Channel edge effects

It should also be noted that in some cases correction factors, Fj, and Fp are applied to the drag and pressure flow terms. They are to allow for edge effects and are solely dependent on the channel width, T, and channel depth, h, in the metering zone. Typical values are illustrated in Fig. 4.11. 

When the film flows in a channel of finite width, with side walls, the flow is no longer two-dimensional in nature, as in Section III, B, 2, but edge effects occur and must be taken into account. Two types of edge effects can occur viscous edge effects, due to the drag of the side walls, and capillary edge effects, due to the capillary surface elevation at the side walls. 

The viscous edge effect will be calculated first. It is assumed that the liquid possesses no surface tension, so that the liquid surface is flat from wall to wall of the channel. In this case, with the other assumptions of Section III, B, 2, Eq. (4) reduces to... 

The velocity distribution equation (27) indicates that in the absence of surface tension effects the maximum velocity in a film flowing in a flat channel of finite width should occur at the free surface of the film at the center of the channel. The surface velocity should then fall off to zero at the side walls. However, experimental observations have shown (BIO, H18, H19, F7) that the surface velocity does not follow this pattern but shows a marked increase as the wall is approached, falling to zero only within a very narrow zone immediately adjacent to the walls. The explanation of this behavior is simple because of surface tension forces, the liquid forms a meniscus near the side walls. Equation (12) shows that the surface velocity increases with the square of the local liquid depth, so the surface velocity increases sharply in the meniscus region until the side wall is approached so closely that the opposing viscous edge effect becomes dominant. 

Horton et al. (H19), 1934 Laminar water flow studied in channel, 14.3 X 86.4 cm. at slopes up to 2°. Measurements of thickness, surface velocity, ratio u,/u. Capillary edge effect noted. Onset of turbulence discussed. 

Binnie (BIO), 1959 Experimental studies of water films in channel 8.4 X 480 cm., small slopes, Nr, up to 2500. Data on onset of rippling and turbulence, capillary edge effect. Comparison with Benjamin stability theory (B5). 

This increase of the portion of channel structure to the overall structure of the deposit in relation to the portion of holes to the overall structure is probably due to changes of the properties of the electroplating solution, caused by the dependences of the viscosity and surface tension of solution on temperature. As a result of this, the formation of holes becomes less possible and hence large holes appear only due to the edge effect, as can be clearly seen from Fig. 40c. It is obvious that the probability of the formation of the nucleus of such a structure decreases with lowering of the break-off diameter of the bubbles. 

The problem of edge effects at channel electrodes has also been considered by Cope and Tallman [51], but under the condition of inviscid flow that is, the solution was assumed to have a constant linear velocity, V. Thus, the convective-diffusion equation [as opposed to eqn. (11)]... 

Whilst the cells/electrodes used in mechanistic work are designed so that edge effects may be neglected, it is evident that enhanced sensitivity will result by maximising the edge effect. To this end, micro and micro-array channel electrodes have been developed [52-60],... 

Since an LC/MS method had already been developed, the focus of this method development was on evaluating the consistency of the 96-well plate based sample preparation and uniformity of results from the various wells in the 96-well plate, namely the edge effect. However we choose to compare the results, it is necessary to evaluate the precision and accuracy of the 96-channel pipettor first. 

Unlike the RDE, convection and diffusion operate in different directions, the electrode surface is non-uniformly accessible and thus the associated mathematical problem is multidimensional. However, this can be simplified under appropriate experimental conditions. Thus, we can often assume that the flow velocity is high enough for the transport by diffusion in the direction of the flow (x-direction) to be negligible relative to convection. This is a valid approximation if the flow rate is fast and the electrode is large. Moreover, edge effects can be neglected provided that the width of the band is much smaller than that of the channel (w d), [Pg.170]

The above regeneration mechanism results in the formation of patches of thin film at the border, with the excess fluid flowing into the border channel. The edge effects determine the drainage, with the rate of thinning varying inversely with film width [7, 8]. This results in thickness fluctuations caused by capillary waves. 

In all the FFF techniques considered so far, the flow took place in the environment of a channel between two wide flat plates. The channel plate widths are orders of magnitude larger than the gap between the plates (e.g. 2 cm X 200-300 pm). However, there is always an edge effect at the two ends of the width of the plate. Much more important, however, is the requirement in flow FFF and electrical FFF that there be a membrane lining the channel to allow crossflow permeation in flow FFF and buffer ion transport in electrical FFF. 

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