Flow into a Capillary

The essential difficulty associated with this flow situation is that neither the stress nor the rate of strain can be calculated as a function of position from pressure-drop versus flow-rate data, which are the only measurements that can be made. As a consequence, only average quantities can be computed. Even so, some rather drastic assumptions have to be made. Cogswell assumed that the entrance pressure drop, Ap, could be separated into a shear contribution and an extensional contribution for free convergence. He derived expressions for the average exten-sional stress, o-g, and the average extension rate, e O.29)  

If and are known, one can calculate an apparent extensional viscosity as the ratio 

The main utility of this technique appears to be the ease of measurement. 

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Capillary Filling, Fig. 1 Velocity profiles corresponding to the flow into a capillary tube from a droplet... 

Capillary Filling, Figure 1 Velocity profiles corresponding to the flow into a capillary tube from a droplet Capillary Filling, Table 3 Coefficients of the fitted polynomial depicting an enhanced flow resistance (as per eq. 5)... 

Dodge, F.T., Bowles, E.B., 1984. Study of vapor flow into a capillary propellant-acquisition device. NASA-CR-167883, Southwest Research Institute, San Antonio, TX. 

Oil Contamination of Helium Gas. For more than 20 years, helium gas has been used in a variety of nuclear experiments to collect, carry, and concentrate fission-recoil fragments and other nuclear reaction products. Reaction products, often isotropically distributed, come to rest in helium at atmospheric concentration by coUisional energy exchange. The helium is then allowed to flow through a capillary and then through a pinhole into a much higher vacuum. The helium thus collects, carries, and concentrates products that are much heavier than itself, electrically charged or neutral, onto a detector... 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

Fig. 2.6.10 Specialized experimental set-up for microfluidic flow dispersion measurements. Fluid is supplied from the top, flows via a capillary through the microfluidic device to be profiled and exits at the bottom. The whole apparatus is inserted into the bore of a superconducting magnet. Spatial information is encoded by MRI techniques, using rf and imaging gradient coils that surround the microfluidic device. They are symbolized by the hollow cylinder in the figure. After the fluid has exited the device, it is led through a capillary to a microcoil, which is used to read the encoded information in a time-resolved manner. The flow rate is controlled by a laboratory-built flow controller at the outlet [59, 60].

To perform this analysis, we first prepare a dilute solution of polymer with an accurately known concentration. We then inject an aliquot of this solution into a viscometer that is maintained at a precisely controlled temperature, typically well above room temperature. We calculate the solution s viscosity from the time that it takes a given volume of the solution to flow through a capillary. Replicate measurements are made for several different concentrations, from which the viscosity at infinite dilution is obtained by extrapolation. We calculate the viscosity average molecular weight from the Mark-Houwink-Sakurada equation (Eq. 5.5). 

The GC was calibrated using a mixture of known quantities of d-limonene, d-limonene oxide (cis and trans), 2-octanone, and carvone. GC analyses were performed by injecting 1 pi samples with 1 40 split (column flow split flow), into a Hewlett-Packard 5840A GC equipped with a flame ionization detector. A fused silica capillary column 50m x 0.25 mm i.d., coated with OV-101 as a liquid phase was used. Column temperature was programmed from 50-250 C at 10 C/min, and helium was used as the carrier gas. 

This technique represents the transposition of classical polyacrylamide or agarose gel electrophoresis into a capillary. Under these conditions, the electro-osmotic flow is relatively weak. In this approach, the capillary is filled with an electrolyte impregnated into a gel that minimises diffusion and convection phenomena. In contrast to its use for proteins that are fragile and thermally unstable, CGE is ideal for separating the more rugged oligonucleotides. 

Example 7.10. Prins et al. [306] used electrowetting to control fluid motion in microchannels. To do so, they coated aluminum electrodes first with a 12 pm thick layer of parylene and then with a 10 nm thick fluoropolymer film. The channels were 0.35 mm wide. Due to the hydrophobic polymer water does not flow into the capillaries. Only after applying voltages of typically 200 V did the capillaries fill with water. When switching the voltage off, the water flowed out of the capillaries again. 

The liquid nature of blood and urine samples lends itself to flow-in or flowthrough containers. One approach, used by Qu, is to suck the sample into a capillary tube, insert an excitation optical fiber at one end of the tube, and... 

Presently a commercially available two stage vacuum system comprising a membrane (Pfeiffer MVP 006-4) and a turbo pump (Pfeiffer HiPace 10) in combination with a pressure sensor (Leybold Vacuum Ionivac ITR 90) establish a pressure of about 0.1 Pa in the system. Three electric valves are used to control the gas flow into the capillary system and for the bypasses. The use of macro devices simplifies the handling of the experimental setup and also the electronic control. Pressure drops for plasma and sample gases are accomplished by an appropriate combination of capillaries with different diameters and lengths as described in Sect. 4. 

In methods where flow is not confined by a column (such as paper and thin-layer chromatography), flow is usually driven by capillarity—the tendency of a liquid to flow into vacant capillaries having a wettable surface. Flow by capillarity will be discussed in Section 4.7. 

The opposite behavior as sketched before was detected for solutions of PS in DOP [112], Again, the critical temperature (an UCST at Tc = 12 °C in the quiescent state) turned out to be a function of the shear rate to which the solution is subjected. But, in contrast to solutions of PS and PB in DOP, here enhancements of the UCST as large as 28 °C were recorded at a shear rate of 220 s-1. Similar results have been found for PS solutions in di(2-ethyl hexyl)phthalate or in a mixture of cis- and frans-decalin [113], The solutions demixed in a converging flow from a reservoir into a capillary tube. It has been observed that an increase in the deformation rate raised the UCST or reduced the region of miscibility. In both of these studies an increase of the cloud point temperature of the polymer solutions was used as an indication of phase separation. 

One of the principal methods for measuring viscosity is based on the rate of flow of a liquid through an orifice according to Harkness (1971). In this test, a defined volume of plasma is transferred into a capillary viscometer and the efflux time required for the plasma to flow from the upper to the lower mark is measured. Using this procedure, the effect of test compounds on the viscosity of blood plasma can be determined. The test can be carried out either ex vivo or in vitro. 

The Reynolds numbers for the flow of a molten metal along a capillary braze gap are usually less than 1000 as will be shown later, and the theoretical laminar flow rates for such configurations have been calculated by Milner (1958) for both horizontal and vertical joints. He regarded the flow into a horizontal joint induced by capillary attraction as being impeded only by viscous drag, and derived a simple parabolic expression to describe such behaviour,... 

The method of capillary Jlow measures the increase in resistance for solvent flow through a capillary (or a porous plug) due to an adsorbed polymer layer. This increase can be translated into a smaller effective capillary (or pore) radius through the Hagen-Polseuille law (1.6.4.18). The hydrodynamic radius d is supposed to be given by the difference between the "covered" and the "bare" radius. In such experiments the observed hydrodynamic thickness sometimes turns out to be flow-rate dependent. In such cases an extrapolation to zero flow rate needs to be carried out. 

When there is a difference of pressure between two points of a capillary tube, the fluid flows from the high pressure side to the low pressure side of the tube. Let us assume that a Newtonian liquid flows through a capillary tube of radius r and length AL (Fig. 13.5). Once steady-state conditions are reached, that is, the applied energy is totally dissipated into friction energy, a simple balance of energy gives... 

Electrospray, also called electrohydrodynamic or electrostatic spray, is an atomization technique in which liquids are dispersed solely by the application of high voltages. A simple electrospray setup is shown in Fig. 4. A liquid flows into a metal capillary tube charged to the kilovolt range and emerges from the tip as a conical meniscus, known as a Taylor cone, due to the intense electric field (Fig. 5). An unstable jet extends continuously from the apex of the cone and disperses into charged droplets further downstream. Electrosprays have been used in industrial... 

With electrospray ionization, a fine mist of highly charged particles is produced when a liquid flows from a capillary tube into a strong electrical field (3 to 6kV).In practice, electrospray ionization sources are often directly coupled with reversed phase HPLC or capillary columns. The ability to couple a liquid chromatograph with an electrospray ionization source and a mass spectrometer allows the online removal of salts and contaminants and the analysis of complex mixtures. Although different from MALDI, electrospray provides similar sensitivity and application to the analysis of large proteins. 

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