Boundary layers internal

Two types of mass- transfer can be distinguished for catalysis with heterogeneous catalyst particles. External mass transfer refers to molecular transport between the bulk reaction mixture and the surface of the enzyme particle through a boundary layer. Internal mass transfer is the molecular transport inside the solid enzyme phase. Internal mass transfer occurs within the pores of the catalyst particle to and from the particle surface. Figure 4.9-4 illustrates the definitions of external and internal mass transfer. 

Momentum and thermal boundary layers internal flow in pipe in developing and developed regions. 

Internal Flow. Depending on the atomizer type and operating conditions, the internal fluid flow can involve compHcated phenomena such as flow separation, boundary layer growth, cavitation, turbulence, vortex formation, and two-phase flow. The internal flow regime is often considered one of the most important stages of Hquid a tomiza tion because it determines the initial Hquid disturbances and conditions that affect the subsequent Hquid breakup and droplet dispersion. 

A thorough description of the internal flow stmcture inside a swid atomizer requires information on velocity and pressure distributions. Unfortunately, this information is still not completely available as of this writing (1996). Useful iasights on the boundary layer flow through the swid chamber are available (9—11). Because of the existence of an air core, the flow stmcture iaside a swid atomizer is difficult to analyze because it iavolves the solution of a free-surface problem. If the location and surface pressure of the Hquid boundary are known, however, the equations of motion of the Hquid phase can be appHed to reveal the detailed distributions of the pressure and velocity. 

ESDU Data Item 82026. 1982. Strong Winds in the Atmospheric Boundary Layer—Part 1 Mean Hourly Wind Speeds. Engineering Sciences Data Unit International, London. 

In the previous section we discussed wall functions, which are used to reduce the number of cells. However, we must be aware that this is an approximation that, if the flow near the boundary is important, can be rather crude. In many internal flows—where all boundaries are either walls, symmetry planes, inlets, or outlets—the boundary layer may not be that important, as the flow field is often pressure determined. However, when we are predicting heat transfer, it is generally not a good idea to use wall functions, because the convective heat transfer at the walls may be inaccurately predicted. The reason is that convective heat transfer is extremely sensitive to the near-wall flow and temperature field. 

Pastor-Bias M.M. and Martm-Martfnez J.M., 1995, Mechanisms of formation of weak boundary layers in styrene-butadiene rubber, in Proceedings of The International Adhesion Symposium, H. Mizumachi (Ed.), Gordon and Breach Science Publishers, Melbourne, 215-233. 

Kuznetsov, M. et al.. Effect of boundary layer on flame acceleration and DDT, Proceedings of the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems on CD, Montreal, 2005. 

This is explained by a possible higher activity of pure rhodium than supported metal catalysts. However, two other reasons are also taken into account to explain the superior performance of the micro reactor boundary-layer mass transfer limitations, which exist for the laboratory-scale monoliths with larger internal dimensions, are less significant for the micro reactor with order-of-magnitude smaller dimensions, and the use of the thermally highly conductive rhodium as construction material facilitates heat transfer from the oxidation to the reforming zone. 

Similarity Variables The physical meaning of the term similarity relates to internal similitude, or self-similitude. Thus, similar solutions in boundary-layer flow over a horizontal flat plate are those for which the horizontal component of velocity u has the property that two velocity profiles located at different coordinates x differ only by a scale factor. The mathematical interpretation of the term similarity is a transformation of variables carried out so that a reduction in the number of independent variables is achieved. There are essentially two methods for finding similarity variables, "separation of variables (not the classical concept) and the use of "continuous transformation groups. The basic theory is available in Ames (1965). 

Kanai, A., and Mtyata, H. Numerical simulation of bubbles in a boundary layer by Maker-Density-Function . Proceedings of the 3rd International Conference on Multiphase Flow, Lion, France (1998). 

Riber, H. H. and Wetzel, R. G. (1987). Boundary layer and internal diffusion effects on phosphorus fluxes in lake periphyton, Limnol. Oceanogr., 32, 1181-1194. 

Ary given catalytic material can be abstracted based on the same underlying similar architecture — for ease of comparison, we describe the catalytic material as a porous network with the active centers responsible for the conversion of educts to products distributed on the internal surface of the pores and the external surface area. Generally, the conversion of any given educt by the aid of the catalytic material is divided into a number of consecutive steps. Figure 11.13 illustrates these different steps. The governing transport phenomenon outside the catalyst responsible for mass transport is the convective fluid flow. This changes dramatically close to the catalyst surface from a certain boundary onwards, named the hydrodynamic boundary layer, mass transport toward and from the catalyst surface only takes place... 

The oxidation of chloride at the anode results in an anode boundary layer that contains less chloride than the bulk anolyte (Fig. 6.2). The membrane is pressed against the anode by differential pressure, and thus is integrated into the anode boundary layer. Good internal mixing is necessary to minimise the layer effect and to maintain a steady supply of chloride to the anode for reaction. The ionic concentration and the thickness of this layer will have an effect on the water content, the... 

The working cathode also generates a boundary layer. The water that is reduced at the cathode is supplied by the bulk catholyte. This stripping effect forms a layer of approximately 37 wt.% caustic on the surface of the cathode. Again, the thickness of this layer is determined by the efficiency of the internal mixing within the cathode compartment. 

There are several resistances which may hinder the movement of a molecule of adsorbate from the bulk fluid outside a pellet to an adsorption site on its internal surface, as shown in Figure 17.15. Some of these are sequential and have to be traversed in series, whilst others derive from possible parallel paths. In broad terms, a molecule, under the influence of concentration gradients, diffuses from the turbulent bulk fluid through a laminar boundary layer around a solid pellet to its external surface. It then diffuses, by various possible mechanisms, through the pores or the lattice vacancies in the pellet until it is held by an adsorption site. During desorption the process is reversed. 

Bennett etal. have presented a model for gaseous pollution sorption by plants. The model includes all the known factors that might have a significant effect on pollution sorption by plant leaves, including gas concentration (ambient air and internal leaf), gas fluxes (external and internal), resistance to flow (leaf boundary layer, stomatal, and internal), nature of leaf surfaces (stomatal presence, cutin, and surface properties), importance of gas solubility and thus solute concentration within the leaf, and ability of the plant to metabolize pollutants (decontaminate itself). They mentioned the reactivity of ozone as another factor to consider. They believe that surface sorption may be important, at least over short periods. They presented a possible mathematical representation of these factors, which they suggested is equivalent to the mathematical statement of Ohm s law. This material is well int ated in the review by Bennett and Hill. ... 

The two predominant mechanisms of failure in adhesively bonded joints are adhesive failure or cohesive failure. Adhesive failure is the interfacial failure between the adhesive and one of the adherends. It indicates a weak boundary layer, often caused by improper surface preparation or adhesive choice. Cohesive failure is the internal failure of either the adhesive or, rarely, one of the adherends. 

Elzinga and Banchero (El) use Meksyn s boundary layer equation (M2) for flow around a rigid sphere, with the boundary condition that the interfacial velocity is not zero, to calculate a shift in the boundary-separation ring from an equivalent rigid-sphere location. Their calculated positions are slightly less than their observed shifts but confirm the thesis that these shifts are due to internal circulation. Similar quantitative results are reported by Garner and Tayeban (G7). 

The dependence of Sh on Pe/(1 + k) at high Pe results because the Hadamard -Rybczynski analysis gives dimensionless velocities iiJU, iio/V) proportional to (1 + k) within and close to the particle (Eqs. (3-7) and (3-8)). Similar dependence is encountered for unsteady external transfer (Section B.2), and for internal transfer at all Pe (Section C.4). These results do not give the rigid sphere values as /c x, because of fundamental diflerences between the boundary layer approximations for the two cases (see Chapter 1), and arc only valid for /c < 2. 

Treatment of liquid drops is considerably more complex than bubbles, since the internal motion must be considered and internal boundary layers are difficult to handle. Early attempts to deal with boundary layers on liquid drops were made by Conkie and Savic (C8), McDonald (M9), and Chao (C4, W7). More useful results have been obtained by Harper and Moore (HIO) and Parlange (PI). The unperturbed internal flow field is given by Hill s spherical vortex (HI3) which, coupled with irrotational flow of the external fluid, leads to a first estimate of drag for a spherical droplet for Re 1 and Rep 1. The internal flow field is then modified to account for convection of vorticity by the internal fluid to the front of the drop from the rear. The drag coefficient. 

Surface-active contaminants play an important role in damping out internal circulation in deformed bubbles and drops, as in spherical fluid particles (see Chapters 3 and 5). No systematic visualization of internal motion in ellipsoidal bubbles and drops has been reported. However, there are indications that deformations tend to decrease internal circulation velocities significantly (MI2), while shape oscillations tend to disrupt the internal circulation pattern of droplets and promote rapid mixing (R3). No secondary vortex of opposite sense to the prime internal vortex has been observed, even when the external boundary layer was found to separate (Sll). 

Finlayson-Pitts, B. J., Chlorine Atoms as a Potential Tropospheric Oxidant in the Marine Boundary Layer, Res. Chem. Interned., 19, 235-249 (1993). 

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