Parallel-plate separators

Couette flow is shear-driven flow, as opposed to pressure-driven. In this instance, two parallel plates, separated by a distances h, are sheared relative to one another. The motion induces shear in the interstitial fluid, generating a linear velocity profile that depends on the motion of the moving surface. If we assume a linear shear rate, the shear stress is given simply by... 

For this non-isothermal flow consider a Newtonian fluid between two parallel plates separated by a distance h. Again we consider the notation presented in Fig. 6.58, however, with both upper and lower plates being fixed. We choose the same exponential viscosity model used in the previous section. We are to solve for the velocity profile between the two plates with an imposed pressure gradient in the x-direction and a temperature gradient in the y-direction. 

The velocity distribution for a fully developed, isothermal drag flow between parallel plates separated by a distance of H and with the upper plate moving at constant velocity, Vq, in a rectangular coordinate system located at the stationary plate, is vx = yVo/H, and the flow rate is q = VqH/2. The fraction of exiting flow rate between... 

Caution should be taken when calculating the doublelayer force between two parallel plates. It is clear that the force is not proportional to the excess concentration of ions at the middle distance (with respect to the concentration of ions at infinity), since this Langmuir equation involved the assumption of ions of negligible sizes. We will use instead the procedure introduced by Verwey and Overbeek,18 which is based on general thermodynamic principles, and does not imply the Boltzmann distribution of ions.19 The force, per unit area, between two parallel plates separated by a distance l is given by... 

The average polarization of a water molecule, m(z), between two identical, charged parallel plates separated by a distance 2d is related to the macroscopic electric field, E(z), and to the local field produced by the neighboring dipoles via23... 

Problem Two black infinite parallel plates separated by a transparent medium of thickness b and thermal conductivity k. Plate 2 is at temperature T2, and a known amount of energy Q(/A is added per unit area to plate 1 and removed at plate 2. What is the temperature Ti of plate 1 ... 

In Figure 2.3a, we have a fluid between two large parallel plates separated by a distance H. This system is initially at rest however, at time t = 0, the lower plate is set in motion by a constant force F in the positive x-direction at a constant velocity v. As time proceeds, the fluid gains momentum, and achieves a linear steady-state velocity profile. Newton s law of viscosity relates the shear stress to the velocity gradient in a Newtonian fluid for a one-dimensional flow we have... 

Radiation heat transfer between two surfaces can be reduced greatly by inserting belsveen the two siirface.s thin, high-reflectivity (low emissivity) sheets of material called radiation shields. Radiation heat transfer between two large parallel plates separated by N radiation shields is... 

A parallel plate separator is a modified type of plate separator using the same mechanism as the conventional gravity separators. The effectiveness of this separator is increased by installation of parallel plates in the separation chamber, without requiring... 

Separators are often made with baffles or other interior devices that increase the residence time and thus the degree of separation. The parallel plate separator is a special model of gravity separator. Many parallel plates are placed perpendicular to the flow, creating areas of low water turbulence where drops of oil can re-coalesce from the water and rise to the surface. 

Then, the radiation heat transfer between two parallel plates separated by a partition is... 

Capacitive sensors are devices that transduce the measured physical parameter, that is in the form of a mechanical displacement, into variations of a capacitor s capacitance. The capacitance between two parallel plates, separated by distance X, is... 

Parallel-plate separators isokinetic sample predicting sample train Parametric pumping Particle size measurement Penetration theory... 

COUETTE FLOW. In one form of layer flow, illustrated in Fig. 5.17, the fluid is bounded between two very large, flat, parallel plates separated by distance B. The lower plate is stationary, and the upper plate is moving to the right at a constant velocity Uq. For a newtonian fluid the velocity profile is linear, and the velocity u is zero at y = 0 and equals Uo t y = B, where y is the vertical distance measured from the lower plate. The velocity gradient is constant and equals uq/B. Considering an area A of both plates, the shear force needed to maintain the motion of the top plate is, from Eqs. (3.3) and (3.4),... 

Although the heat flow and fluid flow in packed beds are quite complex, the heat transfer characteristics can be described by a simple concept of effective thermal conductivity Ke that is based on the assumption that on a macroscopic scale the bed can be described by a continuum. Effective thermal conductivity is a continuum property that depends on temperature, bed material, and structure. It is usually determined by evaluating the steady-state heat flux between two parallel plates separated by a packed bed. The effective thermal conductivity applies very accurately to steady-state heat transfer and to unsteady-state heat transfer if (t d2p) > 1.94 x 107 s/m2 [27] in other cases, for unsteady state heat transfer the thermal... 

Water is contained between two infinite parallel plates separated by a small distance h = m. The bottom plate is held stationary, and the top plate is moved at a constant velocity U = m s so that a simple shear flow is generated between the plates. A thin band of a dye of thickness A = 10 " m is injected between and perpendicular to the plates extending fully across the gap. The band depth is very deep and may be supposed to be infinite. The dye concentration is Cq = 10 mol m, and its molecular diffusion coefficient in water is D = 10 m s ... 

The drops were timed over a distance I = 1.0220 cm. The vertical electric field was produced by appljdng a measured potential difference V across parallel plates separated by a height d = 1.4917 cm. 

Maximum entropy approach for 0-solvents. The volume fraction of polymer in the region between two parallel plates separated by a distance h was determined in a like fashion by introducing a second surface, parallel to the first, and rejecting all conformations that cross it. The relative volume fractions of polymer so calculated are shown in Fig. 17.7 for poly(oxyethylene) of molecular weight 4 000 (272 bonds). 

Mass transfer rates attainable In menbrane separation devices, such as gas permeators or dlalyzers, can be limited by solute transport through the menbrane. The addition Into the menbrane of a mobile carrier species, which reacts rapidly and reversibly with the solute of Interest, can Increase the membrane s solute permeability and selectivity by carrier-facilitated transport. Mass separation is analyzed for the case of fully developed, one-dimensional, laminar flow of a Newtonian fluid in a parallel-plate separation device with reactive menbranes. The effect of the diffusion and reaction parameters on the separation is investigated. The advantage of using a carrier-facilitated membrane process is shown to depend on the wall Sherwood number, tfrien the wall Sherwood nunber Is below ten, the presence of a carrier-facilitated membrane system is desirable to Improve solute separation. 

Consider a fluid contained between two large parallel plates separated by a distance b, as shown in Figure 7.6 and assume that the lower plate is stationary while the top plate is driven with a constant velocity u. 

It is important to note here that the situations depicted by cases 1 and 2 are rather generic in nature and can be judiciously extended to analyze the EDL formation in between two parallel plates separated by a distance of 2 h, for example. When the characteristic EDL thickness (A ) is much less than h, the location of the midplane (centerline) can mathematically be treated as a far-field one, since the charge density gradients are only confined within the EDLs adjacent to the solid surfaces, beyond which the effects of nearwall potential distribution cannot effectively penetrate. In such situations, the mathematical description introduced by case 2 readily applies. On the other hand, case 1 is the representative of a more general situation, in which the EDLs formed in the vicinity of the two plates can penetrate into the midplane and in fact may interfere with each other. We shall discuss about this situation more carefully, later in this article. 

To analyze the fundamentals of a droplet motion actuated by ctMitmuous electrowetting principles, for illustration, one may consider two infinite parallel plates separated by a distance H, with an intervening liquid. For a steady, fully developed incompressible flow along the x-direction, the Navier-Stokes equation assumes the following simplified form ... 

As an example we estimate the timescales required to continuously separate a species in a microchannel (see Fig. 3). Consider a two-dimensional channel, e.g., a fluid between two parallel plates separated by a distance h. For low concentrations (i.e., c stationary solution (i.e., Jm = 0) for the concentration ... 

The physical system to be described consists of a particle of radius R. suspended in the middle of a host gas bounded (for convenience) by infinite parallel plates separated by a distance L. This physical configuration leads to the two Knudsen numbers Kn. = and Knj = g/L- more complex geometry, additional... 

Of particular interest here is the electrical interaction between two parallel plates separated by a distance h (Figure 3.5). When h is small enough, the double layers of the two plates overlap and interaction occnrs. Combining Equations 3.24 and 3.29 and making nse of Equation 3.28, we obtain a relationship between the pressure distribution and the potential distribntion in the region between interacting plates ... 

This figure shows the symbolic representation of a capacitor, schematizing two parallel plates separated by a dielectric material (which can be vacuum). Each plate bears a population of several electric charges with the same sign, but the two populations of charges have opposite signs. 

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