Tapered Capillaries

The picture of the flows in conical (tapered) capillaries has quite different features as compared with the flow in cylindrical capillaries. With an increase in the angle of taper of the capillary, oc, the contribution of the flow, 63, due to the differences in the capillary pressures of the menisci, rises and, at sufficiently large values of 

At some value of the taper a = a the total flow rate vanishes, 2 = 0. Hence, the flow of vapor, Q, and the thermocapiUary flow, Q, equalize out in a direction opposite to the direction of the film flow, Q. Such circulating flows are realized, for example, in heat pipes as well as in porous media completely saturated by a liquid. The local taper of a pore, corresponding to the condition Q = 0, depends on the temperature gradient and the radius of the capillaries. It can be found using the calculating procedure suggested in this section. 

In porous bodies, where the capillaries have a variable radius, bubbles of air, displaced toward the hot side, can be held in expanded pores if the values of r, a, and the imposed temperature gradient, AT, are such that the condition Q = 0 is satisfied. This hold-up means that the air- and, consequently, moisture-content cannot vary with time, in spite of the existence of the imposed temperature gradient, AT, as the flow under the action of the temperature gradient, AT, is compensated by a reverse flow under the action of the difference arising in the capillary pressures. 

The smaller the radius of the capillary, the greater the role of the taper even the absolute value of the taper is insignificant Whereas at r(0) = 10 cm, the effect of the taper starts to be appreciable at a KF, with r = 10- cm, it is already appreciable at a 1(H. 

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Zheng, J., Norton, D., and Shamsi, S. A. (2006). Fabrication of internally tapered capillaries for capillary electrochromatography electrospray ionization mass spectrometry. Anal. Chem. 78, 1323-1330. 

Each column fraction is analyzed for lipid material by spotting on a 5 X 10 cm silica gel thin-layer plate and exposing it to iodine vapor as follows. Prepare seven tapered capillary tubes and use these to place a spot of each solution on the TLC plate. Put at least 10 capillary applications from a single fraction on a spot. Your final plate should then have seven spots, one for each fraction. Set the plate in an iodine chamber and allow it to remain for about 15 minutes or until some spots are yellow or red-brown. The presence of lipid in a fraction is indicated by the red-brown color. Retain all the column fractions that appear to have lipid. Each of these fractions will be analyzed in part B by thin-layer chromatography. 

Small funnel and qualitative grade filter paper Test tubes, 100 X 12 mm Microcapillaries or tapered capillaries Anhydrous sodium sulfate, Na2S04 UV-VIS spectrophotometer Glass cuvettes, 3 or 1 mL Materials for paper chromatography ... 

As an alternative to the formation of frits, the packing material can be retained by means of tapers fabricated on the fused silica column. In such a case, the packed bed is completely fritless. Two types of tapered capillary columns have been prepared for CEC internally [136,137] and externally [133,138] tapered, which have been shown... 

Consider now the same tapered capillary, but placed in the inverted position, namely, wider at the bottom. This represents an unstable equilibrium. The mechanical equivalent is a sphere on the top of a convex surface, as shown in Fig. 4H(c). It is theoretically possible to find an equilibrium position for the sphere, but it will be impossible to maintain it in practice. The slightest disturbance will cause it to roll down. Unstable equilibrium is the result of positive feedback. Removing the system from its state of equilibrium creates a force in the direction of removing it even further from equilibrium. 

Fortunately, the normal manufacturing process of glass tubing produces slightly tapered capillaries, and the problem does not arise, unless one connects the capillary in the electrocapillary electrometer in the wrong direction. 

Capillary forces offer a coherent explanation for the drying periods of many materials. If a tapered capillary is filled with water and exposed to a current of air, the meniscus at the smaller end remains stationary while the tube empties from the wider end. A similar situation exists in a wet particulate bed and the phenomenon is explained by the concept of suction potential. A negative pressure exists below the meniscus of a curved liquid surface which is proportional to the surface tension, X, and inversely proportional to the radius of curvature, r. (The meniscus is assumed to be a part of a hemisphere.) This negative pressure or suction potential may be expressed as the height of liquid, expressed by Eq. (25),... 

Chiu, D. T., Hsiao, A., Gaggar, A., Garza-Lopez, R. A., Orwar, O., and Zare, R. N., Injection of ultra small samples and single molecules into tapered capillaries. Anal. Chem., 69, 1801-1807, 1997. 

To produce micrometer sized focused beams, one employs highly demagnifying optics to image the source onto the sample. Such optics can include Kirkpatrick-Baez mirrors, Fresnel zone plates, tapered capillaries, and compound refractive lenses, all of which have been used to produce submicron focal spots at third generation storage rings. 

For imaging with X-rays, the X-ray beam can be focused on a small spot using zone plates, Kirkpatrick-Baez mirrors, or tapered capillaries (Attwood 2000 Bertsch and Hunter... 

For imaging at the P, S, and Cl -absorption edges and for other heavy element absorption edges, researchers use pinholes (at several synchrotrons), tapered capillaries (GN George, personal communication Steve Heald and colleagues at the APS Bilderback et al. 1994), Kirkpatrick-Baez mirrors (at several synchrotrons), and also zone... 

Fang XH, Adams M, Pawliszyn J (1999) A model of thermally generated pH gradients in tapered capillaries. Analyst 124 335... 

Later, it was discovered that a short tapered capillary ( 1 cm), placed in proximity ( 1 mm) to the MS inlet, could also support electrospray - even in the absence of a power supply, electrical grounding, or ultrasound [109]. Since there was no direct electric contact at the sample capillary, this method was named contactless atmospheric pressure ionization (C-API) [109] or contactless ESI [110]. Figure 2.15 shows the putative mechanism of the ion formation in C-API. Rearrangement of electric charges at the end of the tapered capillary is induced by the electric field present near the MS inlet. 

Type C. The adsorption branch is steep, at intermediate pressures the desorption branch is sloping. These are typical of a heterogeneous distribution of pores of some of the following shapes tapered or double tapered capillaries and wedge formed capillaries with closed sides and open ends. 

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