Collision-slipping region

This is the model for the overall residence time distribution of the particles in the impinging stream contactor under consideration. The model contains several parameters related to equipment structure and operating conditions, i.e. the mean residence times in the four sub-spaces, 7ac, 7im, 7fai and cs. Among the four parameters, the mean residence time in the impingement zone, t m, and that in the collision-slipping region, fcs, are symmetrical parameters, which have the same influence on the overall residence time distribution. It can be seen from Eq. (3.27) or... 

As the pressure is lowered, slip occurs, and the flow mechanism is referred to as transition flow. At pressures so low that collisions between gas molecules are rare compared to the collisions between the gas and the tube wall, the flow is said to be Knudsen flow or free molecular flow. Free molecular flow prevails when Lla > 1. For air at 25°C, this condition means that we have free molecular flow when aPm on < 5. We now consider an intuitive derivation of the result for Fc in the free molecular flow region. 

The abrupt increase of the wall fiiction coefficient to very large values leading to the no-slip condition at a critical density is most likely due to the high fi uency of interparticle collisions in this region. Diffuse wall reflection then dissipates the collective axial momentum in this region, and the no-slip condition is approached as seen in figure 3. 

Show that the collision velocity of two equal-sized particles carrying equal and opposite charge is proportional to the inverse of the cube of their diameter, dpi Assume that motion is in the Stokes region. Neglect slip correction. 

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