Boundary layer, diffusion through

Granting pseudo-steady-state conditions, the three rates—diffusion of A through the boundary layer, diffusion through the layer of product, and reaction at the interface—are identical. By equatmg.the expressions for each of these processes, the concentratio.ij...(,Q4-)c can. be expressed in terms of the known (C ) and the radius of the unreacted core The three... 

At particle scale, leaching of contaminants occurs through a sequence of processes including transport of the reactant to mass transport boundary layer, diffusion through the boundary layer and micropores to the external and internal reaction surfaces, attachment on the surface, chemical surface reaction(s), detachment of the reaction products and finally the transport out into the bulk solution. The slowest process will govern the overall dissolution rate. 

Although Rs values of high Ks compounds derived from Eq. 3.68 may have been partly influenced by particle sampling, it is unlikely that the equation can accurately predict the summed vapor plus particulate phase concentrations, because transport rates through the boundary layer and through the membrane are different for the vapor-phase fraction and the particle-bound fraction, due to differences in effective diffusion coefficients between molecules and small particles. In addition, it will be difficult to define universally applicable calibration curves for the sampling rate of total (particle -I- vapor) atmospheric contaminants. At this stage of development, results obtained with SPMDs for particle-associated compounds provides valuable information on source identification and temporal... 

As described in Section 4.1.1.2, in most catalytic reactions, the reactant molecules diffuse through a boundary layer and through the pores to the active center, react, and diffuse back. If the velocity of any of these two diffusion processes is smaller than the conversion of the reactants at the active center, the overall reaction rate for the whole process is limited by the mass transport and not by the chemical reaction. If the reaction is influenced by mass transport effects, a comparison of the catalytic activity of different catalysts is impossible ... 

Diffusion through the strip-side stagnant LM boundary layer Interdiffusion through the strip-side membrane support (/Zmr) Interaction with the stripping agent on the strip-side LM interface, as a result of different thermodynamic conditions, and partition into the strip phase... 

Formulas (3.4.10) and (3.4.11) cannot be used for sufficiently large x, when the diffusion boundary layer grows through the entire film. To estimate the scope of these formulas, let us consider the original problem (3.4.1)—(3.4.4). 

Diffusion through the boundary layer (boundary layer diffusion, outer diffusion)... 

The rate of dissolving of a solid is determined by the rate of diffusion through a boundary layer of solution. Derive the equation for the net rate of dissolving. Take Co to be the saturation concentration and rf to be the effective thickness of the diffusion layer denote diffusion coefficient by . 

External Fluid Film Resistance. A particle immersed ia a fluid is always surrounded by a laminar fluid film or boundary layer through which an adsorbiag or desorbiag molecule must diffuse. The thickness of this layer, and therefore the mass transfer resistance, depends on the hydrodynamic conditions. Mass transfer ia packed beds and other common contacting devices has been widely studied. The rate data are normally expressed ia terms of a simple linear rate expression of the form... 

Processing variables that affect the properties of the thermal CVD material include the precursor vapors being used, substrate temperature, precursor vapor temperature gradient above substrate, gas flow pattern and velocity, gas composition and pressure, vapor saturation above substrate, diffusion rate through the boundary layer, substrate material, and impurities in the gases. Eor PECVD, plasma uniformity, plasma properties such as ion and electron temperature and densities, and concurrent energetic particle bombardment during deposition are also important. 

Adhesion development depends on diffusion of the CPO component of the primer through the crystalline boundary layers followed by swelling and entanglement with the rubber rich layer [75]. 

If steam condenses on a surface, there is no boundary layer the resistance to heat flow is due to scale, metal thickness, and the condensed liquid layer, resulting in a high heat transfer factor. A thin layer of air or other noncondensing gas forms at the surface through which the steam diffuses. The heat transfer factor diminishes rapidly but is considerably higher than in dry convection. 

The explicit mathematical treatment for such stationary-state situations at certain ion-selective membranes was performed by Iljuschenko and Mirkin 106). As the publication is in Russian and in a not widely distributed journal, their work will be cited in the appendix. The authors obtain an equation (s. (34) on page 28) similar to the one developed by Eisenman et al. 6) for glass membranes using the three-segment potential approach. However, the mobilities used in the stationary-state treatment are those which describe the ion migration in an electric field through a diffusion layer at the phase boundary. A diffusion process through the entire membrane with constant ion mobilities does not have to be assumed. The non-Nernstian behavior of extremely thin layers (i.e., ISFET) can therefore also be described, as well as the role of an electron transfer at solid-state membranes. 

Gaseous by-products of the reaction are diffused away from the surface, through the boundary layer. 

In the case of laminar flow, the velocity of the gas at the deposition surface (the inner wall of the tube) is zero. The boundary is that region in which the flow velocity changes from zero at the wall to essentially that of the bulk gas away from the wall. This boundary layer starts at the inlet of the tube and increases in thickness until the flow becomes stabilized as shown in Fig. 2.4b. The reactant gases flowing above the boundary layer have to diffuse through this layer to reach the deposition surface as is shown in Fig. 2.3. 

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