Layer thickness, definition

Other SFA studies complicate the picture. Chan and Horn [107] and Horn and Israelachvili [108] could explain anomalous viscosities in thin layers if the first layer or two of molecules were immobile and the remaining intervening liquid were of normal viscosity. Other inteipretations are possible and the hydrodynamics not clear, since as Granick points out [109] the measurements average over a wide range of surface separations, thus confusing the definition of a layer thickness. McKenna and co-workers [110] point out that compliance effects can introduce serious corrections in constrained geometry systems. 

The concept of surface concentration Cg j requires closer definition. At the surface itself the ionic concentrations will change not only as a result of the reaction but also because of the electric double layer present at the surface. Surface concentration is understood to be the concentration at a distance from the surface small compared to diffusion-layer thickness, yet so large that the effects of the EDL are no fonger felt. This condition usually is met at points about 1 nm from the surface. 

Fig. 8-3. Definitions of layer thickness, layer separation, and depth to the midpoint of the layer.

Figure 1.25 shows the boundary layer that develops over a flat plate placed in, and aligned parallel to, the fluid having a uniform velocity upstream of the plate. Flow over the wall of a pipe or tube is similar but eventually the boundary layer reaches the centre-line. Although most of the change in the velocity component vx parallel to the wall takes place over a short distance from the wall, it does continue to rise and tends gradually to the value vx in the fluid distant from the wall (the free stream). Consequently, if a boundary layer thickness is to be defined it has to be done in some arbitrary but useful way. The normal definition of the boundary layer thickness is that it is the distance from the solid boundary to the location where vx has risen to 99 per cent of the free stream velocity v . The locus of such points is shown in Figure 1.25. It should be appreciated that this is a time averaged distance the thickness of the boundary layer fluctuates owing to the velocity fluctuations.

The description of the diffusion films as completely stagnant layers, having definite and well-identified thicknesses, represents only a practical approximation useful for a simple mathematical description of interfacial diffusion. A... 

Figure 4-21 The concept of boundary layer and boundary layer thickness 5. (a) Compositional boundary layer surrounding a falling and dissolving spherical crystal. The arrow represents the direction of crystal motion. The shaded circle represents the spherical particle. The region between the solid circle and the dashed oval represents the boundary layer. For clarity, the thickness of the boundary layer is exaggerated, (b) Definition of boundary layer thickness 5. The compositional profile shown is "averaged" over all directions. From the average profile, the "effective" boundary layer thickness is obtained by drawing a tangent at x = 0 (r=a) to the concentration curve. The 5 is the distance between the interface (x = 0) and the point where the tangent line intercepts the bulk concentration.

The diffusion-layer concept is an artifice for handling the flux arising from what would be, if treated in a proper hydrodynamic way, a complicated space variation of concentration at the interface. There is always some gradient of concentration at the interface there is an initial region in which the concentration changes linearly with distance, but there is, in the real case, no sharply defined layer of definite thickness, even when convection (natural or forced) produces a steady-state concentration... 

Among the first practical applications, research studies have been interested to fathom possible potentials and limitations of LAPS-based measurements. One distinguishing feature of the LAPS is its spatial resolution. The resolution of a LAPS system is limited by several factors such as the definition of the light source (e.g., wavelength, beam diameter, beam divergence, beam intensity, etc.) and the LAPS geometry of the build-up (layer scheme, layer thickness, material properties,... 

In order to evaluate the conditions under which it is possible to achieve a stationary cyclic voltammogram, a key parameter is Nemst diffusion layer thickness, <5 , which was introduced in Sect. 2.2.1 for reversible processes when a single potential pulse is applied. It is possible to extend the definition of to a multipulse sequence, <5)f, as... 

By comparing equations (1.17), (1.22), (2.28 )-(2.292) and (3.30 )-(3.322), it is easy to understand that some of the critical layer thicknesses can be considered as practically the same in all three reacting systems A-ApBq-B, A-ApBq-ArB -B and A-ApBq-ArBs-AiBn-B, while the other are definitely different. Practically, not precisely, the same because the value of any critical thickness is dependent, though probably to a negligible extent, upon where the reacting atoms are diffusing from. 

Abstract Makrolon , a commercially available polycarbonate with a glassy ultramicroporous structure (mean pore-volume 0.1 nm3), was often employed as sensitive layer for optical sensors in recent years. Due to the definite pore volume-distribution, it can be used as a size-selective sensitive layer. The interaction behaviour of Makrolon of different layer-thicknesses under the influence of methanol, ethanol and 1-propanol is characterized by Spectral El-lipsometry (SE), Surface Plasmon Resonance Spectroscopy (SPR)... 

While there is no distinct edge to the boundary layer, it is convenient to have some measure of the distance from the wall over which significant effects of viscosity exist. For this reason, it is convenient to arbitrarily define the boundary layer thickness, Su, as the distance from the wall at which u reaches to within 1% of the freestream velocity, i.e., to define 8 as the value of y at which u = 0.99uj. Using the result given in Fig. 3.4 then shows that u = 0.99wi, i.e., / = 0.99, when 17 = 5 which indicates, in view of the definition of 77, that 8U is approximately given by ... 

Equation 8.2 shows how the net flux density of substance depends on its diffusion coefficient, Dj, and on the difference in its concentration, Ac] 1, across a distance Sbl of the air. The net flux density Jj is toward regions of lower Cj, which requires the negative sign associated with the concentration gradient and otherwise is incorporated into the definition of Acyin Equation 8.2. We will specifically consider the diffusion of water vapor and C02 toward lower concentrations in this chapter. Also, we will assume that the same boundary layer thickness (Sbl) derived for heat transfer (Eqs. 7.10-7.16) applies for mass transfer, an example of the similarity principle. Outside Sbl is a region of air turbulence, where we will assume that the concentrations of gases are the same as in the bulk atmosphere (an assumption that we will remove in Chapter 9, Section 9.IB). Equation 8.2 indicates that Jj equals Acbl multiplied by a conductance, gbl, or divided by a resistance, rbl. 

Adsorption is the process of analyte accumulation on the surface under the influence of the surface forces. Determination of the total amount of the analyte adsorbed on the surface requires the definition of the volume where this accumulation is observed, usually called the adsorbed layer volume (U ). In chromatographic systems, adsorbents have large surface area, and even very small variation in the adsorbed layer thickness lead to a significant variation on the adsorbed layer volume. There is no uniform approach to the definition of this volume or adsorbed layer thickness in the literature [14,21,22]. 

The arrows along the abscissa in fig. 5.19 indicate various layer thicknesses the elllpsometric thickness d . the root-mean-square thickness d , and the hydrodynamic thickness d . For a definition of these quantities we refer to sec. 5.6. From fig. 5.19 it is clear that d " and d are meilnly determined by the loops, whereas measures the extension of the tails. We return to this point below. 

A more sophisticated solution is given by the so-called hyperbolic Kubelka-Munk equation considering a definite layer thickness d and expressing the transmitted light Tj and the reflected light / j ... 

Recall that we defined the boundary layer thickness as the distance from the surface for which utV 0.99. We observe from Table 6-3 that the value of tj corresponding to ulV = 0.99 is = 4.91. Substituting rj = 4.9J andy = B into the definition of the similarity variable (Eq. 6-43) gives 4.91 = 5 Vv/vx. Then the velocity boundary layer thickness becomes... 

Solving Eq. (S-58 numerically for the temperature profile for different Prandtl numbers, and using the definition of the thermal boundary layer, it is determined that 8/S, = Pr. Then the thermal boundary layer thickness becomes... 

Details of this method for transfer coating or lamination of perm-selective skin on a porous support can be found in the literature [49,52]. First, the advantage of this method is that a definite predefined skin layer thickness can be achieved. Second, the problem of insufficient wetting of support by coating solution and incompatibflity of the support with solvent can be overcome. 

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