Poiseuille-type flow

Figure 9.9. Deformation of a suspended droplet by shear. The undeformed droplet is shown on the left the deformed droplet, undergoing Poiseuille-type flow, is shown on the right.

Fig. 7.1 Schematic geometry of a thin supported polymer film of thickness h. Temperature fluctuations induce surface waves with wavelength X. The Poiseuille-type flow is indicated by a parabolic flow profile with velocity u...

It is important to emphasize the need to measure the surface conductance as well as the zeta potential. If the surface conductance is neglected in Eq. (18) the zeta potential can be severely underestimated. It should also be noted that the equations derived above neglect electroki-netic effects on the flow by assuming a Poiseuille type flow through the microchannel. In actuality the streaming potential creates a reverse electro-osmotic flow in the channel that decreases the overall flow rate. The decreased velocity creates the appearance of an increased fluid viscosity and is known as the electroviscous effect. Generally this effect is prevalent in microchannels less than 50 xm. 

Bulk or forced flow of the Hagan-Poiseuille type does not in general contribute significantly to the mass transport process in porous catalysts. For fast reactions where there is a change in the number of moles on reaction, significant pressure differentials can arise between the interior and the exterior of the catalyst pellets. This phenomenon occurs because there is insufficient driving force for effective mass transfer by forced flow. Molecular diffusion occurs much more rapidly than forced flow in most porous catalysts. 

Note that, as is easily observed from b.v.p.(6.4.45)-(6.4.55), with a concentration gradient present no unidirectional developed Poiseuille-type channel flow is compatible with the boundary conditions (6.4.51). A fairly complicated two-dimensional flow pattern is thus generally expected even away from the edges of the channel. The appropriate rigorous flow calculation is still to be done. Here we shall content ourselves with the following crude order of magnitude estimate of the contribution of the above-mentioned circulation to the solute transport through the channel. 

Aside from this, the data on burning velocities seem to be in almost quantitative accord with the conduction equation (XIV. 10.23) when adapted to flames in finite systems such as cylinders and spheres. The velocity of flame propagation in tubes is complicated by the viscous drag exerted by the walls on the flowing gas, together with the heat losses at the walls. The resulting Poiseuille type of flow tends to make the flame fronts parabolic in these systems. 

Poiseuille-type of flow ensues, for which we derived [1.6.4.15)... 

Electro-osmosis in a closed cell leads to a hydrodynamic pressure which, in turn, causes a Poiseuille-type back flow (sec. 1.6.4d and fig. 1.6.10), leading to a velocity profile as in fig. 4.8. For the, most common, cylindrical cell, the resulting velocity profile is as in fig. 4.15. The mathematical elaboration is as follows. Let 2 be the axial direction in the cylinder and r the radial one, then the fluid velocity in the z-direction at a distance r from the axis can be written as... 

Basic mechanisms involved in gas and vapor separation using ceramic membranes are schematized in Figure 6.14. In general, single gas permeation mechanisms in a porous ceramic membrane of thickness depend on the ratio of the number of molecule-molecule collisions to that of the molecule-wall collisions. In membranes with large mesopores and macropores the separation selectivity is weak. The number of intermolecular collisions is strongly dominant and gas transport in the porosity is described as a viscous flow that can be quantified by a Hagen-Poiseuille type law ... 

The flow situation in the porous medium comprising the column of packed resin beads is a complex one. One approach long used to model flow through porous media has been to consider the medium as made up of bundles of straight capillaries or assemblages of randomly oriented straight pores or capillaries in which the flow is of Poiseuille type. 

Flow Properties of Perfusion System. Under conditions of Poiseuille type laminar flow in capillary tubes, the Reynold s number (R ) is given b the relation ... 

Since the minimum capillary length used in our system is 4 cm, the inlet region where the fluid flow is not of Poiseuille type represents 4 % or less of the total flow path studied. P.r entrance effect would be reflected in increased protein or platelet deposition under dynamic conditions. Using radiolabeled platelets, when capillaries are cut into 1.0 cm segments for radioactive counting, there is no increase in... 

In summary, total pressure differences may arise in catalyst pores due to either (a) reactions with volume change or (b) the pressure drop in a flow reactor. Whenever such pressure differences arise we can expect a forced flow of molecules to occur. This forced flow may be either of Knudsen or Poiseuille type, depending on whether the mean free path in... 

It is assumed that a Poiseuille type pressure-flow relationship is valid for the individual vessels, whereby the apparent blood viscosity can be diameter dependent (Fahraeus-Lindqvist effect). The symmetric conductance tensor is depen-... 

In the limit of small angles, when we can use the lubrication approximation, the velocity profile Vx(z) of the flow is of the Poiseuille type because... 

This is the profile of the plane Couette flow. If a pressure gradient is applied along the Ox direction, a plane Poiseuille-type solution (equation [1.13]) is superimposed onto the Couette flow [1.30]. 

The properly (equation [1.31]) of bormdary layers regarding the pressure gradient is of the same nature as the property of pressure uniformity in planes perpendicular to the flow direction, which was observed for the Poiseuille and Couette solutions. Figure 1.6(a) shows that the bormdary layer thickness on a flat plate grows with increasing values of x. At a sufficient distance from the inlet of a pipe, the boundary layer thickness eventually exceeds the diameter of the pipe. The flow reverts to the Poiseuille type solutiou presented previously, if the Reynolds number is sufficiently low to allow the flow to remain laminar. Such flows are termed established laminar flows or developed flows , as the velocity field does not change any more when traveling downstream in the pipe, because the boundary... 

Electrical resistance leads to dissipation of electrical energy in the form of Joule heating. Similarly, hydraulic resistance leads to viscous dissipation of mechanical energy into heat by internal friction in the fluid. The role of viscous dissipation can be explained based on the schematic of transient flow behavior shown in Figure 2.9. Let an incompressible Poiseuille fluid flow takes place inside a channel at times t < 0. The constant Poiseuille-type velocity field is maintained by a constant over-pressure AP applied to the left end of the channel. The over-pressure AP is suddenly removed at time, t = 0. However, the fluid flow continues due to the inertia of the fluid. The internal viscous friction of the fluid gradually slows down the motion of the fluid, and eventually in the limit t - c the fluid comes to rest relative to the channel walls. As time passes, the kinetic energy of the fluid at t = 0 is gradually transformed into heat by the viscous friction. 

Two common types of one-dimensional flow regimes examined in interfacial studies Poiseuille and Couette flow [37]. Poiseuille flow is a pressure-driven process commonly used to model flow through pipes. It involves the flow of an incompressible fluid between two infinite stationary plates, where the pressure gradient, Sp/Sx, is constant. At steady state, ignoring gravitational effects, we have... 

Earlier experiments involved the collection of SEC effluent aliquots to measure solution viscosity in batches with the very time consuming Ubbelohde drop-time type viscometers. A continuous capillary type viscometer was first proposed for SEC by Ouano. Basically, as shown in Figure 1, a single capillary tube with a differential pressure transducer was used to monitor the viscosity of SEC effluent at the exit of the SEC column. As liquid continuously flows through the capillary (but not through the pressure transducer), the detected pressure drop (AP) across the capillary provides the measure for the fluid viscosity (h) according to the Poiseuille s viscosity law ... 

The construction of tubular electrodes may be divided into two basic types integral and demountable. Channel electrodes are only of the latter type. Final dimensions must satisfy the entry length criterion for Poiseuille flow (pp. 370 and 372). 

The investigations being very similar for these two flows, we only report here on what was done for the two-layer Poiseuille flow. In [79], the Orr-Sommerfeld equations are rigorously derived, for the second type of perturbations via Laplace and Fourier... 

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