SURFACE TENSION 

Due to molecular attraction, liquids possess certain properties like cohesion and adhesion. Cohesion means inter-molecular attraction between molecules of the identical liquid. Meaning it is tendency of the liquid to stay as one assemblage of particles. Adhesion means attraction between the molecules of a liquid and therefore 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 stay 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 inside of the liquid body has other molecules on  all sides of it, in order that the forces of attraction are in equilibrium and the molecule is equally attracted on all the edges , as a molecule at point A shown in Fig. 1. On the opposite 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, doesn't have any liquid molecule above it, and consequently there's 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 due to the attraction of liquid molecules below the surface, a film or a special layer seems to make on the liquid at the surface, which is in tension and little loads can be supported over it. For e.g , a little needle placed gently upon the water surface will not sink but are going to be supported by the tension at the water surface.

Fig .1. Inter-molecular forces near a liquid surface 

The property of the liquid surface film to exert a tension is named the surface tension. It's denoted by σ(Greek ‘sigma’) and   it's the force required to maintain unit length of the film in equilibrium. In SI units physical phenomenon is expressed in N/m. With in the metric gravitational system of units it is expressed in kg(f)/cm or kg(f)/m. With in the English gravitational system of units it is expressed in lb(f)/in. or lb(f)/ft.

As surface tension is directly dependent upon inter-molecular cohesive forces, its magnitude for all liquids decreases because the temperature rises. it's also dependent on the fluid in contact with the liquid surface; thus surface tensions are usually quoted in touch with air. The surface tension of water in touch 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. More organic liquids have values of physical phenomenon between 0.0206 N/m [or 0.0021 kg (f)/m] and 0.0304 N/m [or 0.0031 kg (f)/m] and mercury features a value of about 0.4944 N/m [or 0.0504 kg(f)/m], at normal temperature and therefore the liquid in each case being in contact with air.

The effect of physical phenomenon 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 most body of liquid, then thanks 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 edges and results in increasing the internal pressure within the droplet. The contraction of the droplet continues till the inward force thanks to surface tension is in balance with the interior pressure and the droplet forms into sphere which is the shape for minimum surface area. the interior 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 more than the outside pressure intensity could also 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 more than the outside pressure intensity. If the droplet is dig two halves, then then forces working on  and the 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

p (πr²) = σ (2πr)

                          p = 2σ/r                                                 ....( 1 )

Equation 1. indicates that the interior pressure intensity increases with the decrease in the size of droplet.

(ii) Pressure intensity inside a bubble . A spherical bubble has two surfaces in contact with air, one inside and therefore the other outside, all of which contributes the same amount of tensile force due to surface tension. Intrinsically on a hemispherical section of a soap bubble of radius r the tensile force due to surface tension is equal to 2σ(2πr). However, 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

p (πr²) = 2σ (2πr)

                         p = 4σ/r                                                              ...( 2 )

 (iii) Pressure intensity inside a liquid jet. Consider a jet of liquid of radius r, length l and having internal pressure intensity p in more than the outside pressure intensity. If the jet is dig two halves, then the forces working 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 (2l). These two forces will be equal and opposite for equilibrium and hence we have

p (2rl) = σ (2l)

                          p = σ/r                                                      ... (3)