Stokes number critical

D Roll diameter cm in St - Critical Stokes number representing ... 

The trajectory calculations mentioned above also yield analytical expressions for the critical Stokes number... 

If we assume that the critical Stokes number for a 1-in-diameter circular orifice is Vs and that the pressure drop for an orifice and collecting plate in series in milliatmospheres is AP = 1.25 x 10-3pmU, where pm = fluid density (g/cm3), and U = orifice gas velocity (cm/s), determine the diameter of the smallest size unit-density spherical particle that can be collected at a pressure drop of 2 in of water. 

Critical conditions required for granule coalscence may be defined in terms of the viscous and deformation Stokes numbers, or St and Stdef, respectively. These represent a complex generalization of the critical Stokes number given by Eq. (21-114) and are discussed in detail elsewhere [Litster and Ennis, The Science and Engineering of Granulation Processes, Kluwer Academic, 2004 Iveson et al.. Powder Technol, 88, 15(1996)]. 

By analyzing the motion of a small panicle in the region near the stagnation point, it can be shown that for an inviscid How, theory predicts that impaction does not occur until a critical Stokes number is reached. For an inviscid flow, the first term in an expansion of the velocity along the streamline in the plane of symmetry which leads to the stagnation point is... 

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... 

Levin (1961) has shown that inertia deposition of particles below a critical size, which corresponds to a critical Stokes number St = 1/12, is impossible. Regarding a finite size of particles, the collision is characterised by Sutherland s formula (10.11). Comparison of the results obtained from Sutherland s relation and by Levin enables to conclude that in the region of small St < St the approximation of the material point, accepted by Levin and useful at fairly big St, becomes unsuitable for Stsmall Stokes numbers were studied by Dukhin (1982 1983b) for particles of finite size. Under these conditions inertia forces retard microflotation. 

While neglecting the finite size of a particle at subcritical Stokes numbers excludes inertia forces at all, the situation changes with the consideration of a finite particle size. Inertia forces become essential at subcritical but not too small Stokes numbers. This effect can turn out to be negative. Thus, a critical Stokes number separates the regions of positive and negative effects of inertia forces on particle deposition. 

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,. 

The existence of the critical Stokes number means that there exists a minimal radius for a particle that can be captured by an obstacle ... 

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. 

The exponents a and in Equation (13.19) are dependent on granule deform-ability and on the granule volumes u and v. In the case of small feed particles in the non-inertial regime, P reduces to the size-independent rate constant Po and the coalescence rate is independent of granule size. Under these conditions the mean granule size increases exponentially with time. Coalescence stops ( = 0) when the critical Stokes number is reached. 

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