Surface capillary rise

Wetting kinetics M E R SHANAHAN Spreading on a solid surface capillary rise... 

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... 

While Eq. 11-14 is exact, its use to determine surface tension from capillary rise experiments is not convenient. More commonly, one measures the height, h, to the bottom of the meniscus. 

The general case has been solved by Bashforth and Adams [14], using an iterative method, and extended by Sugden [15], Lane [16], and Paddy [17]. See also Refs. 11 and 12. In the case of a figure of revolution, the two radii of curvature must be equal at the apex (i.e., at the bottom of the meniscus in the case of capillary rise). If this radius of curvature is denoted by b, and the elevation of a general point on the surface is denoted by z, where z = y - h, then Eq. II-7 can be written... 

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. 

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. 

Bianco and Marmur [143] have developed a means to measure the surface elasticity of soap bubbles. Their results are well modeled by the von Szyszkowski equation (Eq. III-57) and Eq. Ill-118. They find that the elasticity increases with the size of the bubble for small bubbles but that it may go through a maximum for larger bubbles. Li and Neumann [144] have shown the effects of surface elasticity on wetting and capillary rise phenomena, with important implications for measurement of surface tension. 

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]. 

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. 

Surface tension is independent of tube size. However, the extent of capillary rise or depression by surface tension is dependent on tube size. This can be seen from Equation 18.1 in Section 18.4.6.1. For example, in the case of a capillary rise, the greater the tension, the higher the water rises above the free-water surface. For the same amount of water, the smaller the tube is, the higher the water rises. 

The hydrologic cycle, or moisture cycle — that may encompass the processes of rain infiltration in the soil, exfiltration from the soil to the air, surface runoff, evaporation, moisture behavior, groundwater recharge and capillary rise from the groundwater. All these processes are interconnected and are frequently referred to as the hydrologic cycle components. 

A combination of adhesion and surface tension gives rise (pardon the pun) to capillary action. By its adhesion to the solid surface of the soil particles, the water wants to cover as much solid surface as possible. However, by the effect of surface tension, the water molecules adhering to the solid surface are connected with a surface him in which the stresses cannot exceed the surface tension. As water is attracted to the soil particles by adhesion, it will rise upward until attractive forces balance the pull of gravity (Figure 3.28). Smaller-diameter tubes force the air-water surface into a smaller radius, with a lower solid-surface-to-volume ratio, which results in a greater capillary force. Typical heights of capillary rise for several soil types are presented in Table 3.9. The practical relationship between normal subsurface water and capillary rise is presented in the following equation. 

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 method was employed to measure the surface tension of aqueous solutions of disodlum alkyl phosphate at 25 °C. The cmc values of the solutions were obtained from the discontinuity in the surface tension - concentration curves(7). 

Figure 2. Surface tensions of sodium dodecylsulfonate solutions with and without polymer addition as measured by the capillary rise method.

The zone between land surface and the water table, which forms the upper boundary of the groundwater region, is known as the vadose zone. This zone is mostly unsaturated— or more precisely, partially saturated— but it may contain a saturated fraction in the vicinity of the water table due to flucmations in water levels or capillary rise above the water table. The near-surface layer of this zone—the soil—is generally partially saturated, although it can exhibit periods of full saturation. Soil acts as a buffer that controls the flow of water among atmosphere, land, and sea and functions as a sink for anthropogenic contaminants. 

The various surface forces are seen to be responsible for capillary rise. The lower the surface tension, the lower the height of the column in the capillary. The magnitude of y is determined from the measured value h for a fluid with known pL. The magnitude of h can be measured directly by using a suitable device (e.g., a photograph image). 

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. 

The experimental data on the subject of the surface tensions of such solutions is scanty. The early work of Valson (G.R. LXXIV. 103, 1872) and of Morgan (cf. J.A.G.S. xxxv. 1753, 1913) cannot be considered as reliable. More accurate appear to be the data of Stocker (vibrating jet) Zeit Phys. Ghem. xciv, 149, 1920), who compared his values with those of Grabowski and Pann (Diss. Kdnigsberg, 1904) (capillary rise) and Sentis (hanging drops) Thhe, Paris, 1897). 

Concrete dampproofers are integral admixtures that alter the concrete surface so that it becomes water repellent, or less wettable . This is illustrated in Fig. 4.1, which shows a close up of a water drop on a surface of a concrete that has had a dampproofer incorporated into it. This water repellency conferred on the concrete is only effective in preventing water from entering the surface when the applied pressure is small, e.g. rainfall in windy conditions, or capillary rise. The latter effect is shown in Fig. 4.2. In view of this, these materials are used normally for improving the quality of concrete pavers, tiles, bricks, blocks and cladding panels where the additional benefits of reduced efflorescence, the maintenance of clean surfaces and the more even drying out of adjacent bricks and panels are also obtained. 

The pressure required to enter the surface is positive, therefore, capillary rise should be nil. In fact, because of incomplete coating there may be some slight rise in moisture, but this will be considerably reduced in comparison to an untreated concrete. 

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