Capillary constant

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]. 

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.)... 

As illustrated in Fig. XU-13, a drop of water is placed between two large parallel plates it wets both surfaces. Both the capillary constant a and d in the figure are much greater than the plate separation x. Derive an equation for the force between the two plates and calculate the value for a 1-cm drop of water at 20°C, with x = 0.5, 1, and 2 mm. 

For the Hg mass flow-rate m = k heB = he(SjK, where heB is the effective Hg column height (corrected for capillary back-pressure, see p. 118) and is known as the capillary constant, we then find... 

P. Curie, On the formation of crystals and on the capillary constants of their different faces,/. Chem. Eden., 47,1970, 636-7 (translation of Bull. Soc. Franc. Min. Cryst., 8,1885, 145-50)... 

The surface tension.—The surface tension of liquid chlorine13 at —72° is 33-65 dynes per cm., 3T61 at —6T5° 29"28 at —49-5° 26-55 at 35 3° and 25 33 at —28"7. The temp, coeff. of the moleoular surface energy is 2 04, very near to the characteristic value for non-associated liquids, and hence it is supposed the molecules of liquid chlorine are present in the state of two-atom molecules, Cl2. The surface tension, a, of liquid bromine 14 at 0° is o-=42-OO(l-O-OO3810) dynes per cm. The values observed by W. Ramsay and E. Aston are 40 27 dynes per cm. at 10"6 34"68 at 46° and 29 51 at 78-1°. The temp, coeff. agrees with the assumption that the molecules are not more complex than is represented by Br2. According to R. Schiff, the atomic cohesion, a2, on the assumption that the capillary constant is an additive quality, are, in terms of hydrogen unity, 7, 13, and 19 for chlorine, bromine, and iodine respectively. 

The capillary constants 31 of molten sodium and potassium sulphate are respectively a2=17 64 and 17 25 sq. mm. while the surface tensions are respectively 182 and 177 7 dynes per cm. F. M. Jager s values for the surface tension (dynes per cm.), sp. gr., and mol. surface energy (ergs per sq. cm.) of molten alkali sulphates are indicated in Table XXXVIII. 

The flowrate is virtually constant if (Ppn - Pc) kcap is much greater than (Pc - PQ) kc and if Ppn is much greater than Pc where Fc = flow through the column, Ppn = inlet pressure ahead of capillary, Pc = pressure at head of column, P0 = outlet pressure, kcap = capillary constant, and kc = column constant. 

R. Lorenz and W. Herz studied some relations of the surface tensions of the family of halides. N. de Kolossowsky studied the relation between the capillary constants and the heat of vaporization. 

What is a large and what is a small structure In practice this is a relevant question because for small structures we can neglect pgh and use the simpler equation. Several authors define the capillary constant y/2 /pg (as a source of confusion other authors have defined y/jJpg as the capillary constant). For liquid structures whose curvature is much smaller than the capillary constant the influence of gravitation can be neglected. At 25° C the capillary constant is 3.8 mm for water and 2.4 mm for hexane. 

For many applications the wetting behavior of a network of fibres is important. An example is the water repellent ability of clothing. As a simple model we consider a bundle of parallel cylinders which are separated by a certain spacing. This spacing is assumed to be small compared to the capillary constant, so that the shape of the liquid surface is assumed to be determined only by the Laplace equation. Practically, this leads to cylindrical liquid surfaces. 

Table 62—Values of Capillary Constant Kc after Keen (1918-1919) and...

Work of Richards—L. A. Richards (1931) gave an excellent theoretical presentation of the factors involved in a study of capillary constants. He succeeded in establishing a general capillary equation and gave a method for determining conductivity. The conductivity was defined as the constant contained in Darcy s equation (Eq 13-2)... 

The capillary constant. A quantity which occurs so often that it must be defined at once is the so-called capillary constant . The approximate formula (5) of Chapter I, for the rise of a liquid in... 

A few writers, including Rayleigh, have used another capillary constant, with the same symbol a, half that defined above this is, however, much the commonest. 

For drops with an x90 three or four times greater than the capillary constant, Worthington, (1885), derived the approximate expression... 

The diffusion coefficient of sodium bromide is 0 86 at 10° for soln. of sodium bromide containing 2 9 mols. per litre and for iV-soln. of potassium bromide, 1 13 per sq. cm. per day. The capillary constant of fused sodium bromide is 2=4-08, and potassium bromide, 4.-49 gq mm. The surfftce tensions are respectively 49 0 and 48 4 dynes per cm. W. Herz and G. Anders 21 measured the viscosities of soln. of alkali bromides and F. Korber the effect of press, on the viscosities as indicated in Table XIX. 

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