Boundary layer, eliminated

Weak boundary layers—coupling agents eliminate weak boundary layers. 

Figure 8.5 shows a Venturi meter. The theory is the same as for the orifice meter but a much higher proportion of the pressure drop is recoverable than is the case with orifice meters. The gradual approach to and the gradual exit from the orifice substantially eliminates boundary layer separation. Thus, form drag and eddy formation are reduced to a minimum. 

Princen [57, 64, 82] and others [84] also noted the presence of wall-slip in rheological experiments on HIPEs and foams. However, instead of attempting to eliminate this phenomenon, Princen [64] employed it to examine the flow properties of the boundary layer between the bulk emulsion and the container walls, and demonstrated the existence of a wall-slip yield stress, below that of the bulk emulsion. This was attributed to roughness of the viscometer walls. Princen and Kiss [57], and others [85], have also showed that wall-slip could be eliminated, up to a certain finite stress value, by roughening the walls of the viscometer. Alternatively [82, 86], it was demonstrated that wall-slip can be corrected for and effectively removed from calculations. Thus, viscometers with smooth walls can be used. This is preferable, as the degree of roughness required to completely eradicate wall-slip is difficult to determine. 

The radial velocity profile is linear and the circumferential velocity is zero outside the viscous boundary layer, which indicates that the vorticity is constant in that region. Thus, for substantial ranges of the flow and rotation Reynolds numbers, the flow is inviscid, but rotational, outside the viscous boundary layer. For sufficiently low flow, the boundary-layer can grow to fill the gap, eliminating any region of inviscid flow. 

In this model (shown conceptually in Figure 3.22) a stagnant boundary layer exists on the fluid side of the crystal interface. Across this layer there exists a concentration gradient taken as the bulk fluid concentration (c) minus the interfacial concentration (c, ) in the fluid. Because the interfacial concentration (c,) is difficult to measure, Equations 3.12 and 3.13 are usually combined by eliminating a to obtain ... 

Rehder et al. (2004) measured the dissociation rates of methane and carbon dioxide hydrates in seawater during a seafloor experiment. The seafloor conditions provided constant temperature and pressure conditions, and enabled heat transfer limitations to be largely eliminated. Hydrate dissociation was caused by differences in concentration of the guest molecule in the hydrate surface and in the bulk solution. In this case, a solubility-controlled boundary layer model (mass transfer limited) was able to predict the dissociation data. The results showed that carbon dioxide hydrate dissociated much more rapidly than methane hydrate due to the higher solubility in water of carbon dioxide compared to methane. 

Accuracy is improved if the flowing gas stream is directed at the probe by a venturi nozzle, or by placing the sensor in the throat of the venturi (Figure 3.74). The venturi ensures a smooth velocity profile and eliminates boundary layer effects while concentrating the flow onto the sensor. These units are available for both liquid and gas services. Other designs are of the insertion probe type. Their flow ranges are a function only of the size of the pipe into which they are inserted, and their performance is a function of the correctness of the insertion depth (as are all Pitot tubes). 

Among experimental studies of chemical reactions in turbulent media, fast reactions in tubular reactors with multijet injection of reactants are very popular, since the first experiments of Mao and Toor (34) and Vassiliatos and Toor (35). Their data have been (and are still) extensively exploited for testing theoretical models, although one may ask if homogeneous isotropic turbulence was perfectly controlled in these experiments. In order to rule out this objection, a new series of experiments was recently performed by Bennani et al. (28, 29, 30, 36) in a 0.29 m i.d. tube eliminating the influence of boundary layers. Turbulence was created by a grid and carefully controlled by velocity fluctuation measurements. Previous studies (2) had confirmed that the decrease of Ig with a non-reacting species (passive scalar) obeys Corrsin s equation ... 

If the mass transfer of a gaseous reaction partner into the liquid is accompanied by a chemical reaction, the following case can occur depending on the reaction rate and the mobility of the reaction partners The concentration of A is not only reduced to zero in the solution in addition, the reaction front shifts from the liquid bulk to the liquid-side boundary layer. As a result, the liquid-side boundary is apparently reduced and finally eliminated in a chemical way ( chemisorption ), see Fig. 86. This process increases the mass transfer coefficient by the enhancement factor E as compared to its numerical value for purely physical absorption. 

When van der Waals and double-layer forces are effective over a distance which is short compared to the diffusion boundary-layer thickness, the rate of deposition may be calculated by lumping the effect of the particle-collector interactions into a boundary condition on the usual convective-diffusion equation. This condition takes the form of a first-order irreversible reaction (10, 11). Using this boundary condition to eliminate the solute concentration next to the disk from Levich s (12) boundaiy-kyersolution of the convective-diffusion equation for a rotating disk, one obtains... 

By eliminating the solid, solubilization actually may decrease the total driving force for the transport since an unsaturated solution necessarily has a lower activity than the undissolved material and the saturated boundary layer. In extreme cases, solubilization may thus slow down the rate of transport. This explains why so many germicides lose their effectiveness when incorporated into soap. They become so well solu-... 

Integrate x-momentum equation with respect to y over the boundary layer thickness 8(x). Eliminate velocity component v(x,y) in the equation by means of the continuity equation, resulting in the momentum integral equation. 

The weak boundary layer was partially eliminated by bombardment of the polymer with high energy electrons. The results in Figure 4 show that stronger joints were obtained—but not shown is the fact that bulk properties of the polymer were seriously affected. Although the yc was raised, since irradiation was done in air, joint strengths were about the same as those obtained by the solvent extraction technique. 

Surface modification of a polymer prior to metallization is widely used to improve adhesion. The most common surface modifications employed are electric discharge (corona and plasma) and, more recently, ion-beam treatments QJ- Several mechanisms have been proposed for the improved adhesion after such surface modifications (2). These include mechanical interlocking, the elimination of weak boundary layers, electrostatic attractions, and chemical bonding. All of these can play a role in adhesion depending on the surface modification used, metal/polymer system, type of metal deposition, and the extent of polymer preparation employed. However, for low power, short exposure modifications, the formation of new chemical species which can provide nucleation and chemical bonding sites for subsequent overlayers is considered to be of prime importance (3-51. 

In these equations it is assumed that a steady state has developed and that the consumption of A by reaction equals the fluxes through the boundary layers of the gas phase and of the liquid phase at the gas side and surrounding the catalyst pellet. Combining them with Equation 4.5 and eliminating the unknown concentrations CAM,CAXI,CAJg, and CAA gives... 

Hanjalic et al. (HI) have used a dissipation-model equation to study a variety of boundary-layer flows in an extended MTEN model. Their formulation is purported to work in the viscous region, eliminating the need for wall-solution patching [see Eq. (62)]. 

The product D 5 is the intrinsic permeability that can be obtained from experimentally determined values of D and S or through experiments at very high levels of mrbulence such that the boundary layer resistance is eliminated K = L/D S). A number of correlations are available in the literature for reliable estimates of for various geometries of the modules [29,45]. 

Sufficient turbulence at the membrane surface is required to eliminate CP. In PV fluxes are measured at different mrbulence rates in the feed side are determined till a constant flux is achieved. At this mrbulence, the rate of mass transfer in the membrane phase boundary layer may be assumed to be eliminated ( l 3> S/L). Proper hydraulic management on the feed side generally... 

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