Boundary layers solution stability

With the initial values for ug, Eq. (10.30) may be solved for Uj+ij explicitly, usually by starting from the flat plate and working outward until Ujj+i/uj+i, = 1- e = 0.995 or some other predetermined value of e. Because of the asymptotic nature of the boundary layer condition, the location of the outer boundary is found as the solution proceeds. The values of Vj+ij can be computed from Eq. (10.31), starting at the point next to the lower boundary and computing upwards in the positive y direction. The stability criteria for this method are... 

So far, we have been talking about the stability of zero pressure gradient flows. It is possible to extend the studies to include flows with pressure gradient using quasi-parallel flow assumption. To study the effects in a systematic manner, one can also use the equilibrium solution provided by the self-similar velocity profiles of the Falkner-Skan family. These similarity profiles are for wedge flows, whose external velocity distribution is of the form, 11 = k x . This family of similarity flow is characterized by the Hartree parameter jSh = 2 1 the shape factor, H =. Some typical non-dimensional flow profiles of this family are plotted against non-dimensional wall-normal co-ordinate in Fig. 2.7. The wall-normal distance is normalized by the boundary layer thickness of the shear layer. 

Results of an analysis has been presented here for spatial stability properties of a mixed convection boundary layer developing over a heated horizontal fiat plate. A similarity solution (as given by (6.3.11) and (6.3.13)) for the mean flow is used following Schneider (1979). Such boundary layers are characterized by the buoyancy parameter K = Gr and is solved... 

By towing a concave wall of 500mm radius of curvature at a constant speed in a tank filled with an aqueous solution of polythylene oxide of about i xio molecular weight, the neutral stability of Gortler vortices was determined for the 2 and 5wppm solutions with the hydrogen bubble technique and the streamwise velocity of basic flow in boundary layer along the wall was also measured. 

After the surfactant has entered the solution phase, the next step required for performance may be adsorption at another interface (e.g., the air—water interface). This probably occurs via a series of steps which mirror those involved in getting the surfactant into solution that is, the next to last step in adsorption is probably that of entering the unstirred boundary layer at this new interface, and the last step is diffusion through this quiet boundary layer and adsorption at the interface. Now, at last, the surfactant can modify the surface physics of the interface so as to stabilize foam, for example, or do other useful things. 

Only polyurethane adhesives should be used to bond PVC soles. The adhesion problems of PVC derive from the presence of plasticizers and stabilizers (stearate type) able to migrate to the surface impeding the contact with the adhesive (creation of weak boundary layers). A solvent wiping on the PVC surface is usually effective in improving adhesion and solvents such as MEK are adequate. On the other hand, treatment with 10 wt% aqueous solutions of sodium hydroxide has been successfully applied to increase the adhesion performance of plasticized PVC soles (Abbott et al. 2003). 

At the interface between two similar solutions (a) and (p) merely differing in their composition, a transition layer will develop within which the concentrations of each component j exhibit a smooth change from their values cj in phase (a) to the values cf in phase (p). The thickness of this transition layer depends on how this boundary has been realized and stabilized. When a porous diaphragm is used, it corresponds to the thickness of this diaphragm, since within each of the phases outside the diaphragm, the concentrations are practically constant, owing to the liquid flows. 

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