Boundary layer transition region

Similar boundary layers (transition regions) exist for temperature as well as species concentrations. 

Van Ingen, J.L. (1956). A suggested semi-empirical method for the calculation of the boundary layer transition region. Inst. Of Technology, Dept, of Aeronautics and Engg.Rept. VTH-74-... 

The boundary layers, or interphases as they are also called, form the mesophase with properties different from those of the bulk matrix and result from the long-range effects of the solid phase on the ambient matrix regions. Even for low-molecular liquids the effects of this kind spread to liquid layers as thick as tens or hundreds or Angstrom [57, 58], As a result the liquid layers at interphases acquire properties different from properties in the bulk, e.g., higher shear strength, modified thermophysical characteristics, etc. [58, 59], The transition from the properties prevalent in the boundary layers to those in the bulk may be sharp enough and very similar in a way to the first-order phase transition [59]. 

Indeed, the multi-layered model, applied to fiber reinforced composites, presented a basic inconsistency, as it appeared in previous publications17). This was its incompatibility with the assumption that the boundary layer, constituting the mesophase between inclusions and matrix, should extent to a thickness well defined by thermodynamic measurements, yielding jumps in the heat capacity values at the glass-transition temperature region of the composites. By leaving this layer in the first models to extent freely and tend, in an asymptotic manner, to its limiting value of Em, it was allowed to the mesophase layer to extend several times further, than the peel anticipated from thermodynamic measurements, fact which does not happen in its new versions. 

If Re is of the order of 105, the drag on the sphere may be reduced if the fluid stream is turbulent. The flow in the boundary layer changes from streamline to turbulent and the size of the eddies in the wake of the particle is reduced. The higher the turbulence of the fluid, the lower is the value of Re at which the transition from region (c) to region (d) occurs. The value of Re at which R /pu2 is 0.15 is known as the turbulence number and is taken as an indication of the degree of turbulence in the fluid. 

Fig. 5.11 Position of boundary layer separation and laminar/turbulent transition in the critical region and beyond. Experimental results of Achenbach (A3) and Raithby and Eckert (R3).

The cause of this initial smooth zone and the subsequent fairly sudden transition to wavy flow is not completely clear. Working on a much larger scale, with mostly turbulent flow of the liquid layers on dam spillways, Bauer (Bl) has shown that the length of the smooth initial region is the same as the distance required for the turbulent boundary layer, which... 

As discussed in the previous chapter, transition from laminar to turbulent flow in the boundary layer does not occur sharply at a point. Instead there is a region of mixed flow over which the transition occurs, the extent of this region being... 

Initially, the boundary-layer development is laminar, but at some critical distance from the leading edge, depending on the flow field and fluid properties, small disturbances in the flow begin to become amplified, and a transition process takes place until the flow becomes turbulent. The turbulent-flow region may be pictured as a random churning action with chunks of fluid moving to and fro in all directions. The transition from laminar to turbulent flow occurs when... 

Monte Carlo and molecular dynamics calculations of the density profile of model system of benzene-water [70], 1,2-dichloroethane-water [71], and decane-water [72] interfaces show that the thickness of the transition region at the interface is molecu-larly sharp, typically within 0.5 nm, rather than diffuse (Fig. 4). A similar sharp density profile has been reported also at several liquid-vapor interfaces [73, 74]. The sharpness of interfaces thus seems to be a general characteristic of the boundary between two stable phases and it is likely that the presence of supporting electrolytes would not significantly alter the thickness of the transition region at an ITIES. The interfacial mixed solvent layer [54, 55], if any, would probably have a thickness comparable with this thin inner layer. 

Aside from the core-mantle boundary region, a pyrolite lower-mantle composition appears to be consistent with seismological constraints. Silica enrichment of the lower mantle can be accommodated if the lower mantle is hotter than expected for a simple adiabat rooted at the 660 km y— pv + mw transition (Figure 9). Because any chemical boundary layer between the upper and lower mantle would be accompanied by a corresponding thermal boundary layer, such a model... 

B 90° is due to the transition from laminar to turbulent flow. The later decrease ill Nu is again due to the thickening of the boundary layer. Nug reaches its second minimum at about 6 140°, which is the flow separation point in turbulent flow, and increases with 0 as a result of die intense mixing in the turbulent wake region. 

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