Thickness of diffusion boundary layer

Some classification of parameters in their connection with physical or mechanical processes is to be done. The main parameter connecting hydrodynamic and diffusion parts of the film flow problem with surfactant is Marangoni number Ma. The both variants of positive (Ma > 0) and negative (Ma < 0) solutal systems are considered. The main hydrodynamic parameters are Re, 7 or equivalently S. 7. This two values determine the mean film thickness i/, mean velocity and flow rate as well as parameter k. The diffusion parameters Pe,co determine the local thickness of diffusion boundary layer h and smallness parameter e. Two values T, Di characterize the masstransfer of surfactant by the adsorption-desorption and the intensity of dissipation by the surface diffusion. Besides the limiting case of fast desorption (T = 0) the more general case (T 1) are considered. Intensity of the surfactant evaporation by parameter Bi is determined. The remaining parameter G gives an indication to the typical value of surface excess concentration A in comparison with c. ... 

Pressure controls the thickness of the boundary layer and consequently the degree of diffusion as was shown above. By operating at low pressure, the diffusion process can be minimized and surface kinetics becomes rate controlling. Under these conditions, deposited structures tend to be fine-grained, which is usually a desirable condition (Fig. 2.13c). Fine-grained structures can also be obtained at low temperature and high supersaturation as well as low pressure. 

In Example 8.5, we saw how the diffusive boundary layer could grow. The boundary never achieves 1 m in thickness or even 5 cm in thickness, because of the interaction of turbulence and the boundary layer thickness. The diffusive boundary layer is continually trying to grow, just as the boundary layer of Example 8.5. However, turbulent eddies periodically sweep down and mix a portion of the diffusive boundary layer with the remainder of the fluid. It is this unsteady character of the turbulence... 

All fluid interfaces contain an undisturbed layer of solution adjacent to the interface. Mass transport in this boundary layer occurs only by diffusion. The thickness of the boundary layer depends on temperature, stirring, and the interface itself. It is up to 0.1 cm thick in unstirred systems and approaches 10"3 cm in vigorously stirred systems3,31,32). 

SER is the specific emission rate, D is the diffusion coefficient, 8is the thickness of the boundary layer, Cs is the concentration of the target VOC at the source surface and Q is the concentration of the target VOC in the air and fcg is the gas-phase mass transfer coefficient. 

This model is applicable if the thickness of the boundary layer x 2(Dt)1/2 is small as compared to the distance between the reactor walls (where t is the residence time in the reactor and D the diffusion coefficient). In this case, component concentration equations are obtained from the mass and momentum conservation laws and the continuity equation... 

This point can be appreciated more quantitatively after consideration of an important (but simple) model of transport-controlled adsorption kinetics, the film diffusion process.34 35 This process involves the movement of an adsorptive species from a bulk aqueous-solution phase through a quiescent boundary layer ( Nemst film ) to an adsorbent surface. The thickness of the boundary layer, 5, will be largest for adsorbents that adsorb water strongly and smallest for aqueous solution phases that are well stirred. If j is the rate at which an... 

In the above equations n and N are the atom fractions of nitrogen-15 species in the gas phase and the liquid phase respectively c (moles/cc.), d (cm.2/sec.), b (cm.) for the gas phase are respectively the concentration of oxides of nitrogen, the diffusion coefficient, and the thickness of the boundary layer, while C, D, and B are the same quantities for the liquid phase k (cc./moles-sec.) is a rate constant for the exchange of oxides of nitrogen between the gas and liquid phase. The specific transfer rate kr (moles/sec.-cm. ) when multiplied by the interfacial area a (cm.2/cc.) in a 1 cm. length of column per cm. of cross-sectional area gives an interphase transfer rate fc a (moles/sec.-cc.). If chemical reaction is rate limiting, fc a will be determined by the first term of Equation 25, otherwise it will be determined by the diffusion terms. 

The diffusion of reactive species within the boundary layer will be the limiting factor in mass transfer limited regime. Applying the laws of diffusion and considering a constant average thickness of the boundary layer, leads to the expression of the growth rate as follows ... 

If one considers, that kt was defined according to the Two-film theory [594, 327) by kt X D/6, see Fig. 4.1 (D is the diffusivity of the gas in the liquid S is the thickness of the liquid-side boundary layer), a strong dependence kt = /(boundary layer not only depends upon the viscosity of the liquid, but also upon the bubble diameter di,. 

---