Boundary layer separation solid sphere

The behavior of Co with particle Reynolds number for spheres, disks, and cylinders is shown in Figure 4-1. Note that the curves appear to pass through regions of behavior. Also, note the obvious bend in the curves for spheres and cylinders in the vicinity of Rcp = 10. These kinks are due to a phenomenon called boundary layer separation, which takes place when the fluid s velocity change is so large that the fluid no longer adheres to the solid surface. 

An aerosol with particles in the micron size range flows around a smooth solid sphere a few millimeters in diameter. At sufficiently high Reynolds numbers, a laminar boundary layer develop.s over the sphere from the stagnation point up to an angle of about 110 at which. separation takes place. The removal of particles by direct interception can be calculated from the velocity distribution over the forward. surface of the sphere, up to 90 from the forward stagnation point (Fig. 4.P4). 

Figure 3. Possible conditions of the momentum boundary layer around a submerged solid sphere with increasing relative velocity. Key a, envelope of pseudo-stagnant fluid b, streamline flow c, flow separation and vortex formation d, vortex shedding e, localized turbulent eddy formation. Reproduced, with permission, from Ref. 38. Copyright 1981, Springer-Verlag.

Fig. 10. Simulation of an electron-capture supernova following the collapse of an O-Ne core. The time evolution of the radius of various mass shells is displayed with the inner boundaries of the O+Ne, C+O and He shells marked by thick lines. The inner core of about 0.8 M is mainly made of Ne at the onset of collapse ([21], and references therein). The explosion is driven by the baryonic wind caused by neutrino heating around the PNS. The thick solid, dashed, and dash-dotted lines mark the neutrino spheres of ve, ve, and heavy-lepton neutrinos, respectively. The thin dashed line indicates the gain radius which separates the layers cooled from those heated by the neutrino flow. The thick line starting at t = 0 is the outward moving supernova shock (from [22])...

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