Cross flow over spheres

The average drag coefficients C j, for cross-flow over a smooth single circu lar cylinder and a sphere aie given in Fig, 7-17. The curves exhibit different behaviors in different ranges of Reynolds numbers ... 

Average drag coefficient for cross-flow over a smooth circular cylinder and a smooth sphere. From //. ScMichtift. Boyndary Layer Theory 7c. Copyright Q i979 The McGrow-Hill Companies. 

The average Nusselt numbers for cross flow over a cylinder and sphere are... 

Based on the slip-line field theory [e.g., see Hill (1950)], Adachi and Yoshioka (1973) also extended the analysis of Ansley and Smith (1967) for spheres to include the creeping cross-flow over cylinders and obtained the following approximation expression for X ... 

Let us now compare the complications in the pulsating flow caused by an easily penetrable roughness present near a wall. The flow profiles calculated by (3.24)-(3.27) have been displayed in the top parts of Figs. 3.4 and 3.5 for EPR of the density A = 50 occupying a significant portion of the duct s cross-section. (Remember that the disposition of the EPR and, correspondingly, the flow in the duct are symmetric over the axis z = 1). The layers near the walls filled with EPR obstacles in a form of small spheres have also been schematically shown in Figures. 

We have already discussed confinement effects in the channel flow of colloidal glasses. Such effects are also seen in hard-sphere colloidal crystals sheared between parallel plates. Cohen et al. [103] found that when the plate separation was smaller than 11 particle diameters, commensurability effects became dominant, with the emergence of new crystalline orderings. In particular, the colloids organise into z-buckled" layers which show up in xy slices as one, two or three particle strips separated by fluid bands see Fig. 15. By comparing osmotic pressure and viscous stresses in the different particle configurations, tlie cross-over from buckled to non-buckled states could be accurately predicted. 

The couple on the sphere vanishes unless it is restrained from rotating. If the sphere is also neutrally buoyant then F = 0, and only the last term in Eq. (147a) survives. By noting that the local rate of mechanical energy dissipation in the unperturbed flow is 2/iSjj Sjj, this ultimately leads to a simple proof of Einstein s law of suspension viscosity (Ela) for flow through cylinders (B17), provided that the spheres are randomly distributed over the duct cross section. 

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