Narrow gaps parallel plates

Figure 6.2 Some narrow gap, "parallel plate" cell geometries, (a) The Monsanto vertical plate stack (b) The BASF stacked carbon disc cell (c) A cylindrical cell (d) A zero-gap membrane cell.

THE PROBLEM A synthesis is to be performed in an undivided narrow gap parallel plate cell. Calculate the mass transfer coefficients in the absence and presence of a mesh-type turbulence promoter. The following data are available electrode height =lm electrode width = 0.1m electrolyte gap = 0.001 m Sc = 1500 v = 10 m /s superficial electrolyte velocity = 0.36 m/s. 

When the inlet length is expressed in terms of number of gap widths , the difference between the flow in a tube and the flow in an annulus of narrow gap differs only by 25% [(0.05 - 0.04)/0.05]. This situation is an indication that the growth of the laminar boundary layers from the wall to the center of the channel is similar in both cases. Because duct friction coefficients, a measure of momentum transfer, do not vary by more than a factor of 2 for ducts of regular cross sections when expressed in terms of hydraulic diameters, the use of the inlet length for tubes or parallel plates can be expected to be a reasonable approximation for the inlet lengths of other cross sections under laminar flow conditions. In the annular denuder, the dimensionless inlet length for laminar flow development, L, can be expressed as... 

Parallel Plate Viscometer, This instrument resembles the cone and plate viscometer, except that it has a flat horizontal rotating plate in place of the cone. The shear rate within the narrow gap of the two plates is not as uniform as for the cone and plate viscometer. The limiting shear rates for the parallel plate viscometer are similar to those of the cone and plate instrument. This type of a viscometer is suitable for rheological measurements of suspensions and emulsions. 

The hydrodynamic resistance of dispersion medium in the gap between particles against flowing out is one of the kinetic stability factors. The decrease in thickness of fluid layer between the particles during coagulation is related to viscous flow of liquid out of a narrow gap between the particles. For solid particles the liquid flow velocity is zero at the interface and highest in the center of a gap. The rate with which the gap between two circular plane-parallel plates of radius r (Fig. VII-7) shrinks, dh/dt, is related to the volume of liquid that flows per second across the side surface of cylindrical gap, dV/dt, via the following relationship ... 

Viscous flow between two infinitely wide parallel plates with a very narrow gap separating the two walls. When one wall is catalytically active, the following solntion is apphcable (Solbrig and Gidaspow, 1967) ... 

Aspect Ratio Required to Achieve Viscous Flow between Two Parallel Plates with a Narrow Gap... 

Adhesives used to fill spaces underneath a flip-chip device or BGA package must flow readily and rapidly when dispensed at the edges of the chip in order to completely fill the gap and free space surrounding the solder bumps. To be effective, the adhesive must be drawn into the narrow space by capillary action. The theory behind underfilling is based on capillary-flow behavior between closely spaced parallel plates (Fig. 2.5) by considering the drop in pressure (p) across a liquid-vapor interface ... 

Very narrow gap Ri,IRc > 0.99). This is similar to flow between parallel plates. Taking the shear rate at radius (/ , + Rc)f2,... 

Consider parallel plate electrodes with the current uniformly distributed along one edge, i.e., unidirectional current flow. For reactors with narrow electrode gaps, primary and secondary current density distributions for linear polarizations are given by ... 

In a system where paste fills a narrow gap between two parallel plates, when only one plate is moved in parallel at ear rate D, the shearing stress x required to move the plate is expressed with the following equation. Poise or pascal seconds from the SI system of units are used as the unit for viscosity q, and the following relationship obtains [5]. 

When a dc voltage V is applied to a large parallel plate capacitor having a narrow vacuum gap d between the plates, then the plates are charged with q and q charges per unit area immediately. The electric displacement flux Dq that develops may be given by ... 

For very narrow gaps ( = RijRo > 0.99), the curvature can be neglected and the shear strain will be the same as that between parallel plates (eq. 5.2.1)... 

For 100 ixm diameter spheres in water and a 10 mm rheometer gap, the particle density must be within 2% of that of water to prevent settling during typical measurements (1000 s). As pointed out in Chapter 5, gravitational settling will affect torque readings in a concentric cylinder rtieometer much less than in a cone and plate or parallel plate rheometer because in the concentric cylinders gravity normally acts parallel rather than perpendicular to the narrow gap of the rheometer. Thus, typically for concentric cylinders, h 50 mm, versus h = rsinfi <3 mm for cone and plate. 

A simple flow geometry of practical interest is schematically shown in Eigure 2.2. ft consists of two parallel plates forming a narrow gap whose distance h is very small compared with the width w of the plates (i.e., w h). Referring to Figure 2.2a, a fluid is placed in the gap between the two parallel plates, and then the upper plate is forced... 

Anyhow, the LSC activity within each of the two or more plates is based on the same phenomenon of total reflection14,15 outside the critical cone. Once a light ray is totally reflected, it continues an indefinite number of total reflections on the three conditions of two absolutely planar parallel surfaces of the plate, and absence of (even very weak) absorption and of scattering due to turbidity, air bubbles, and so on. On the other hand, nearly all the luminescence irradiated inside the critical cone is lost through the surfaces of the plate16. The narrow air gap between the upper and the second plate seen on Fig. 2 is a necessary isolation preventing trapped luminescence in the upper plate to penetrate into the lower plate and getting absorbed. 

In our experiments samples were placed between parallel gold-plated electrodes of 20 mm diameter and the value of the gap (between the electrodes) was fixed to 0.1mm (by a narrow PTFE cross shape piece). 

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