Poisseuille flow

An important advantage of the use of EOF to pump liquids in a micro-channel network is that the velocity over the microchannel cross section is constant, in contrast to pressure-driven (Poisseuille) flow, which exhibits a parabolic velocity profile. EOF-based microreactors therefore are nearly ideal plug-flow reactors, with corresponding narrow residence time distribution, which improves reaction selectivity. 

FIG. 15.2 Types of simple shear flow. (A) Couette flow between two coaxial cylinders (B) torsional flow between parallel plates (C) torsional flow between a cone and a plate and (D) Poisseuille flow in a cylindrical tube. After Te Nijenhuis (2007). 

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. 

The departure from equilibrium occurs primarily on account of appearance of gradients such as temperature and concentration leading to flow of heat or of some species and subsequently leading to a specific non-equilibrium state. Earlier in the first instance, uncoupled flows, e.g. heat conduction, Poisseuille flow and electrical conduction, were the subject of investigation. Discussion of such processes has been given due attention in conventional Physical Chemistry texts. However, complex and exotic phenomena in the non-equilibrium thermodynamics provide a good tool for understanding such phenomena. 

Middleman, S. (1977). Fundamentals of Polymer Processing, McGraw-Hill, New York, pp. 301-306 (for RTD) and 86-88 (for Poisseuille flow). 

For laminar flow of fluid through a pipe experieneing viseous drag. Carman (1937, 1956) applied the Flagen-Poisseuille Equation... 

For all capillary instruments the time t needed for a certain volume V of the solution to flow through a thin capillary of length l and radius R is measured. Assuming a laminar flow, the Hagen-Poisseuille equation can be applied, leading to... 

The Mean Velocity of Laminar Pipe Flow Use the macroscopic mass-balance equation (Eq. 2.4.1) to calculate the mean velocity in laminar pipe flow of a Newtonian fluid. The velocity profile is the celebrated Poisseuille equation ... 

Velocity profiles across the capillary have a Poisseuille shaped flow and the expression predicts that the electroosmotic coefficient of permeability should vary with the square of the radius. In practice, it is found generally that this law is not as satisfactory as the Helmholtz-Smoluchowski approach for predicting electroosmotic behavior in soils. The failure of small pore theory may be because most clays have an aggregate structure with the flow determined by the larger pores [6], Another theoretical approach is referred to as the Spiegler Friction theory [25,6]. Its assumption, that the medium for electroosmosis is a perfect permselective membrane, is obviously not valid for soils, where the pore fluid comprises dilute electrol d e. An expression is derived for the net electroosmotic flow, Q, in moles/Faraday,... 

Laminar flow is characterized by a parabolic velocity profile according to the Hagen-Poisseuille law ... 

Figure V - 8. Schematic drawings depicting Poisseuille (or viscous flow) and Knudseo flow.

The contribution of convective flow is the main term in any description of transport through porous membranes. In nonporous membranes, however, the convective flow term can be neglected and only diffusional flow contributes to transport.It can be shown by simple calculations that only convective flow contributes to transport in the case of porous membranes (microfiltration). Thus, for a membrane with a thickness of 100 pm, an average pore diameter of 0.1 pm, a tortuosity C of 1 (capillar) membrane) and a porosity e of 0.6, water flow at 1 bar pressure difference can be calculated from the Poisseuille equation (convective flow), i.e. 

Reply bv the Authors We make the assumption that the parabolic temperature approximation is adequate in regions where reverse (Poisseuille dominated) flow takes place, even though it is strictly only true for planar Couette flow. To do anything better would also mean abandoning the mean cross-film viscosity assumption, which would make the modelling much more complex. The mean film temperature therefore bears the same relationship to the contact surface temperatures as elsewhere. Compression effects and increasing shear in the inlet region lead to a small rise... 

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