Parallel plate flow

Parallel plates, flow between, 15 720t Parallel plate viscometers, 21 735-736 Parallel-pore model, 25 306 Parallel pores, 25 301 Parallel synthesis, microwaves in, 16 549-552... 

Divided parallel plate flow-through cells are especially advantageous for laboratory use because they can easily be constructed from two Teflon cell body halves according to Figure 22.14. In such a construction, ion-exchange membranes can easily be applied for the separation of the two cell compartments. For anodic oxidations, cation exchange membranes like Nafion are most often used. For cathodic reactions, anion exchange membranes are applicable. Asbestos or microporous membranes can also be used as separators. 

Figure 22.14 Divided parallel-plate flow-through cell (D = diaphragm W = working electrode AUX = auxiliary electrode R = reference electrode).

The field of transport phenomena is the basis of modeling in polymer processing. This chapter presents the derivation of the balance equations and combines them with constitutive models to allow modeling of polymer processes. The chapter also presents ways to simplify the complex equations in order to model basic systems such as flow in a tube or Hagen-Poiseulle flow, pressure flow between parallel plates, flow between two rotating concentric cylinders or Couette flow, and many more. These simple systems, or combinations of them, can be used to model actual systems in order to gain insight into the processes, and predict pressures, flow rates, rates of deformation, etc. 

The fluid that is confined between the parallel plates flows due to a drag flow caused by an upper plate velocity, uq, and a pressure flow caused by a pressure drop in the x-direction of Ap. The combined analytical velocity field is given by... 

Example Oblique Transmission through Parallel Plate Flow... 

Applications of optical methods to study dilute colloidal dispersions subject to flow were pioneered by Mason and coworkers. These authors used simple turbidity measurements to follow the orientation dynamics of ellipsoidal particles during transient shear flow experiments [175,176], In addition, the superposition of shear and electric fields were studied. The goal of this work was to verify the predictions of theories predicting the orientation distributions of prolate and oblate particles, such as that discussed in section 7.2.I.2. This simple technique clearly demonstrated the phenomena of particle rotations within Jeffery orbits, as well as the effects of Brownian motion and particle size distributions. The method employed a parallel plate flow cell with the light sent down the velocity gradient axis. 

Figure 10.5 Top view of a parallel-plate flow cell where the light beam is directed normal to...

Example 2.5 Parallel Plate Flow The methodology for formulating and solving flow problems involves the following well-defined and straightforward steps ... 

Optimum Gap Size in Parallel Plate Flow Show that for the flow situation in Example 2.5, for a given net flow rate the optimum gap size for maximum pressure rise is... 

Parallel-Plate Flow with Viscous Dissipation Consider the nonisothermal flow... 

Fig. E3.6c Dimensionless flow rate versus dimensionless pressure gradient, with the Power Law exponent n as a parameter, for parallel-plate flow, as given in Eq. E3.6-24.

The simplifying assumptions for solving this flow problem are the same as those used in Example 2.5 for parallel plate flow, namely, we assume the flow to be an incompressible,... 

Parallel-Plate Flow of Newtonian Fluids A Newtonian polymeric melt with viscosity 0.21b(S/in2 and density 481b/ft3, is pumped in a parallel-plate pump at steady state and isothermal conditions. The plates are 2 in wide, 20 in long, and 0.2 in apart. It is required to maintain a flow rate of 50 lb/h. (a) Calculate the velocity of the moving plate for a total pressure rise of 100 psi. (b) Calculate the optimum gap size for the maximum pressure rise, (c) Evaluate the power input for the parts (a) and (b). (d) What can you say about the isothermal assumption ... 

Example 7.3 Effect of Viscosity Ratio on Shear Strain in Parallel-Plate Geometry Consider a two-parallel plate flow in which a minor component of viscosity /t2is sandwiched between two layers of major component of viscosities /q and m (Fig. E7.3). We assume that the liquids are incompressible, Newtonian, and immiscible. The equation of motion for steady state, using the common simplifying assumption of negligible interfacial tension, indicates a constant shear stress throughout the system. Thus, we have... 

Strain Distribution Function in Parallel Plate Flow (a) Derive the SDF F(y) for the parallel-plate flow with a superimposed pressure gradient in the range — 1/3 < qp/qd < 1/3. The velocity profile is given by... 

Distributed Parameter Models Both non-Newtonian and shear-thinning properties of polymeric melts in particular, as well as the nonisothermal nature of the flow, significantly affect the melt extmsion process. Moreover, the non-Newtonian and nonisothermal effects interact and reinforce each other. We analyzed the non-Newtonian effect in the simple case of unidirectional parallel plate flow in Example 3.6 where Fig.E 3.6c plots flow rate versus the pressure gradient, illustrating the effect of the shear-dependent viscosity on flow rate using a Power Law model fluid. These curves are equivalent to screw characteristic curves with the cross-channel flow neglected. The Newtonian straight lines are replaced with S-shaped curves. 

Next, we explore some nonisothermal effects on of a shear-thinning temperature-dependent fluid in parallel plate flow and screw channels. The following example explores simple temperature dependent drag flow. 

This holds everywhere in the parallel-plate flow region formed by the slit, where z-constant lines are isobars as a consequence. Integrating Eq.12.3-1 yields... 

Pw Total power input in parallel plate flow (E2.5-22)... 

Shear stress The shear stress in the four mentioned geometries can be determined by measuring the moment M (in Nm), or pressure AP (in N/m2) during flow. For the Couette flow and the cone and plate flow the relationships for shear stress and shear rate are easy to handle in order to determine the viscosity. For the parallel plates flow and Poisseuile flow, however, more effort is needed to determine the shear stress at the edge of the plate, qR, in parallel plates flow or the shear rate at the wall, qw, in Poisseuile flow. In Table 15.1 equations for shear stresses and shear rates are shown. 

Cell Adhesion to Immobilized Platelets Parallel-Plate Flow Chamber... 

Assemble the platelet-coated coverslip on a parallel-plate flow chamber which is then mounted on the stage of an inverted microscope equipped with a CCD camera connected to a VCR and TV monitor. 

The mechanical force most relevant to platelet-mediated thrombosis is shear stress. The normal time-averaged levels of venous and arterial shear stresses range between 1-5 dyn/cm2 and 6 10 dyn/cm2, respectively. However, fluid shear stress may reach levels well over 200 dyn/cm2 in small arteries and arterioles partially obstructed by atherosclerosis or vascular spasm. The cone-and-plate viscometer and parallel-plate flow chamber are two of the most common devices used to simulate fluid mechanical shearing stress conditions in blood vessels. 

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