deviations from this simple picture, showing particle velocities larger than the one corresponding to the gas phase, will be examined using a simple kinetic-theory correction. This correction assumes that the particle flow withing the injector tube is a rarefied flow of gas molecules which 'slips' at the tube walls.