The Capillary

Separation occurs in the capillary. Ideally, the capillary should be chemically and physically resistant, precisely produced with narrow internal, diameters (typical dimensions for the internal diameter of these capillaries ranges from 20 to 100 ju.m), not prone to adsorb solutes, endowed with a high thermal conductivity, transparent to UV radiation, and inexpensive. Fused silica capillaries meet almost all the foregoing requirements (except that, in some instances, they tend to adsorb large proteins) for these reasons, they are the first choice in CE. 

The internal surface of the capillaries can be uncoated, to allow the inner silica surface to be in contact with buffers and analytes, or coated (to shield the silica surface from interactions with analytes prior to filling). The external surfaces of the capillaries are coated with a layer of polyimide for flexibility. Where the capillary needs to be optically transparent to allow detection, the external coating is removed. In this window the capillary is very fragile but is transparent, even in the low UV region. When detection is carried out directly in the capillary, its effective length is from the injection end to the detection window, whereas the total length corresponds to the distance from the two ends of the capillary (Fig. 3.7). Capillaries may vary in length from 20 to 100 cm. 

Washing the capillary (in general with NaOH, 0.1-1.0 Af) dissolves a thin film of silica from the inner wall, exposing a clean surface. A more sophisticated 

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Beckmann thermometer A very sensitive mercury thermometer with a small temperature range which can be changed by transferring mercury between the capillary and a bulb reservoir. Used for accurate temperature measurements in the determination of molecular weights by freezing point depression or boiling point elevation. 

A base, formed by the bacterial degradation of histidine, and present in ergot and in many animal tissues, where it is liberated in response to injury and to antigen-antibody reactions. If injected it causes a condition of shock with dilatation of many blood vessels, loss of plasma from the capillaries to the tissues and a rapid fall in blood pressure. It is normally prepared from protein degradation products. 

The capillary effect is apparent whenever two non-miscible fluids are in contact, and is a result of the interaction of attractive forces between molecules in the two liquids (surface tension effects), and between the fluids and the solid surface (wettability effects). 

Notice that the capillary pressure is greater for smaller capillaries (or throat sizes), and that when the capillary has an infinite radius, as on the outside of the capillaries in the tray of water, P, is zero. 

Consider the pressure profile in just one of the capillaries in the experiment. 

Inside the capillary tube, the capillary pressure (P ) is the pressure difference between the oil phase pressure (PJ and the water phase pressure (P ) at the interface between the oil and the water. 

The capillary pressure can be related to the height of the interface above the level at which the capillary pressure is zero (called the free water level) by using the hydrostatic pressure equation. Assuming the pressure at the free water level is PI ... 

This is consistent with the observation that the largest difference between the oil-water interface and the free water level (FWL) occurs in the narrowest capillaries, where the capillary pressure is greatest. In the tighter reservoir rocks, which contain the narrower capillaries, the difference between the oil-water interface and the FWL is larger. 

If a pressure measuring device were run inside the capillary, an oil gradient would be measured in the oil column. A pressure discontinuity would be apparent across the interface (the difference being the capillary pressure), and a water gradient would be measured below the interface. If the device also measured resistivity, a contact would be determined at this interface, and would be described as the oil-water contact (OWC). Note that if oil and water pressure measurements alone were used to construct a pressure-depth plot, and the gradient intercept technigue was used to determine an interface, it is the free water level which would be determined, not the OWC. 

On a microscopic scale (the inset represents about 1 - 2mm ), even in parts of the reservoir which have been swept by water, some oil remains as residual oil. The surface tension at the oil-water interface is so high that as the water attempts to displace the oil out of the pore space through the small capillaries, the continuous phase of oil breaks up, leaving small droplets of oil (snapped off, or capillary trapped oil) in the pore space. Typical residual oil saturation (S ) is in the range 10-40 % of the pore space, and is higher in tighter sands, where the capillaries are smaller. 

Since the blocked gas inside of the capillary is dissolving in the liquid and then diffusing towards the exit of the channel, the meniscus of the liquid crosses the position l and goes deeper. This second stage of capillary filling with liquid is called diffusive imbibition and plays an important role in PT processes. The effect of diffusive imbibition upon PT sensitivity has been studied in [7]. 

As a rule, in practice, the surface defects are revealed by the magnetic-powder and capillary methods. However, in the case of nonmagnetic materials the magnetic-powder methods are not applicable and the capillary ones do not detect the subsurface defects or defects filled with the lubricant after the grinding, wire-drawing and so on. 

An approximate treatment of the phenomenon of capillary rise is easily made in terms of the Young-Laplace equation. If the liquid completely wets the wall of the capillary, the liquids surface is thereby constrained to lie parallel to the wall at the region of contact and the surface must be concave in shape. The... 

Similarly, the identical expression holds for a liquid that completely fails to wet the capillary walls, where there will be an angle of contact between the liquid and the wall of 180°, a convex meniscus and a capillary depression of depth h. 

The total weight of the column of liquid in the capillary follows from Eq. 11-12 ... 

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. 

The capillary rise method is generally considered to be the most accurate means to measure 7, partly because the theory has been worked out with considerable exactitude and partly because the experimental variables can be closely controlled. This is to some extent a historical accident, and other methods now rival or surpass the capillary rise one in value. 

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. 

The general attributes of the capillary rise method may be summarized as follows. It is considered to be one of the best and most accurate absolute methods, good to a few hundredths of a percent in precision. On the other hand, for practical reasons, a zero contact angle is required, and fairly large volumes of solution are needed. With glass capillaries, there are limitations as to the alkalinity of the solution. For variations in the capillary rise method, see Refs. 11, 12, and 22-26. 

The table is used in much the same manner as are Eqs. 11-19 and 11-20 in the case of capillary rise. As a first approximation, one assumes the simple Eq. II-10 to apply, that is, that X=r, this gives (he first approximation ai to the capillary constant. From this, one obtains r/ai and reads the corresponding value of X/r from Table II-2. From the derivation of X(X = a /h), a second approximation a to the capillary constant is obtained, and so on. Some mote recent calculations have been made by Johnson and Lane [28]. 

Calculate to 1% accuracy the capillary rise for water at 20°C in a 1.2-cm-diameter capillary. 

Derive the equation for the capillary rise between parallel plates, including the correction term for meniscus weight. Assume zero contact angle, a cylindrical meniscus, and neglect end effects. 

Derive, from simple considerations, the capillary rise between two parallel plates of infinite length inclined at an angle of d to each other, and meeting at the liquid surface, as illustrated in Fig. 11-23. Assume zero contact angle and a circular cross section for the meniscus. Remember that the area of the liquid surface changes with its position. 

The following values for the surface tension of a 10 Af solution of sodium oleate at 25°C are reported by various authors (a) by the capillary rise method, y - 43 mN/m (b) by the drop weight method, 7 = 50 mN/m and (c) by the sessile drop method, 7 = 40 mN/m. Explain how these discrepancies might arise. Which value should be the most reliable and why ... 

A liquid of density 2.0 g/cm forms a meniscus of shape corresponding to /3 = 80 in a metal capillary tube with which the contact angle is 30°. The capillary rise is 0.063 cm. Calculate the surface tension of the liquid and the radius of the capillary, using Table II-l. 

While Eq. III-18 has been verified for small droplets, attempts to do so for liquids in capillaries (where Rm is negative and there should be a pressure reduction) have led to startling discrepancies. Potential problems include the presence of impurities leached from the capillary walls and allowance for the film of adsorbed vapor that should be present (see Chapter X). There is room for another real effect arising from structural peiturbations in the liquid induced by the vicinity of the solid capillary wall (see Chapter VI). Fisher and Israelachvili [19] review much of the literature on the verification of the Kelvin equation and report confirmatory measurements for liquid bridges between crossed mica cylinders. The situation is similar to that of the meniscus in a capillary since Rm is negative some of their results are shown in Fig. III-3. Studies in capillaries have been reviewed by Melrose [20] who concludes that the Kelvin equation is obeyed for radii at least down to 1 fim. 

Calculate the vapor pressure of water when present in a capillary of 0.1 m radius (assume zero contact angle). Express your result as percent change from the normal value at 25°C. Suppose now that the effective radius of the capillary is reduced because of the presence of an adsorbed film of water 100 A thick. Show what the percent reduction in vapor pressure should now be. 

The scattering techniques, dynamic light scattering or photon correlation spectroscopy involve measurement of the fluctuations in light intensity due to density fluctuations in the sample, in this case from the capillary wave motion. The light scattered from thermal capillary waves contains two observables. The Doppler-shifted peak propagates at a rate such that its frequency follows Eq. IV-28 and... 

Usually one varies the head of mercury or applied gas pressure so as to bring the meniscus to a fixed reference point [118], Grahame and co-workers [119], Hansen and co-workers [120] (see also Ref. 121), and Hills and Payne [122] have given more or less elaborate descriptions of the capillary electrometer apparatus. Nowadays, the capillary electrometer is customarily used in conjunction with capacitance measurements (see below). Vos and Vos [111] describe the use of sessile drop profiles (Section II-7B) for interfacial tension measurements, thus avoiding an assumption as to the solution-Hg-glass contact angle. 

The capillary rise on a Wilhelmy plate (Section II-6C) is a nice means to obtain contact angles by measurement of the height, h, of the meniscus on a partially immersed plate (see Fig. 11-14) [111, 112]. Neumann has automated this technique to replace manual measurement of h with digital image analysis to obtain an accuracy of 0.06° (and a repeatability to 95%, in practice, of 0.01°) [108]. The contact angle is obtained directly from the height through... 

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