Average string velocity

Figure 7. Average string velocity (dimensional form on left ordinate dimensionless form on right ordinate) in a 10 %PDA S/PIB emulsion. Bars on data points denote standard uncertainties equal to the standard deviation.

This simple example Illustrates the important kinematic properties of shock waves, particularly the concepts of particle velocity and shock velocity. The particle velocity is the average velocity acquired by the beads. In this example, it is the piston velocity, v. The shock velocity is the velocity at which the disturbance travels down the string of beads. In general, at time n//2v, the disturbance has propagated to the nth bead. The distance the disturbance has traveled is therefore n d -b /), and the shock velocity is... 

If we have a gas-liquid mixture with the volume concentration of liquid Wo = 5 10 " m /m at the entrance of the string droplet catcher, then at the exit, we have Wi = 4 10 m /m. The dependence of t on gas velocity U is shown in Fig. 19.10. For the chosen values of parameters, the critical velocity, i.e. the velocity at which S = S r, is equal to Uc = 1.56 m/s. It means that when U < UcP, the efficiency of the droplet catcher section is practically equal to zero. Keep in mind that if drop have different radii, then the critical Stokes number will be determined by the average radius of drops. 

---