Liquid capillary rise

However, the model applied in this study is hardly realistic, since it is assumed that the foam consists of capillaries (borders) whose length is equal to the foam column height but the liquid capillary rise in them varies with time. 

K Maximum height of liquid capillary rise cm in W Roll width cm in... 

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... 

The exact treatment of capillary rise must take into account the deviation of the meniscus from sphericity, that is, the curvature must correspond to the AP = Ap gy at each point on the meniscus, where y is the elevation of that point above the flat liquid surface. The formal statement of the condition is obtained by writing the Young-Laplace equation for a general point (x, y) on the meniscus, with R and R2 replaced by the expressions from analytical geometry given in... 

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 is evident firom the theory of the method, h must be the height of rise above a surface for which AP is zero, that is, a flat liquid surface. In practice, then, h is measured relative to the surface of the liquid in a wide outer tube or dish, as illustrated in Fig. n-6, and it is important to realize that there may not be an appreciable capillary rise in relatively wide tubes. Thus, for water, the rise is 0.04 mm in a tube 1.6 cm in radius, although it is only 0.0009 mm in one of 2.7-cm radius. 

If APmax is expressed in terms of the corresponding height of a column of the liquid, that is, APmax = Ap gh, then the relationship becomes identical to that for the simple capillary rise situation as given by Eq. II-10. 

As in the case of capillary rise, Sugden [27] has made use of Bashforth s and Adams tables to calculate correction factors for this method. Because the figure is again one of revolution, the equation h = a lb + z is exact, where b is the value of / i = R2 at the origin and z is the distance of OC. The equation simply states that AP, expressed as height of a column of liquid, equals the sum of the hydrostatic head and the pressure... 

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. 

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. 

For some types of wetting more than just the contact angle is involved in the basic mechanism of the action. This is true in the laying of dust and the wetting of a fabric since in these situations the liquid is required to penetrate between dust particles or between the fibers of the fabric. TTie phenomenon is related to that of capillary rise, where the driving force is the pressure difference across the curved surface of the meniscus. The relevant equation is then Eq. X-36,... 

The Washburn model is consistent with recent studies by Rye and co-workers of liquid flow in V-shaped grooves [49] however, the experiments are unable to distinguish between this and more sophisticated models. Equation XIII-8 is also used in studies of wicking. Wicking is the measurement of the rate of capillary rise in a porous medium to determine the average pore radius [50], surface area [51] or contact angle [52]. 

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. 

Although a number of methods are available to characterize the interstitial voids of a solid, the most useful of these is mercury intrusion porosimetry [52], This method is widely used to determine the pore-size distribution of a porous material, and the void size of tablets and compacts. The method is based on the capillary rise phenomenon, in which excess pressure is required to force a nonwetting liquid into a narrow volume. 

One of the most common ways to characterize the hydrophobicity (or hydrophilicity) of a material is through measurement of the contact angle, which is the angle between the liquid-gas interface and the solid surface measured at the triple point at which all three phases interconnect. The two most popular techniques to measure contact angles for diffusion layers are the sessile drop method and the capillary rise method (or Wihelmy method) [9,192]. 

As can be seen in Figure 5, despite the use of narrow bore capillaries, the temperature difference between the wall of the capillary and the surrounding air/liquid can rise up to several degrees (exceeding due to self-heating of the capillary because of the power... 

Lim, C. Wang, C. Y. Measurement of contact angles of liquid water in PEM fuel cell gas diffusion layer (GDL) by sessile drop and capillary rise methods. Penn State University Electrochemical Engine Center (ECEC) Technical Report no. 2001 03, Perm State University State College, PA, 2001. 

The capillary rise in a small vertical open tube of circular cross section dipping into a pool of liquid is given by... 

The capillary rise h, which has been discussed hitherto is of course the height of the capillary meniscus above that of an unbounded expanse of liquid, whose level is therefore unaffected by surface tension. In practice it is not usually convenient to employ so large a quantity of liquid as is demanded by this condition, but instead two interconnected tubes one of capillary, and one of wide bore are filled with liquid. The height h between the two liquid levels is now the difference between two quantities hi and defined by... 

In Ramsay s experiments the forms of apparatus used were capable of sustaining pressures up to 100 atmospheres. The wide and narrow tubes were concentric the wide tube was therefore annular in shape, and the allowance for the capillary rise in it becomes difficult to calculate. Ramsay did not make a sufficient allowance for the rise in the annular tube and in consequence all his values, and those of later workers who have adopted his figures for purposes of calibration for surface tensions are too low. Sugden has used an approximate method of correcting for the rise in the annulus, in which he considers a capillary tube of circular bore which gives an identical rise at a particular temperature and for a particular liquid, and assumes that the rise in the two tubes will be the same for all other temperatures and liquids. By this means he has, with the help of later measurements, corrected all Ramsay s values for which sufficient data are given in the original papers. 

---