Pressure driven flows

Hydrodynamic flow (HDF) in microchannels can be driven by pressure, and this is normally achieved by using a pump as in HPLC or by using suction. 

Pressure-driven liquid flow can also be achieved by a piezoelectric actuator and a pivoted lever for linear displacement amplification (nine-fold) on a PMM A chip. Flow rate of 1 nL/min has been attained [380]. 

Hydrostatic flow (based on liquid level difference) has been used to introduce beads into microchannels. This method has been found to be superior to the use of HDF [959], 

A reduced pressure was employed to create liquid flow so as to facilitate filling of PDMS channels with aqueous solutions. Better results, without trapped air bubbles, are achieved, as compared with the methods by capillary force or pressure gradient. This technique also allowed the filling of a 3D microchip when a single solution entry was used, and a reduced pressure was simultaneously applied to all 11 reservoirs. This was achieved by placing the whole chip under a reduced pressure [381]. 

FIGURE 3.2 Basic mechanism of aerodynamic focusing by air sheath flow. Undisturbed interaction of injected liquid flow with the channel walls and air sheath flow produces a stable two-phase flow configuration throughout the microchannel. Channel height is 100 pm [382]. Reprinted with permission from Springer Science and Business Media. 

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The flow profiles of electrodriven and pressure driven separations are illustrated in Figure 9.2. Electroosmotic flow, since it originates near the capillary walls, is characterized by a flat flow profile. A laminar profile is observed in pressure-driven systems. In pressure-driven flow systems, the highest velocities are reached in the center of the flow channels, while the lowest velocities are attained near the column walls. Since a zone of analyte-distributing events across the flow conduit has different velocities across a laminar profile, band broadening results as the analyte zone is transferred through the conduit. The flat electroosmotic flow profile created in electrodriven separations is a principal advantage of capillary electrophoretic techniques and results in extremely efficient separations. 

Figure 8.4 illustrates pressure-driven flow between flat plates. The downstream direction is The cross-flow direction is y, with y = 0 at the centerline and y = Y at the walls so that the channel height is 2Y. Suppose the slit width (x-direction) is very large so that sidewall effects are negligible. The velocity profile for a laminar, Newtonian fluid of constant viscosity is... 

FIGURE 8.4 Pressure driven flow between parallel plates with both plates stationary. 

This velocity profile is commonly called drag flow. It is used to model the flow of lubricant between sliding metal surfaces or the flow of polymer in extruders. A pressure-driven flow—typically in the opposite direction—is sometimes superimposed on the drag flow, but we will avoid this complication. Equation (8.51) also represents a limiting case of Couette flow (which is flow between coaxial cylinders, one of which is rotating) when the gap width is small. Equation (8.38) continues to govern convective diffusion in the flat-plate geometry, but the boundary conditions are different. The zero-flux condition applies at both walls, but there is no line of symmetry. Calculations must be made over the entire channel width and not just the half-width. 

Repeat Example 8.1 and obtain an analytical solution for the case of first-order reaction and pressure-driven flow between flat plates. Feel free to use software for the S5anbolic manipulations, but do substantiate your results. 

Which is better for isothermal chemical reactions, pressure driven flow or drag flow between flat plates Assume laminar flow with first-order chemical reaction and compare systems with the same values for the slit width (2Y=H), length, mean velocity, and reaction rate constant. 

Derive the equations necessary to calculate Vz y) given iJi y) for pressure-driven flow between flat plates. 

Fernandez-Suarez, M., Wong, S. Y. F., Warrington, B. H., Synthesis of a three-member array of cycloadducts in a glass microchip under pressure driven flow. 

In chemical micro process technology there is a clear dominance of pressure-driven flows over alternative mechanisms for fluid transport However, any kind of supplementary mechanism allowing promotion of mixing is a useful addition to the toolbox of chemical engineering. Also in conventional process technology, actuation of the fluids by external sources has proven successful for process intensification. An example is mass transfer enhancement by ultrasonic fields which is utilized in sonochemical reactors [143], There exist a number of microfluidic principles to promote mixing which rely on input of various forms of energy into the fluid. 

Dutta, D., Leighton, D. T, Dispersion reduction in pressure-driven flow through microetched channels. Anal. Chem. 75,1 (2001) 57-70. 

The aim of one study was to show that arrays of cycloadducts, from various precursors, can be made in a single run in one chip [18]. In addition, this study served more generally to demonstrate the feasibility and advantages of pressure-driven flow in micro chips exemplary of one prominent organic reaction. The advantages and drawbacks of pressure-driven flow as compared with electroosmotic flow (for EOF see [14]) were discussed [18]. 

Viscometric flow theories describe how to extract material properties from macroscopic measurements, which are integrated quantities such as the torque or volume flow rate. For example, in pipe flow, the standard measurements are the volume flow rate and the pressure drop. The fundamental difference with spatially resolved measurements is that the local characteristics of the flows are exploited. Here we focus on one such example, steady, pressure driven flow through a tube of circular cross section. The standard assumptions are made, namely, that the flow is uni-directional and axisymmetric, with the axial component of velocity depending on the radius only. The conservation of mass is satisfied exactly and the z component of the conservation of linear momentum reduces to... 

R. E. Hampton, A. A. Mammoli, A. L. Graham, N. Tetlow, S.A. Altobelli 1997, (Migration of particles undergoing pressure-driven flow in a circular conduit), /. Rheol. 41, 621. 

An intact polythene membrane within the concrete base of a building will prevent pressure driven flow of radon into the building from the soil, even if the concrete is cracked. Diffusive flow of radon into the building will also be reduced because of the comparatively low diffusion coefficient of radon in polythene ( v 10 7 cm2 s"1). No significant improvement was achieved by substituting a 50 ym sheet of mylar for polythene (mylar diffusion coefficient x 10"11 cm2 s"1). In this case additional difficulties were experienced in sealing the less flexible material to the walls. 

A new concrete floor incorporating barriers to radon transport from the subsoil appeared to be only partially successful in reducing radon decay-product concentrations. It was shown that the Venturi effect of the wind across two chimney stacks caused pressure-driven flow of radon from the ground. Covering the fireplaces to eliminate this effect resulted in concentrations below the reference level. 

Careful sealing of the floor-to-wall joints and of the ground floor walls was unsuccessful in reducing pressure-driven flow of radon from the subsoil. This merely diverted the flow of radon up through the internal walls of the dwelling and into upstairs rooms. The problem arose in this old dwelling because it has very porous walls and no damp proof course, thus allowing radon to by-pass the sealed floor. Incorporation of a passive radon barrier into the floor of a modern house with less porous walls is likely to be effective. 

Indoor radon in most houses come primarily from soil gas infiltrating into the house because of pressure-driven flow. The radon decays into a series of decay products to which most of the health effects are attributed. These decay products begin attached to ultrafine particles that either plateout on surfaces such as walls, furniture, etc., or become attached to larger particles that are present in the indoor air. The nature of those particles depends on the kinds of sources that exist in the house such as smokers, gas stoves, etc. 

Among the most important fluid handling components in an LOC are pumps and valves. There are two main methods by which fluid actuation through microchannels can be achieved pressure driven and electroosmotic flow. In pressure driven flow, the fluid is... 

Pressure design, piping system, 79 480-482 Pressure-driven filtration, 27 665 Pressure-driven flow, in microfluidics, 26 962, 963... 

Resistance functions have been evaluated in numerical compu-tations15831 for low Reynolds number flows past spherical particles, droplets and bubbles in cylindrical tubes. The undisturbed fluid may be at rest or subject to a pressure-driven flow. A spectral boundary element method was employed to calculate the resistance force for torque-free bodies in three cases (a) rigid solids, (b) fluid droplets with viscosity ratio of unity, and (c) bubbles with viscosity ratio of zero. A lubrication theory was developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions were derived to accurately represent the numerical data over the entire range of particle positions in a tube for all particle diameters ranging from nearly zero up to almost the tube diameter. The resistance functions formulated are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels. 

An advantage of CEC is that the pressure drop across the column is very low so that small particles and longer columns can be used. Also, the electroosmotic flow results in a plug flow profile as opposed to a parabolic or laminar flow derived from a pressure-driven flow (Figure 1). The combination of these advantages leads to highly efficient columns that can be applied to separate components in a mixture. 

The shear rate in the channel contains contributions from the rotational motion of the screw and the pressure-driven flow. The calcuiation of the shear rate, 7, using Eq. 1.24, is based on the rotational component only and ignores the smaller contribution due to pressure flow. For the calculations here, Eq. 1.24 can be used. 

Eqs. 7.22 and 7.24 represent the velocities due to screw rotation for the observer in Fig. 7.9, which corresponds to the laboratory observation. Eq. 7.25 is equivalent to Eq. 7.24 for a solution that does not incorporate the effect of channel width on the z-direction velocity. For a wide channel it is the z velocity expected at the center of the channel where x = FK/2 and is generally considered to hold across the whole channel. The laboratory and transformed velocities will predict very different shear rates in the channel, as will be shown in the section below relating to energy dissipation and temperature estimation. Finally, it is emphasized that as a consequence of this simplified screw rotation theory, the rotation-induced flow in the channel is reduced to two components x-direction flow, which pushes the fluid toward the outlet, and z-direction flow, which tends to carry the fluid back to the inlet. Equations 7.26 and 7.27 are the velocities for pressure-driven flow and are only a function of the screw geometry, viscosity, and pressure gradient. 

The mass generalized pressure-driven flow for screws with multiple flight starts from Eq. Ill is as follows ... 

The combined mass flow for rotation-driven and pressure-driven flow is given by Eq. 1.28 and is the expected rate of the process. The average shear viscosity is calculated using the average shear rate in the channel for screw rotation and the bulk temperature. This method is also known as the generalized Newtonian method. 

The calculation method and equations presented in the previous sections are for Newtonian fluids such that the flow due to screw rotation and the downstream pressure gradient can be solved independently, that is, via the principle of superposition. Since most resins are highly non-Newtonian, the rotational flow and pressure-driven flow in principle cannot be separated using superposition. That is, the shear dependency of the viscosity couples the equations such that they cannot be solved independently. Potente [50] states that the flows and pressure gradients should only be calculated using three-dimensional (3-D) numerical methods because of the limitations of the Newtonian model. 

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