Capillary, surface tension

F. In which of the five cases is the greatest weight supported by capillary (surface tension) forces ... 

Other possible means of fluid flow include capillary (surface tension), centrifugal -ultrasonic, electromagnetic, electro-hydrodynamic and pneumatic force. 

Our interest lies in developing a model which can address capillary (surface tension) forces at the interface. By choosing the liquid density (pi), the size/height of the liquid body (a) and the farfield velocity (U) as dimensions, the gas/liquid density ratio... 

Capillary filling refers to the filling of an open or closed conduit or a reservoir with the aid of capillary (surface tension) actuation mechanisms. 

In the bulk container, the paint should be of sufficiently low viscosity so that it can be readily utilized in the applicator. For application by a brush or a hand roller, the paint should readily penetrate the spaces between the bristles of a brush or the porous surface of the roller. The paint is then held by capillary/surface tension forces during the transfer to the surface to be painted. Control of brush loading is crucial in any paint application. If the brush loading is too high, the total weight of the paint becomes sufficient to overcome the capillary forces, leading to paint drip or run-off the brush, clearly an undesirable result. In contrast, if the brush load is too low, this results in a thin paint film, or a nonuniform film with thicker film over a smaller surface area [30]. To achieve the optimum film thickness one should control the flow-out properties as will be discussed below. 

According to Eq. (2.65) (not taking into account the temperature gradient and possible chemical interaction of the melt with the surface of a capillary), the depth of infiltration is directly dependent on the diameter of the capillary, surface tension, and wetting angle and is inversely proportional to the viscosity. 

The drop weight method measures the weight of a drop (or several drops) emerging from a capillary of known dimensions [318,336,344-347]. Slight vacuum is applied to the apparatus through a tubing until the drop, forming at the outlet of the capillary, assumes almost its full size. The drop is then allowed to detach itself from the capillary. Surface tension is calculated from the equation... 

The capillary effect is apparent whenever two non-miscible fluids are in contact, and is a result of the interaction of attractive forces between molecules in the two liquids (surface tension effects), and between the fluids and the solid surface (wettability effects). 

On a microscopic scale (the inset represents about 1 - 2mm ), even in parts of the reservoir which have been swept by water, some oil remains as residual oil. The surface tension at the oil-water interface is so high that as the water attempts to displace the oil out of the pore space through the small capillaries, the continuous phase of oil breaks up, leaving small droplets of oil (snapped off, or capillary trapped oil) in the pore space. Typical residual oil saturation (S ) is in the range 10-40 % of the pore space, and is higher in tighter sands, where the capillaries are smaller. 

This is exact—see Problem 11-8. Notice that Eq. 11-14 is exactly what one would write, assuming the meniscus to be hanging from the wall of the capillary and its weight to be supported by the vertical component of the surface tension, 7 cos 6, multiplied by the circumference of the capillary cross section, 2ar. Thus, once again, the mathematical identity of the concepts of surface tension and surface free energy is observed. 

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. 

Several convenient ways to measure surface tension involve the detachment of a solid from the liquid surface. These include the measurement of the weight in a drop falling from a capillary and the force to detach a ring, wire, or thin plate from the surface of a liquid. In this section we briefly describe these methods and their use. 

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. 

Another approach to measurement of surface tension, density, and viscosity is the analysis of capillary waves or ripples whose properties are governed by surface tension rather than gravity. Space limitations prevent more than a summary presentation here readers are referred to several articles [123,124]. 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

Since capillary tubing is involved in osmotic experiments, there are several points pertaining to this feature that should be noted. First, tubes that are carefully matched in diameter should be used so that no correction for surface tension effects need be considered. Next it should be appreciated that an equilibrium osmotic pressure can develop in a capillary tube with a minimum flow of solvent, and therefore the measured value of II applies to the solution as prepared. The pressure, of course, is independent of the cross-sectional area of the liquid column, but if too much solvent transfer were involved, then the effects of dilution would also have to be considered. Now let us examine the practical units that are used to express the concentration of solutions in these experiments. 

The capillary retention forces in the pores of the filter cake are affected by the size and size range of the particles forming the cake, and by the way the particles have been deposited when the cake was formed. There is no fundamental relation to allow the prediction of cake permeabiUty but, for the sake of the order-of-magnitude estimates, the pore size in the cake may be taken loosely as though it were a cylinder which would just pass between three touching, monosized spheres. If dis the diameter of the spherical particles, the cylinder radius would be 0.0825 d. The capillary pressure of 100 kPa (1 bar) corresponds to d of 17.6 pm, given that the surface tension of water at 20°C is 12.1 b mN /m (= dyn/cm). 

Another valuable property of mercury is its relatively high surface tension, 480.3 mN /m(= dyn/cm) at 0 °C, as compared to 75.6 mN /m for water. Because of its high surface tension, mercury does not wet glass and exhibits a reverse miniscus in a capillary tube. 

The principal physical properties influencing ink performance ate surface tension and viscosity. High surface tension is desired for good droplet formation and capillary refill in dtop-on-demand ink jet. Low viscosity is desired because less energy is required to pump and eject ink. Conductivity is also an important parameter. Continuous ink-jet inks must have some conductivity to allow for charging. Low conductivity is generally preferred for impulse, particularly thermal ink jet, because excess ions can cause corrosion of the printhead. 

There are three types of Hquid content in a packed bed (/) in a submerged bed, there is Hquid filling the larger channels, pores, and interstitial spaces (2) in a drained bed, there is Hquid held by capillary action and surface tension at points of particle contact, or near-contact, as weU as a zone saturated with Hquid corresponding to a capillary height in the bed at the Hquid discharge face of the cake and (3) essentially undrainable Hquid exists within the body of each particle or in fine, deep pores without free access to the surface except perhaps by diffusion or compaction. 

---