Contact Angle capillary rise

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. 

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. 

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. 

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... 

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]. 

The wetting ability of the anode electrode was evaluated as the contact angle measured by the capillary rise method. The value of fractal dimension of anode electrode of MCFC was calculated by use of the nitrogen adsorption (fractal FHH equation) and the mercury porosimetry. 

Here, A is the contacting surface area of anode electrode facing with electrolyte and P is the porosity of anode electrode. The average effective radius of pore,, could be calculated from the results of the capillary rise method using ethanol, which shows a contact angle of 0° with the anode electrode. And then, the contact angle 0 could be acquired as the slope from the plot of m versus... 

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. 

Explain the relationship between surface tension, contact angle and capillary rise. 

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]. 

The capillary rise technique is considered to be very useful for DL materials, especially if the angle is less than 90° and/or for measurements that are taken under different temperature conditions [192]. In this method, a sample material is immersed in a container filled with water and the meniscus height is measured with a microscope (see Figure 4.23). Contact angles between the water and DL are calculated using Equation 4.1 and by measuring the... 

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. 

Fig. 2.3. Capillary rise, showing the contact angle, 0, and height of meniscus, h.

The capillary rise method, althongh simple, is in practice, not as useful as the pendant drop method because of several experimental problems, snch as the need to determine the contact angle, non-sphericity of the meniscns and nneven bore of the capillary. 

Equation (10.18) was derived for capillary rise or depression assuming complete wetting, that is, 6 = 180°. In the case of contact angles greater than 0° and less than 180°, equation (10.18) must be modified. As liquid moves up the capillary during capillary rise the solid-vapor interface disappears and the solid-liquid interface appears. The work required for this process is... 

The situation shown in Figure 6.2b is one in which surface tension and contact angle considerations pull a liquid upward in opposition to gravity. A mass of liquid is drawn up as if it were suspended by the surface from the supporting walls. At equilibrium the upward pull of the surface and the downward pull of gravity on the elevated mass must balance. This elementary statement of force balance applies to two techniques by which 7 can be measured if 6 is known the Wilhelmy plate and capillary rise. 

A simple —but incorrect — relationship between the height of capillary rise, capillary radius, contact angle, and surface tension is easily derived. At equilibrium the vertical component of the surface tension (2icRcy cos 0) equals the weight of the liquid column, approximated as the weight of a cylinder of height h and radius Rc. This leads to the approximation... 

An important application of Young s equation and a procedure for measuring the contact angle at the same time, is the rise of a liquid in a capillary tube. If a capillary is lowered into a liquid, the liquid often rises in the capillary until a certain height is reached (Fig. 7.3 top left). For a capillary with a circular cross-section of radius rc, this height is given by... 

Not only does a capillary rise occur but, depending on the interfacial tensions, liquid can also be expelled from a capillary. A liquid rises for partially wetted surfaces (0 < 90°). If the liquid does not wet the inner surface of the capillary and the contact angle is higher than 90° the liquid is pressed out of the capillary. For this reason it is very difficult to get water into polymeric capillaries, as long as the capillary is hydrophobic. This can achieved only by applying an external pressure. 

Comparing the two pressures directly leads to the contact angle. One limitation of the capillary rise method is that it averages over many particles and the actual size distribution remains unknown. In addition, it relies on the assumption that a powder can be treated as a bundle of capillaries and depends on the specific model applied [239,240],... 

Contact angles are commonly measured by the sessile drop, the captive bubble, and the Wilhelmy plate method. To characterize the wetting properties of powders the capillary rise method is used. 

In practice, the capillary rise method is only used when the contact angle is zero, owing to the uncertainty in measuring contact angles... 

Figure 3.7 Illustration of capillary rise with a wetting contact angle.

Because the pressure is lower on the convex side of an interface, liquids will rise up in small tubes (capillaries), whose surface they wet , with contact angle 0 less than 90°, as shown in Fig. 7. 

---