Stokes number large

This response time should be compared to the turbulent eddy lifetime to estimate whether the drops will follow the turbulent flow. The timescale for the large turbulent eddies can be estimated from the turbulent kinetic energy k and the rate of dissipation e, Xc = 30-50 ms, for most chemical reactors. The Stokes number is an estimation of the effect of external flow on the particle movement, St = r /tc. If the Stokes number is above 1, the particles will have some random movement that increases the probability for coalescence. If St 1, the drops move with the turbulent eddies, and the rates of collisions and coalescence are very small. Coalescence will mainly be seen in shear layers at a high volume fraction of the dispersed phase. 

Although these wall correction factors appear to be independent of Reynolds number for small (Stokes) and large (> 1000) values of NRe, the value of Kxv is a function of both lVRe and d/D for intermediate Reynolds numbers (Chhabra, 1992). 

SOLUTION To analyze the problem, consider particle deposition on a single cylinder placed normal to an aerosol flow. The Reynolds number for the flow, based on the cylinder diameter, is 2320, which is sufficiently large to use the potential flow approximation for the stagnation region. We know that the critical Stokes number for the cylinder is... 

When St 1 the kinetic equation will be uncoupled from the gas phase and the disperse phase will behave as a granular gas. In the opposite limit where St c 1, p 0 and [/p u, so that the disperse-phase Mach number will be very large and 03 1. At intermediate values of the Stokes number, a rich variety of flow phenomena depending on all the values of the dimensionless parameters can be observed. 

The Reynolds number for a particle Rep of supercritical size, deposited on the surface of a sufficiently large bubble (for which a potential distribution of the liquid velocity field is valid), is much larger than imity. In this case, the hydrodynamic resistance is expressed by a resistance coefficient. In aerosol mechanics a technique is used (Fuks, 1961) in which the non-linearity from the resistance term is displaced by the inertia term. As a result, a factor appears in the Stokes number which, taking into account Eq. (11.20), can be reduced to (l + Rep /b). This allows us to find the upper and the lower limits of the effect by introducing K instead of K " into Eq. (10.47) and the factor X in the third term. 

There large imcertainty in the calculated results for the super-critical Stokes numbers is due to three reasons. The Basset integral (Basset 1988, Thomas 1992) is not incorporated in the calculation for the trajectory, and the particle tangential velocity according to Eq. (11.76) is used to calculate the centrifugal forces, 0 and 0,. 

Keep viscous Stokes number constant. By adhering to the scaling rules described earlier, St should automatically be similar at small and large scale leading to similar eonsolidation and growth behavior. 

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