Vertical capillaries

The simplest situation (Figure la) shows AP in a simple capillary vertically... 

This is exact—see Problem 11-8. Notice that Eq. 11-14 is exactly what one would write, assuming the meniscus to be hanging from the wall of the capillary and its weight to be supported by the vertical component of the surface tension, 7 cos 6, multiplied by the circumference of the capillary cross section, 2ar. Thus, once again, the mathematical identity of the concepts of surface tension and surface free energy is observed. 

Perhaps the best discussions of the experimental aspects of the capillary rise method are still those given by Richards and Carver [20] and Harkins and Brown [21]. For the most accurate work, it is necessary that the liquid wet the wall of the capillary so that there be no uncertainty as to the contact angle. Because of its transparency and because it is wet by most liquids, a glass capillary is most commonly used. The glass must be very clean, and even so it is wise to use a receding meniscus. The capillary must be accurately vertical, of accurately known and uniform radius, and should not deviate from circularity in cross section by more than a few percent. 

As an extension of Problem 11, integrate a second time to obtain the equation for the meniscus profile in the Neumann method. Plot this profile as y/a versus x/a, where y is the vertical elevation of a point on the meniscus (above the flat liquid surface), x is the distance of the point from the slide, and a is the capillary constant. (All meniscus profiles, regardless of contact angle, can be located on this plot.)... 

Now roll up the Carius tube (while still in a vertical position) in a strip of ordinary thick drying paper, and then place it in the heavy iron protector tube if the Carius tube is too short and tends to disappear within the iron tube, a short section of old glass tubing should first be placed in the iron tube so that the capillary of the Carius tube just projects. The function of the paper is to protect the Carius tubing from being scratched, and also (more important) to prevent the local overheating which would otherwise occur at places where the Carius tube is in direct contact with the iron tube. The sealed tube, throughout its manipulation, should be left as nearly vertical as possible, so that the contents do not leave the rounded end. 

The apparatus consists of a tube T (Fig. 76) usually of total height about 75 cm. the upper portion of the tube has an internal diameter of about I cm., whilst the lower portion is blown out as shown into a bulb of about 100 ml. capacity. Near the top of T is the delivery-tube D of coarse-bored capillary, bent as shown. The tube T is suspended in an outer glass jacket J which contains the heating liquid this jacket is fitted around T by a split cork F which has a vertical groove cut or filed m the side to allow the subsequent expansion of the air in J. The open end of the side-arm D can be placed in a trough W containing water, end a tube C, calibrated in ml. from the top downwards, can be secured ts shown over the open end of D. 

Apparatus. The apparatus is made of Pyrex glass, in one piece. It consists of a shaped bulb A (Fig. 89 of about 30 ml. capacity in which the reaction takes place, provided with an inclined inlet B at the side and a vertical ascension tube D. B serves not only as an inlet for the admission of the carrier gas but also as the route by which the reagents and test sample are introduced into the apparatus. B ends in a small ground-glass joint into which fits ajoint carrying a capillary-tube which projects well down into the bulb A (the end of the capillary should be just above the liquid level when the apparatus is charged for the determination). The upper extension of this capillary beyond the joint is provided with a tap C to control the rate of flow of the carrier gas. 

Figure 3.10 is a plot of potential against distance from the wall for a liquid in a capillary of sufficient width for its middle A to be outside the range of forces from the wall. Since the capillary condensate is in equilibrium with the vapour, its chemical potential (=p represented by the horizontal line GF, will be lower than that of the free liquid the difference in chemical potential of the condensate at A, represented by the vertical distance AF, is brought about entirely by the pressure drop, Ap = 2y/r , across the meniscus (cf. Equation (3.6)) but at some point B. say, nearer the wall, the chemical potential receives a contribution represented by the line BC, from the adsorption potential. Consequently, the reduction Ap in pressure across the meniscus must be less at B than at A, so that again... 

The flows of gas and liquid need not be concentric for aerosol formation and, indeed, the two flows could meet at any angle. In the cross-flow nebulizers, the flows of gas and sample solution are approximately at right angles to each other. In the simplest arrangement (Figure 19.11), a vertical capillary tube carries the sample solution. A stream of gas from a second capillary is blown across this vertical tube and creates a partial vacuum, so some sample solution lifts above the top of the capillary. There, the fast-flowing gas stream breaks down the thin film of sample... 

The Cannon-Fenske viscometer (Fig. 24b) is excellent for general use. A long capillary and small upper reservoir result in a small kinetic energy correction the large diameter of the lower reservoir minimises head errors. Because the upper and lower bulbs He on the same vertical axis, variations in the head are minimal even if the viscometer is used in positions that are not perfecdy vertical. A reverse-flow Cannon-Fen ske viscometer is used for opaque hquids. In this type of viscometer the Hquid flows upward past the timing marks, rather than downward as in the normal direct-flow instmment. Thus the position of the meniscus is not obscured by the film of Hquid on the glass wall. 

Example The capillary curve for one vertical plate is given by d y dx ... 

Capillary viscometers are simple and inexpensive. They are normally constructed from glass and resemble a U-tube with a capillary section between two bulbs. The initial design originated with Ostwald and is shown as part A in Figure 3.2-1. The Cannon-Fenske type, a popular modification of the Ostwald design that moves the bulbs into the same vertical axis, is shown as part B in Figure 3.2-1. 

When the adjustment has been completed, rinse the capillary well with a stream of distilled water from a wash bottle and then dry by blotting with filter paper. Insert the capillary through an inverted cone of quantitative filter paper and clamp vertically over a small beaker. Lower the levelling bulb until the mercury drops just cease to flow,... 

The expression for the capillary rise in Exercise 5.29 assumes that the tube is vertical. How will the expression be modified when the tube is held at an angle 6 (theta) to the vertical ... 

We deal here with the stability of flow in a heated capillary tube when liquid is evaporating on the meniscus. The capillary, as shown in Fig. 11.1, is a straight vertical pipe with diameter d and length 1. The wall heat flux is uniform = const. The thermal conditions on the capillary inlet and outlet are ... 

Figure 33. The micro sampler dispenser. The capillaries are shown on the turntable, and one capillary is in position, ready to be lifted to the vertical position to be emptied into the cup.

Fig. 5.1.2 Non-ideal capillary flow reactor (a) propagators [13] and (b) corresponding RTDs calculated from the propagator data, (a) The propagators indicate the distribution of average velocities over each observation time (A) ranging from 50 ms to 1 s. As the observation time increases the spins exhibit a narrowing distribution of average velocities due to the motional narrowing effect of molecular diffusion across the streamlines. The dashed vertical line represents the maximum velocity that would be present in the absence of molecular...

A liquid-solid contact angle away from 90° induces the formation of a meniscus on the free surface of the liquid in a vertical tube (the solid phase). In the nonwetting case, the meniscus concaves upwards to the air. The upwards meniscus is the result of a downward surface tension at the liquid-tube interface, causing a capillary depression. In the wetting case, the meniscus has a concave-downward configuration. The downwards meniscus is the result of an upward surface tension at the liquid-tube interface, causing a capillary rise. 

With the progressive removal of the liquid, the curve at first rises almost vertically but subsequently tapers off to acquire a gradual slope. The intersection of the tangents extended from the steep and the flat portions of the curve occurs at about S = 0.9. At this saturation, the capillary pressure is known as entry suction Pe, and the pellet strength attains its maximum (R5). 

The surface tension can be measured as a function of the applied potential as follows. Figure 2.1(b) shows the mercury in the capillary. On changing the applied potential, the height of mercury in the capillary is adjusted such that the weight of the mercury is exactly balanced by the vertical component of the surface tension, and the mercury column is thus stationary. Thus ... 

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