Capillary flow velocity constant

For forced flow separations a constant plate height independent of the solvent-front migration distance is obtained. Figure 6.3. The minimum plate height for capillary flow is always greater than the minimum for forced flow. This is an indication that the limited range of capillary flow velocities is inadequate to realize the optimum kinetic performance for the layers. At the mobile phase optimum velocity, forced flow affords more compact zones and shorter separation times compared with capillary flow. As expected the intrinsic efficiency increases with a reduction of the average particle size for the layer. 

Unlike at adiabatic conditions, the height of the liquid level in a heated capillary tube depends not only on cr, r, pl and 6, but also on the viscosities and thermal conductivities of the two phases, the wall heat flux and the heat loss at the inlet. The latter affects the rate of liquid evaporation and hydraulic resistance of the capillary tube. The process becomes much more complicated when the flow undergoes small perturbations triggering unsteady flow of both phases. The rising velocity, pressure and temperature fluctuations are the cause for oscillations of the position of the meniscus, its shape and, accordingly, the fluctuations of the capillary pressure. Under constant wall temperature, the velocity and temperature fluctuations promote oscillations of the wall heat flux. 

Conventionally, the sample is initially saturated with one fluid phase, perhaps including the other phase at the irreducible saturation. The second fluid phase is injected at a constant flow rate. The pressure drop and cumulative production are measured. A relatively high flow velocity is used to try to negate capillary pressure effects, so as to simplify the associated estimation problem. However, as relative permeability functions depend on capillary number, these functions should be determined under the conditions characteristic of reservoir or aquifer conditions [33]. Under these conditions, capillary pressure effects are important, and should be included within the mathematical model of the experiment used to obtain property estimates. 

Figure 7 reports calculations of the effect of flow velocity on the critical capillary pressure for the constant-charge electrostatic model and for different initial film thicknesses. 

The influence of interphase mass transfer between liquid-liquid slugs was investigated for nitration of aromatic compounds in a capillary-flow reactor (see Figure 5.2) [22]. This was achieved by changing flow velocity via volume flow setting, while residence time was kept constant by increasing the capillary length. 

The flow in a capillary is inhomogeneous in the sense that the shearing stress, T, and the rate of shear, G, vary with the position of the fluid inside the capillary. The velocity of the flow is maximum along the central axis but gradually drops to zero at the wall, whereas the reverse is true for the shearing stress and rate of shear. For a Newtonian flow the viscosity, j ( = r/6), remains constant at any point inside the capillary even though both T and G vary considerably from one point to another. On the other hand, for a non-Newtonian flow the viscosity varies along the radial distance of the axis. 

The above equations neglected the electro-osmotic effect. In an unobstructed capillary, the shape of the electro-osmotic flow profile is piston like. The flow velocity is constant over most of the tube cross section and drops to zero only near the tube walls. This is fortunate, as the flat flow profile of electro-osmosis will add the same velocity component to all solutes, regardless of their radial position, and thus will not cause any significant dispersion of the zone. Electro-osmotic flow causes the above equations to be modified. The migration time becomes... 

These and other equations shown in this chapter assume that the velocity at the wall of the capillary is zero, that is, there is no slip at the wall. Other typical assumptions are as follows the flow is laminar and isothermal, it is time-independent, steady along the capillary, the velocity of any fluid element is a function of the radius only, and the pressure gradient along the tube is constant. These assumptions will be discussed later. 

Flow velocity in the capillaries is calculated according to Kirch-hofFs laws and is constant over the capillary cross section. 

An alternative approach to forced flow is to seal the layer with a flexible membrane or an optically flat, rigid surface under hydraulic pressure, and to deliver the mobile phase to the layer by a pump [9,41,43-46]. Adjusting the solvent volume delivered to the layer optimizes the mobile phase velocity. In the linear development mode, the mobile phase velocity (uf) will be constant and the position of the solvent front (Zf) at any time (t) after the start of development is described by Zf = Uft. The mobile phase velocity no longer depends on the contact angle and solvent selection is unrestricted for reversed-phase layers in forced flow, unlike capillary flow systems. 

True electroosmotic flow has been demonstrated in horizontally mounted layers at modest field strengths (< 1 kV / cm) with mobile phases of high dielectric constant. Still unclear is which solvents can be used, the need for prewetted layers and ions as current carriers, the effect of local heating on zone profiles, and the effect of binder chemistry on flow, mass transfer, and thermal effects. Compared with capillary flow faster separations have been demonstrated, but the influence of flow velocity on efficiency was only treated in a qualitative sense. So far no comprehensive analysis of the kinetic properties of separations under conditions of electroosmotic flow have been performed in thin-... 

For continuous development, the mobile phase is allowed to traverse the layer under the influence of capillary forces until it reaches a predetermined position on the plate, where it is continuously evaporated. Evaporation of the mobile phase usually occurs at the plate atmospheric boundary by either natural or forced evaporation. The movement of the mobile phase to the air boundary occurs by capillary flow, but once it reaches the boundary, additional forces are applied by evaporation of the solvent. Eventually a steady state (constant velocity) is established, where the mass of solvent evaporating at the boundary is equivalent to the amount of new solvent entering the layer. Sandwich-type chambers for continuous development were reviewed by Soczewinski [124]. Perry [125] has outlined the use of the short-bed continuous development chamber for optimized continuous development with variable selection of the plate length, and Nurok [126] has proposed a theoretical model to optimize experimental conditions. Continuous development is used primarily to separate simple mixtures with a short development distance and a weaker (more selective solvent) than employed for conventional development [8]. It is not widely used in contemporary practice. 

The craze tip growth velocity V can be limited by the liquid flow velocity within the craze. Figure 10.17 shows a craze containing a length L of liquid. The liquid pressure pi at the crack tip is atmospheric, but p2 at the liquid/air interface due to the capillary attraction. If the liquid moves inside the craze with the same velocity V as the advancing craze tip, and the pore area A of the craze cross section is constant, D Arcy s law for the flow of a liquid of viscosity tj through a porous medium... 

Forced flow separations overcome the principal deficiencies of capillary flow separations by establishing a constant and optimum mobile phase velocity. Forced flow separations require specially designed developing chambers exploiting either centrifugal or pneumatic forces to drive the mobile phase through the layer. Centrifugal methods are more popular for preparative-scale separations and have been little used for analysis. The preferred approach for analytical separations is to seal the open face of the layer by contact with a flexible membrane, under hydraulic pressure, and deliver the mobile phase to... 

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