Capillary velocity

Consequently, the time-dependent fluid front position in a surface-directed microfluidic device tends to be dependent on system geometry, intrinsic fluid properties, fluid-substrate interactions, and the square root of time. This dependency has been derived theoretically and observed for a number of capillary-driven microfluidic systems such as the v-groove geometry [5,6]. Noting that the ratio ylfi is a characteristic capillary velocity, U, enables the rearrangement X UcL cos This relation perhaps leads... 

Figure 3.34. Cross section of the flow in the capillary. The flow velocity is parallel to the center line of the capillary. Velocity field is parabolic.

An interesting application of the formula (1.43) is the direct deduction of the average friction length A—and consequently the capillary velocity— when the hydraulic resistance R j is known, according to... 

Let us recall that tables for such resistances as a function of the shape and dimensions of the channels have been reported in the literature for many different confined channels [28,33-36]. In the following section, we deduce velocity expressions for different usual geometrical shapes of the channel cross section. We then propose a simple method to determine the capillary velocity in an arbitrary cross section channel. Finally, we investigate the conditions for obtaining large velocities in capillary-based systems. 

It appears from Figure 1.14, that the highest velocities are obtained for channel shapes close to a circle, whereas angular and/or elongated shapes correspond to smaller velocities. Concave shapes are more detrimental to capillary velocity. This result is consistent with the observations already made by Zimmermann et al. [15] and Safavieh and Juncker [38], who used constricted channels as flow resistances to reduce the capillary flow velocity (Figure 1.15). 

Finding the average capillary velocity, < >, in exactly the same way as... 

In order to find the capillary wall shear rates, y , for both Newtonian and non-Newtonian fluids, we simply find d V /dr atr = R. This is then expressed in terms of the average capillary velocity, . For the non-Newtonian case, the wall shear rate is ... 

The second mechanism can be explained by the wall liquid film flow from one meniscus to another. Thin adsorptive liquid layer exists on the surface of capillary channel. The larger is a curvature of a film, the smaller is a pressure in a liquid under the corresponding part of its film. A curvature is increasing in top s direction. Therefore a pressure drop and flow s velocity are directed to the top. 

Templeton obtained data of the following type for the rate of displacement of water in a 30-/im capillary by oil (n-cetane) (the capillary having previously been wet by water). The capillary was 10 cm long, and the driving pressure was 45 cm of water. When the meniscus was 2 cm from the oil end of the capillary, the velocity of motion of the meniscus was 3.6 x 10 cm/sec, and when the meniscus was 8 cm from the oil end, its velocity was 1 x 10 cm/sec. Water wet the capillary, and the water-oil interfacial tension was 30 dyn/cm. Calculate the apparent viscosities of the oil and the water. Assuming that both come out to be 0.9 of the actual bulk viscosities, calculate the thickness of the stagnant annular film of liquid in the capillary. 

The most common mobile phases for GC are He, Ar, and N2, which have the advantage of being chemically inert toward both the sample and the stationary phase. The choice of which carrier gas to use is often determined by the instrument s detector. With packed columns the mobile-phase velocity is usually within the range of 25-150 mF/min, whereas flow rates for capillary columns are 1-25 mF/min. Actual flow rates are determined with a flow meter placed at the column outlet. 

The velocity with which the solute moves through the capillary due to the electroosmotic flow (Veof)-... 

McKillop and associates have examined the electrophoretic separation of alkylpyridines by CZE. Separations were carried out using either 50-pm or 75-pm inner diameter capillaries, with a total length of 57 cm and a length of 50 cm from the point of injection to the detector. The run buffer was a pH 2.5 lithium phosphate buffer. Separations were achieved using an applied voltage of 15 kV. The electroosmotic flow velocity, as measured using a neutral marker, was found to be 6.398 X 10 cm s k The diffusion coefficient,... 

In pneumatic nebulizers, the relative velocity of gas and liquid first induces a reduction in pressure above the surface of the liquid (see the calculation in Figure 19.4). The reduction in pressure is sufficient to cause liquids to flow out of capillary tubes, in accord with Poiseuille s formula (Figure 19.5). As the relative velocity of a liquid and a gas increases — particularly if the mass of liquid is small — this partial vacuum and rapid flow cause the surface of the liquid to be broken into droplets. An aerosol is formed. 

Using Poiseuille s formula, the calculation shows that for concentric-tube nebulizers, with dimension.s similar to those in use for ICP/MS, the reduced pressure arising from the relative linear velocity of gas and liquid causes the sample solution to be pulled from the end of the inner capillary tube. It can be estimated that the rate at which a sample passes through the inner capillary will be about 0.7 ml/min. For cross-flow nebulizers, the flows are similar once the gas and liquid stream intersection has been optimized. 

In a concentric-tube nebulizer, the sample solution is drawn through the inner capillary by the vacuum created when the argon gas stream flows over the end (nozzle) at high linear velocity. As the solution is drawn out, the edges of the liquid forming a film over the end of the inner capillary are blown away as a spray of droplets and solvent vapor. This aerosol may pass through spray and desolvation chambers before reaching the plasma flame. 

In the cross-flow arrangement, the argon gas flows at high linear velocity across the face of an orthogonal capillary tube containing sample solution. The partial vacuum causes liquid to lift above the end of the capillary. Here, it meets the argon and is nebulized. 

Figure 9.5a shows a portion of a cylindrical capillary of radius R and length 1. We measure the general distance from the center axis of the liquid in the capillary in terms of the variable r and consider specifically the cylindrical shell of thickness dr designated by the broken line in Fig. 9.5a. In general, gravitational, pressure, and viscous forces act on such a volume element, with the viscous forces depending on the velocity gradient in the liquid. Our first task, then, is to examine how the velocity of flow in a cylindrical shell such as this varies with the radius of the shell.

Equation (9.28) describes the velocity with which a cylindrical shell of liquid moves through a capillary under stationary-state conditions. This velocity times the cross-sectional area of the shell gives the incremental volume of liquid dV which is delivered from the capillary in an interval of time At. The total volume delivered in this interval AV is obtained by integrating this product over all values of r ... 

J ct Spra.y, The mechanism that controls the breakup of a Hquid jet has been analy2ed by many researchers (22,23). These studies indicate that Hquid jet atomisation can be attributed to various effects such as Hquid—gas aerodynamic interaction, gas- and Hquid-phase turbulence, capillary pinching, gas pressure fluctuation, and disturbances initiated inside the atomiser. In spite of different theories and experimental observations, there is agreement that capillary pinching is the dominant mechanism for low velocity jets. As jet velocity increases, there is some uncertainty as to which effect is most important in causing breakup. 

The potential dependence of the velocity of an electrochemical phase boundary reaction is represented by a current-potential curve I(U). It is convenient to relate such curves to the geometric electrode surface area S, i.e., to present them as current-density-potential curves J(U). The determination of such curves is represented schematically in Fig. 2-3. A current is conducted to the counterelectrode Ej in the electrolyte by means of an external circuit (voltage source Uq, ammeter, resistances R and R") and via the electrode E, to be measured, back to the external circuit. In the diagram, the current indicated (0) is positive. The potential of E, is measured with a high-resistance voltmeter as the voltage difference of electrodes El and E2. To accomplish this, the reference electrode, E2, must be equipped with a Haber-Luggin capillary whose probe end must be brought as close as possible to... 

---