Angle contact

The contact angle is a measure of the wettability of a membrane, and, thus, the membrane hydrophobicity. The angle between a water droplet and the membrane was measured as described in Chapter 4. For an ideally hydrophilic membrane, the angle is 0 degrees. The membranes were cleaned with MilliQ, then stored at 4 C and measured dry. Bouchard et al (1997) reported a change in contact 

The value measured for the CA-UF membranes corresponds very well to the values of 54 to 58 for CA membranes reported by Combe eta/. (1999). 

In equilibrium the liquid makes an angle 9 with the solid surface, which is given by Young s equation  

Applications. The following uses of contact angle were reported in the literature surface energy of different sizes for fibers, correlation between contact angle of fiber and interlaminar shear strength of composite, effect of surface treatment of fillers for paints, the matrix-filler adhesion parameter for PS filled with CaCO, dispersion stability of PEO-modified kaolin particles, determination of contact angle of carbon fibers and its dependence on treatment, wettability of fiber sur- 

In addition to the sessile drop method which measures the contact angle directly, Neumann and Renzow (1969) have developed the Wilhelmy slide technique to measure it to 0.1° precision. As shown in Fig. 2.20, the meniscus at a partially immersed plate rises to a finite length, h, if the contact angle, 0, is finite. 6 is calculated from 

A simple and direct method of contact angle measurement has also been proposed (Yamaki and Katayama, 1975 Carroll, 1976) by observing the shape of the liquid droplet attached to a single fiber, the so-called droplet aspect ratio method . The liquid is assumed to form a symmetrical droplet about the fiber axis as shown schematically in Fig. 2.21. Neglecting the effect of gravity, the droplet shape can be defined by the following expression  

k) and E( p, k) are elliptical integrals of the first and second kind, respectively. n can be plotted versus L for a range of small values of contact angle, 0. By measuring the relative dimensions of the droplet, ci and x, as illustrated in Fig. 2.21, 9 can then be evaluated (Carroll, 1976). 

In contrast to carbon fibers, no simple correlation has been reported between the work of adhesion to various polymer resins determined from the contact angle 

Interlaminar shear strength (ILSS), AES atomic percent, contact angle, 0, and surface energy, y, data for untreated and electrochemically oxidized pitch-based carbon hber  

A CA less than 90° suggests that wetting of the surface is favorable a CA greater than 90° means that the liquid prefers to minimize the contact with the surface. 

CA measurement is a facile, easy to apply technique that produces surface wetting and/or surface tension information. For polyurethane biomaterials, the conunonly used liquid in this test is water. The CA gives us important information about the polyurethane, snch as hydrophiUcity/hydrophobicity, surface tension, and surface reorganization kinetics [26-29]. 

Although CA seems like a very easy measurement, care must be taken during CA measurements since many factors can interfere with CA results The water must be as pure as possible since impurity such as surfactants will drastically change the interfacial tension of water the polymer surface must be thoroughly cleaned and should not have any extractable low molecular weight (MW) contaminants, such as unreacted monomers or wax or additives. 

There are two categories of CAs static and dynamic. Each category has several test methods/instmments. Some of these methods will be discussed in the following section. 

A typical static sessile drop is created by a microsyringe with an automated plunger to place a tiny drop of water on the polymer surface. Ideally, the polymer sample should be in a humidity chamber to minimize the water evaporation that would change the shape, and thus the C A of the droplet. The shape of the droplet is captured by a camera and CA is measured by an image analysis software [30]. 

Another fundamental concept in the theory of surface effects in microfluidics is the contact angle that appears at the contact line between three different phases, typically the solid wall of a channel and two immiscible fluids inside that channel. The two concepts, that is, contact angle and surface tension, allow understanding of the capillary forces that act on two-fluid flows inside microchannels of lab-on-a-chip (LCX)) systems. 

The analytical tool selection for characterizing sihcone surface modification for biomedical apphcation is critical. The surface chemistry should be analyzed after every surface modification for the quantity and the quahty of the attached bioactive compound. The techniques of contact angle. X-ray photoelectron spectroscopy, time of flight secondary ion mass spectrometry (ToF-SlMS), and atomic force microscopy (AFM) have been successfully implemented on silicone surfaces as discussed in this section. 

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Here a - surface tension pa - atmospheric pressure 9 - contact angle of crack s wall wetting by penetrant n - coefficient, characterizing residual filling of defect s hollow by a penetrant before developer s application IT and h - porosity and thickness of developer s layer respectively W - minimum width of crack s indication, which can be registered visually or with the use of special optical system. The peculiarity of the case Re < H is that the whole penetrant volume is extracted by a developer. As a result the whole penetrant s volume, which was trapped during the stage of penetrant application, imbibes developer s layer and forms an indication of a defect. 

Equations II-12 and 11-13 illustrate that the shape of a liquid surface obeying the Young-Laplace equation with a body force is governed by differential equations requiring boundary conditions. It is through these boundary conditions describing the interaction between the liquid and solid wall that the contact angle enters. 

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 maximum bubble pressure method is good to a few tenths percent accuracy, does not depend on contact angle (except insofar as to whether the inner or outer radius of the tube is to be used), and requires only an approximate knowledge of the density of the liquid (if twin tubes are used), and the measurements can be made rapidly. The method is also amenable to remote operation and can be used to measure surface tensions of not easily accessible liquids such as molten metals [29]. 

A zero or near-zero contact angle is necessary otherwise results will be low. This was found to be the case with surfactant solutions where adsorption on the ring changed its wetting characteristics, and where liquid-liquid interfacial tensions were measured. In such cases a Teflon or polyethylene ring may be used [47]. When used to study monolayers, it may be necessary to know the increase in area at detachment, and some calculations of this are available [48]. Finally, an alternative method obtains y from the slope of the plot of W versus z, the elevation of the ring above the liquid surface [49]. 

The basic observation is that a thin plate, such as a microscope cover glass or piece of platinum foil, will support a meniscus whose weight both as measured statically or by detachment is given very accurately by the ideal equation (assuming zero contact angle) ... 

The Wilhelmy slide has been operated in dynamic immersion studies to measure advancing and receding contact angles [59] (see Chapter X). It can also... 

This very simple result is independent of the value of the contact angle because the configuration involved is only that between the equatorial plane and the apex. 

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. 

Equation 11-30 may be integrated to obtain the profile of a meniscus against a vertical plate the integrated form is given in Ref. 53. Calculate the meniscus profile for water at 20°C for (a) the case where water wets the plate and (b) the case where the contact angle is 40°. For (b) obtain from your plot the value of h, and compare with that calculated from Eq. 11-28. [Hint Obtain from 11-15.]... 

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. 

A. W. Neumann et al.. Applied Surface Thermodyrmmics. Interfacial Tension and Contact Angles, Marcel Dekker, New York, 1996. 

This method suffers from two disadvantages. Since it measures 7 or changes in 7 rather than t directly, temperature drifts or adventitious impurities can alter 7 and be mistakenly attributed to changes in film pressure. Second, while ensuring that zero contact angle is seldom a problem in the case of pure liquids, it may be with film-covered surfaces as film material may adsorb on the slide. This problem can be a serious one roughening the plate may help, and some of the literature on techniques is summarized by Gaines [69]. On the other hand, the equipment for the Wilhelmy slide method is simple and inexpensive and can be just as accurate as the film balance described below. 

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. 

In the context of the structural perturbations at fluid-solid interfaces, it is interesting to investigate the viscosity of thin liquid films. Eaily work on thin-film viscosity by Deijaguin and co-workers used a blow off technique to cause a liquid film to thin. This work showed elevated viscosities for some materials [98] and thin film viscosities lower than the bulk for others [99, 100]. Some controversial issues were raised particularly regarding surface roughness and contact angles in the experiments [101-103]. Entirely different types of data on clays caused Low [104] to conclude that the viscosity of interlayer water in clays is greater than that of bulk water. 

In practice, 7s 7sv is negligible as is dys/dT for systems having large contact angles. Also, low energy surfaces have a relatively constant value of dyst/dT = 0.07 0.02 erg cm K , leaving... 

The preceding definitions have been directed toward the treatment of the solid-liquid-gas contact angle. It is also quite possible to have a solid-liquid-liquid contact angle where two mutually immiscible liquids are involved. The same relationships apply, only now more care must be taken to specify the extent of mutual saturations. Thus for a solid and liquids A and B, Young s equation becomes... 

There are some subtleties with respect to the physicochemical meaning of the contact angle equation, and these are taken up in Section X-7. The preceding, however, serves to introduce the conventional definitions to permit discussion of the experimental observations. 

Fig. X-3. Variation of contact angle with /oh. the fraction of the surface covered by HS(CH2)uOH in a mixture with HS(CH2)uCH3. Solid line is comparison with Eq. X-27, and dashed line is from Eq. X-28. (From Ref. 44.)...

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