Boundary layer, fluid

Schematic representation of the conceptual variation in the thickness of the transition layers as a function of the position along the reacting surface. 

Note that 5 is directly proportional to and and inversely proportional to and These dependencies of 5 clearly emphasize the role of substrate diameter and slurry viscosity, density, and velocity. It is also noted that these concepts apply in the absence of the abrasive particles which can penetrate the boundary layer and change the above formulaism. Abrasive-slurry fluid interface, on the other hand, will also suffer from similar boundary layer issues. Applied pressure, usually transmitted to the substrate or pad via the abrasive particles that separate the two, will also affect the boundary layer stability. 

The concept of the boundary layer is, however, useful in exploring the effect of the fluid viscosity, density, and velocity, not only during CMP but also during subsequent cleaning of the polished surface. 

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Step 8. Product species diffuse across the fluid boundary layer at the external surface of the catalyst ... 

As depicted in Figure 2.8, mass transport of substrate from the bulk water phase takes place through a fluid boundary layer (liquid film) and into a biofilm followed by a combined diffusion and utilization of the substrate in the biofilm. 

Figure 19.16 Spherical structure (particle, bubble, droplet) with radius r0 surrounded by a concentric fluid boundary layer with thickness 5. r is the spherical coordinate. The concentration inside the sphere is Cs. There is a phase change at the surface of the sphere with the equilibrium partition coefficient KSlf = Csl Cp Cp is the fluid concentration in equilibrium with Cs.

Finally, in Fig. 3.4-12 [24], a comparison is given for the overall, gas-based, mass transfer coefficient for several liquid-to-gas and solid-to-gas packed beds and column systems. In Fig. 3.4-12, for a given data point, the vertical distance up to the Tan et al. [27] correlation (which is for a solid-to-fluid boundary layer) would provide a measure of the liquid-side mass-transfer resistance associated with the liquid. This is so because amount of the large gas... 

Carling, P. A. 1992. The nature of the fluid boundary layer and the selection of parameters for benthic ecology. Freshwater Biology 28 273—284. 

When a fluid is present in contact with each solid wall, there will be an additional resistance to heat transfer in each fluid boundary layer or film . The combined mechanism of heat transfer from a hot fluid through a dividing wall to a cold fluid has many similarities to conduction through a composite slab reviewed earlier. 

Secondly, we assume that net forward and backward reaction requires kinetic interaction of boundary layer reactant and product species (adjacent to the adsorption layer) with the adsorption layer species at reaction sites. As the empirical equation 3 shows, the rate of backward reaction is proportional to the bulk fluid (= boundary layer) activity product of the species Ca " and HCOl. We conclude that net backward reaction involves simultaneous interaction (collision) of one boundary layer Ca " and one boundary layer HCOi with the adsorption layer speciation at a reaction site. We are unable, however, to make the mechanistic distinction between the ion pair CaHCOs and individual Ca " and HCOl collision at reaction sites both mechanistic models are proportional to the boundary layer product aCa aHCOs. 

Chemistry plays a very signiticant role in the CMP process. Several variables listed in Chapter 3, the fluid boundary layer formation at the solid-liquid interface, chemical composition of the surface being polished, the formation of the passivating layer at the solid surface caused by an oxidizer, dissolution of the solid surface or of the mechanically abraded solid fragments or atoms/molecules of the original or passivated layer, the isoelectric point (see Chapter 5) related to abrasive and solid surface charge layers, effective removal or redeposition of the polished material, polished surface contamination and post-CMP passivation, and lifetime and properties of the pad all are determined by the chemical interactions induced by the chemicals in the slurry and the solid surfaces. Thus the choice of chemicals (thus of an appropriate chemistry) in making the slurry is very important. 

Fig. 2.4 Temperature profile for the boundary condition (2.23). The tangent to the temperature curve at the solid surface meets the guide-point R at the fluid temperature p at a distance away from the surface s = A fa = Lo/Bi. The subtangent of the temperature profile in the fluid boundary layer is su = Ap/ce = Lq/Nu.

Originally, the concept of fluid boundary layer was presented by Prandtl [122]. Prandtl s idea was that for flow next to a solid boundary a thin fluid layer (i.e.,... 

A second example is the use of a mass transfer coefficient to relate the flux across a fluid boundary layer (fluid region over which the solute concentration changes from the... 

A large value of Sh indicates that the mass transfer resistance in the fluid boundary layer is insignificant. A small value means that boundary layer mass transfer resistance dominates. 

Gaudioso (j>) proposed a theory of ink release from this type of plate, suggesting that ink solvent diffusion from the ink into the plate non-printing area is essential to the formation of a weak fluid boundary layer. This allows more complete removal of residual ink from these areas. 

The concentration gradients in an asymmetric membrane are complex because the driving force for diffusion in the skin layer is the concentration gradient of gas dissolved in the dense polymer, and the driving force in the porous support layer is a concentration or pressure gradient in the gas-filled pore. When the porous layer is thick, diffusion does not contribute very much to the flux, and gas flows by laminar flow in the tortuous pores. For high-flux membranes, there may also be significant mass-transfer resistances in the fluid boundary layers on both sides. 

Included in this diagram is the drop in concentration across the menbrane and, also, possible drops due to resistances in the fluid boundary layers or films on either side of the membrane. 

To obtain higher output from the heat transfer surfaces of the still, the resistance to the flow of heat along the path through the surface must be reduced. Numerous investigators have shown that generally the fluid boundary layer or film immediately adjacent to the heat transfer surface represents the major portion of over-all resistance. In fact, the use of high fluid velocities and turbulence inducers to minimize these fluid films is well known. 

Asa rule the micromixing time is short in comparison to the macromixing time however, in fluid boundary layers close to solid surfaces (walls, heat exchanger, tube bundles, etc.), the local specific power input e can be very low with the consequence of long micromixing times. 

Fluid boundary layer separation at vascular bifurcations or curves (as found in the carotid and coronary arteries) may be considered 2D if evaluating centerline flow (Steinman and Ethier, 1994). Along this plane, the secondary flows brought on by the vessel cross-sectional curvature will not affect the flow patterns. These models may be used to evaluate boundary layer separation in the carotid artery, the coronaries, and graft anastomoses. 

Figure 2.6 Mass transfer in a chemically mediated membrane process. The chemical potential gradient from the bulk feed to the bulk permeate streams is the driving force for mass transfer (shown as yellow line). Three main resistances to mass transfer are shown—fluid boundary layers on the feed and permeate sides of the membrane and diffusion through the membrane.

As noted in Section 1.5, many commercial adsorbents consist of smaU microporous crystals formed into a macroporous pellet Such adsorbents offer two distinct diffusional resistances to mass transfer the micrq>ore resistance of the adsorbent crystals or microparticles and the ihacropore diffdkional resistance of the pellet. When adsorption occurs from a binary (or multicomponent) fluid mixture, there may be an additional resistance to mass transfer associated with transport through the laminar fluid boundary layer surrounding the particle (see Section 6.7). The general situation is as sketched in Figure... 

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