Isokinetic sampling of particle concentration

Time-averaged particle mass flux in general can be expressed in terms of the time-averaged particle velocity Up, time-averaged mass concentration CJ (phase density), and particle diffusive mass flux m (covariance of particle mass concentration and velocity) as 

However, for a fully developed gas-solid pipe flow, the particle diffusive mass flux is usually negligibly small compared with the particle mass flux (Zhu et al., 1991a). Hence, the isokinetic sampling of a gas-solid suspension flow in principle is able to yield the particle mass concentration provided that the particle velocity can be determined. This principle has served as the most primary method for the calibration of measuring systems on particle mass concentration. 

The information of the velocity slip between the particles and gas is important to assist the determination of particle velocity since the isokinetic condition refers to gas phase and, in many cases, only the velocity information of gas phase is available. The general relationship between the particle velocity and gas phase velocity is governed by the momentum equation of particles. For the linear motion of a spherical particle, the governing equation takes the form (Fan and Zhu, 1997) 

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