Surface Tension

Surface tension is an important fluid property which can explain events like a piece of camphor dancing on the surface of water, a water spider skating on a pond without wetting its legs, a needle floating on water, and so on. It is a molecular phenomenon which occurs at the surface of separation between two phases, such as a liquid in contact with air.

We begin with some important definitions. The force of attraction between the molecules of two different substances is known as the force of adhesion or adhesive force. The force of attraction between the molecules of the same substance is known as the force of cohesion or cohesive force. The molecular range of a substance is the maximum distance between its two molecules up to which the cohesive force is effective. If a plane is imagined within the liquid parallel to its free surface at a distance equalling the molecular range, the portion of the liquid lying between the free surface and the plane is known as the surface film.

All molecules lying in the surface film of a liquid experience a net inward force. Every time an external agent wants to increase the area of the free surface of a liquid, it must do so by raising molecules from the bulk of the liquid to the surface against the said inward force. The work done by the external agent is stored as potential energy in the free surface and known as free surface energy. Thus, the larger the surface area of a liquid, the more free surface energy it possesses. Since stable equilibrium is attained at minimum potential energy, the liquid surface behaves like a stretched elastic skin always trying to contract in area.

The force of surface tension, or simply surface tension, is defined as the tensile force acting across and perpendicular to a short, straight line on the surface of liquid divided by the length of that line. The dimensions of surface tension are [MT-2], and its SI unit is newton per metre (N/m). It can be shown that, in general, the surface tension of a liquid is equal to its free surface energy per unit surface area.

When a liquid comes into contact with a solid wall, the liquid surface near the point of contact is usually curved. The angle between the tangent to the liquid surface at the point of contact and the solid surface measured from within the liquid is known as the angle of contact for that pair of liquid and solid. This angle of contact may be an acute angle (< 90°) as in the case of methylene iodide and glass, an obtuse angle (> 90°) as in the case of mercury and glass, or a right angle ( = 90°) as in the case of water and silver.

The curved liquid surface near a solid wall is known as a meniscus. The possible shapes of a meniscus can be explained on the basis of the intermolecular forces of adhesion and cohesion. A typical liquid molecule on the meniscus experiences adhesive forces exerted by the solid molecules, cohesive forces exerted by other molecules of the liquid, and the force of gravity which is comparatively small. Thus, the relative strengths of adhesive and cohesive forces determine whether the meniscus would be concave, convex or flat.

The excess pressure within a liquid drop is given by the formula:

` P - Pa = 2γ / R`

where P is the pressure inside the liquid drop of radius R, Pa is atmospheric pressure and γ is the surface tension of the liquid.

The excess pressure within a soap bubble is given by the formula:

` P - Pa = 4γ / R`

where the symbols have similar meanings as before. When we derive these two important formulas, we shall see why a multiplication factor of 2 is coming in the case of a soap bubble. More rigorous calculation will be required to determine the force between two plates separated by a liquid film such as water or mercury.

An important effect of surface tension is the rise or fall of a liquid in a capillary tube. An open tube of very small cross section is known as a capillary tube, and the said effect is called capillarity. If the angle of contact between the liquid and the material of the tube is less than 90°, as in the case of water and glass, the liquid rises in the tube. Conversely, if the angle is greater than 90° as with mercury and glass, the liquid level falls in the tube. The common formula for the rise or fall, as the case may be, is:

`h = 2γ cosφ / rρg `

In this expression, h is the elevation or depression, γ and ρ are the surface tension and density of the liquid respectively, φ is the angle of contact, r is tube radius, g is acceleration due to gravity. The inverse relation between h and r is sometimes referred to as Jurin's law. The rise of ink through the pores of a blotting paper or of oil through the wick of a lamp is an example of capillary action.

The factors affecting surface tension are contamination of the liquid surface, presence of dissolved substances, variation in temperature, and nature of medium in contact.

Basic level videos

Theory Of Surface Tension 1:24:58 Basic
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Examples Of Surface Tension 1:16:11 Basic
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Angle Of Contact And Shape Of Meniscus 50:49 Basic
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Problems On Theory Of Surface Tension And Angle Of Contact 1:24:58 Basic
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Excess Pressure Within Liquid Drop And Soap Bubble 45:00 Basic
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Problems On Excess Pressure Within Liquid Drop And Soap Bubble 50:49 Basic
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Force Between Two Plates Separated By A Liquid Film 1:04:49 Basic
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Rise Or Fall Of A Liquid In A Capillary Tube 01:34:58 Basic
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Problems On Rise Or Fall Of A Liquid In A Capillary Tube 1:38:25 Basic
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Experimental Determination Of Surface Tension, And Factors Affecting Surface Tension 34:00 Basic
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Advanced level Videos Note: (CE) Stands for Problems from Competitive Examination Papers

Advanced-level problems on surface tension I 1:10:01
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Advanced-level problems on surface tension II 57:09
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Advanced-level problems on surface tension III 1:17:08
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Advanced-level problems on surface tension IV 1:07:28
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Advanced-level problems on surface tension V 1:13:43
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