Flow, fluid pressure-driven

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... 

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. 

The ions in the same direction as the EOF are moved faster, while the movement against the EOF is slowed down. Neutral species move at the same rate as EOF. The important feature of EOF is that fluid is electrically driven and there is no pressure drop across the overall capillary. This is in contrast to the hydrodynamic flow using pressure-driven methods such as HPLC, which is shown in Fig. 2. The advantage is the occurrence of a flat profile plug with the same velocity driven by EOF regardless of their cross-sectional position in the capillary. This can give rise to a narrow zone and higher separation efficiency for CE method. 

Holt et al. [16] measured water and gas flow through the pores of double-walled carbon nanotubes. These tubes had inner diameters less than 2 nm with nearly defect-free graphitic walls. Five hydrocarbon and eight non-hydrocarbon gases were tested to determine flow rates and to demonstrate molecular weight selectivity compared with helium. Water flow was pressure driven at 0.82 atm and measured by following the level of the meniscus in a feed tube. The results for both gas and liquid show dramatic enhancements over flux rates predicted with continuum flow models. Gas flow rates were between 16 and 120 times than expected according to the Knudsen diffusion model in which fluid molecule-wall collisions dominate the flow. 

The shear-driven fluidic approach is based on a radical modification of the fluidic channel concept. This recently developed technique for the transport of fluids in ultrathin channels based on the SDF [2] relies on a very basic hydrodynamic effect the viscous drag. This effect is present in every fluid flow, be it a liquid or a gas flow. In pressure-driven flows, the viscous drag manifests itself in an undesirable manner, as the stationary column and particle surfaces tend to slow down the fluid flow. In SDF, the viscous drag effect is... 

Basic to establishing whether power recovery is even feasible, let alone economical, are considerations of the flowing-fluid capacity available, the differential pressure available for the power recovery, and corrosive or erosive properties of the fluid stream. A further important consideration in feasibihty and economics is the probable physical location, with respect to each other, of fluid source, power-production point, and final fluid destination. In general, the tendency has been to locate the power-recoveiy driver and its driven unit where dictated by the driven-unit requirement and pipe the power-recoveiy fluid to and away from the driver. While early installations were in noncorrosive, nonerosive services such as rich-hydrocarbon absorption oil, the trend has been to put units into mildly severe seiwices such as amine plants, hot-carbonate units, and hydrocracker letdown. 

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... 

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. 

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. 

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... 

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... 

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 screw rotation analysis leads to the model equation for the extruder discharge rate. There are now two screw-rotation-driven velocities, and and a pressure-driven velocity, Pp that affect the rate. and transport the polymer fluid at right angles to one another. In order to calculate the net flow from screw rotation It Is necessary to resolve the two screw-rotation-driven velocities into one velocity, Vpi, that can be used to calculate the screw rotation-driven flow down the screw parallel to the screw axis (or centerline) as discussed in Chapter 1 and as depicted in Fig. 7.14. The resolved velocity will then be integrated over the screw channel area normal to the axis of the screw. 

The principal determinants of lOP are the rate of aqueous fluid production by the ciliary epithelium and the rate of fluid drainage (outflow) in the canal of Schlemm. Aqueous fluid production involves passive, near-isosmolar fluid secretion driven by active salt transport across the ciliary epithelium. Ion and solute transporters have been identified on pigmented and non-pigmented layers of the ciliary epithelium that probably facilitate active solute secretion. Aqueous fluid drainage is believed to involve pressure-driven bulk fluid flow in the canal of Schlemm, as well as fluid movement through the sclera by seepage across the ciliary muscle and supraciliary space. 

C. Kleinstreuer and G. Belfort, Mathematical Modeling of Fluid Flow and Solute Distribution in Pressure-driven Membrane Modules, in Synthetic Membrane Processes,... 

Pressure Driven Flow of a Newtonian Fluid Through a Slit... 

The most important assumptions when solving this problem are a steady, incompressible and isothermal flow. Let us now consider a power-law fluid, but neglect the elastic effects. Furthermore, for the solution of this specific problem, let us assume that the flow is primarily driven by drag and that there are no significant pressure drops across the die. 

Derive the cumulative residence time distribution, F(t), for pressure driven flow inside a slit of a power law fluid. Use the notation presented in Fig. 6.78. 

Poiseuille flow of a Newtonian fluid in a circular tube. For a pressure driven flow of a Newtonian fluid in a circular tube, we can obtain an analytical solution as we already did in Chapter 5. Ignoring the entrance effects, the solution for the velocity field as a function of the radial direction (see Fig. 10.18) is as follows... 

Determine the velocity profile and traction profiles in a pressure driven slit flow of a Newtonian fluid. Use Ap =1000 Pa, //, =1000 Pa-s, h 1 mm and a distance from entrance to exit of 1000 mm. Solve the problem using isoparametric 2D quadratic elements and different gauss points, compare your solutions with the analytical solution for slit flow. 

---