Surface tension is a force per unit length (or surface energy per unit area) acting in the plane of the interface between the plane of the liquid and any other substance. It is also an extra energy that the molecules at the interface have as compared to molecules in the interior. Due to molecular attraction, liquids possess certain properties such as cohesion and adhesion. Cohesion means inter molecular attraction between molecules of the same liquid. That means it is a tendency of the liquid to remain as one assemblage of particles. Adhesion means attraction between the molecules of a liquid and the molecules of a solid boundary surface in contact with the liquid. The property of cohesion enables a liquid to resist tensile stress, while adhesion enables it to stick to another body. Surface tension is due to cohesion between liquid particles at the surface, whereas capillarity is due to both cohesion and adhesion.
A liquid molecule on the interior of the liquid body has other molecules on all sides of it, so that the forces of attraction are in equilibrium and the molecule is equally attracted on all the sides, as a molecule at point A shown in Fig.1. On the other hand, a liquid molecule at the surface of the liquid, (i.e., at the interface between a liquid and a gas) as at point B, does not have any liquid molecule above it, and consequently there is a net downward force on the molecule due to the attraction of the molecules below it. This force on the molecules at the liquid surface, is normal to the liquid surface. Apparently owing to the attraction of liquid molecules below the surface, a film or a special layer seems to form on the liquid at the surface, which is in tension and small loads can be supported over it. For example, a small needle placed gently upon the water surface will not sink but will be supported by the tension at the water surface.
The property of the liquid surface film to exert a tension is called the surface tension. It is denoted by ‘σ’ (Greek ‘sigma’) and it is the force required to maintain unit length of the film in equilibrium. In SI units, surface tension is expressed in N/m. In the metric gravitational system of units, it is expressed in kg(f)/cm or kg(f)/m. As surface tension is directly dependent upon inter molecular cohesive forces, its magnitude for all liquids decreases as the temperature rises. It is also dependent on the fluid in contact with the liquid surface; thus surface tensions are usually quoted in contact with air. The surface tension of water in contact with air varies from 0.0736 N/m [or 0.0075 kg (f)/m] at 19°C to 0.0589 N/m [or 0.006 kg (f)/m] at 100°C.
Surface tension has a role in capillary action, or capillarity, in which liquids climb up narrow tubes or narrow gaps between surfaces. Capillarity, which is important in the flow of water through soils as well as in flows in the human body, is the result of free surface forces and fluid-solid attractive forces. In space travel, where the pull of gravity is small, capillarity causes liquids to crawl out of open containers. Therefore, space travelers must drink with special straws that clamp shut when not in use to prevent snacks from climbing up the straw and floating freely throughout the cabin.
Surface forces are important in a wide variety of technical applications, including the breakup of jets, processes involving thin films and foams. Wicking, the drawing of fluid up into a fabric or wick as in a candle or away from the body as in the design of exercise clothing, is another process that works by capillary action. The opposite effect, waterproofing, is a manipulation of surface forces to prevent wicking. Surface tension causes striking effects that are exploited to make engaging fountain displays. In soap and water solutions, for example, variation of the concentration of the solute can cause the surface tension to vary, which in turn causes flow.
Flow driven by surface tension gradients called the Marangoni effect which stabilizes soap bubbles, among other effects. The emerging field of micromechanics creates machinery that works on nearly molecular size scales. The properties of any liquids involved in micro machines are dominated by interfacial forces. Interfacial forces are not always important, however, even when a large amount of free surface is present. In an ocean, wave motion depends on viscous forces and gravity forces, but the contribution of surface tension forces to the momentum balance in oceanic flows is negligible.
Fig. 5 Soap bubbles are composed of thin fluid layers sandwiched between two free surfaces. Surfactant molecules occupy the free surfaces and reduce the surface tension of the bubble surface compared to the surface tension of pure water. If an external force deforms or inflates the bubble, more surface is generated, reducing the concentration of surfactant molecules at the bubble surfaces. Lower surfactant concentration implies higher surface tension, however, and this locally higher surface tension pulls fluid into the thinning layer, stabilizing the film and preventing bubble rupture
Whenever a liquid is in contact with other liquids or gases, or in this case a gas/solid surface, an interface develops that acts like a stretched elastic membrane, creating surface tension. There are two features to this membrane: the contact angle ′θ′, and the magnitude of the surface tension, ′σ′ (N/m or lbf/ft). Both of these depend on the type of liquid and the type of solid surface (or other liquid or gas) with which it shares an interface. The examples of surface tension effects arise when you are able to place a needle on a water surface and, similarly, when small water insects are able to walk on the surface of the water.
For a soap bubble in air, surface tension acts on both inside and outside interfaces between the soap film and air along the curved bubble surface. Surface tension also leads to the phenomena of capillary. In engineering, probably the most important effect of surface tension is the creation of a curved meniscus that appears in manometers or barometers, leading to a (usually unwanted) capillary rise (or depression).
(a) A wetted surface (b) A non-wetted surface
Fig. 6 Surface tension effects on water droplets
The effect of surface tension is illustrated in the case of a droplet as well as a liquid jet. When a droplet is separated initially from the surface of the main body of liquid, then due to surface tension there is a net inward force exerted over the entire surface of the droplet which causes the surface of the droplet to contract from all the sides and results in increasing the internal pressure within the droplet. The contraction of the droplet continues till the inward force due to surface tension is in balance with the internal pressure and the droplet forms into sphere which is the shape for minimum surface area. The internal pressure within a jet of liquid is also increased due to surface tension. The internal pressure intensity within a droplet and a jet of liquid in excess of the outside pressure intensity may be determined by the expressions derived below.
i) Pressure Intensity Inside a Droplet
Consider a spherical droplet of radius ‘r’ having internal pressure intensity ‘p’ in excess of the outside pressure intensity. If the droplet is cut into two halves, then the forces acting on one half will be those due to pressure intensity p on the projected area (πr2) and the tensile force due to surface tension ‘σ’ acting around the circumference (2πr). These two forces will be equal and opposite for equilibrium and hence we have
This equation indicates that the internal pressure intensity increases with the decrease in the size of droplet.
ii) Pressure Intensity Inside a Soap Bubble
A spherical soap bubble has two surfaces in contact with air, one inside and the other outside, each one of which contributes the same amount of tensile force due to surface tension. As such on a hemispherical section of a soap bubble of radius r the tensile force due to surface tension is equal to 2σ (2πr). The pressure force acting on the hemispherical section of the soap bubble is same as in the case of a droplet and it is equal to p (πr2). Thus equating these two forces for equilibrium, we have
iii) Pressure Intensity Inside a Liquid Jet
Consider a jet of liquid of radius ‘r’, length ‘l’ and having internal pressure intensity ‘p’ in excess of the outside pressure intensity. If the jet is cut into two halves, then the forces acting on one half will be those due to pressure intensity p on the projected area (2rl) and the tensile force due to surface tension ‘σ’ acting along the two sides. These two forces will be equal and opposite for equilibrium and hence we have
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