Relationship Between Excess Pressure And Surface Tension

Agnes Luise Wilhelmina Pickles discovered the concept of Surface tension. She was a self-trained chemist from Germany. Initially, she worked in establishing some modern disciplines in the field of surface science, which mainly describe the physical and chemical properties of solid and liquid surfaces.

She discovered this concept with the help of an experiment in which she wanted to evaluate impurities in water with the help of a sliding trough. Impurities did not mean harmful toxicities, instead they were just household impurities like soap and oil.

With the help of her apparatus, she discovered that surface tension is nothing but an amount of force that is required to remove the disk from the surface of the liquid.

Surface Tension

Surface tension is a phenomenon that is defined as a property of the surface of the liquid which has the capability to resist some kind of external force. This can be possible because the liquid (that is., the water molecules) have a cohesive nature. The formula for surface tension can be represented as 

𝛄 = (1/2) (F/L) 

Where 𝛄 = surface tension

 F = force exerting on the given liquid

 L = length of the liquid surface

The SI unit of surface tension is represented as Newton per metre (N/m). It is very easy to understand and remember this SI unit. Because the unit for Force is Newton and for length is metre. Hence for F/L, the unit will be N/m.

Causes for surface tension

As we know, the surface tension phenomenon will occur only due to the cohesive nature between the molecules of the liquid. But there are some special cases wherein the bulk of liquid molecules are very closely packed with each and other neighbouring molecules. Hence, they are supposed to pull each other equally in all directions, which will lead to the zero value of the net force.

If the force of attraction between the neighbouring particles is high, then the surface tension will also be high.

Excess pressure

Because of the surface tension, the number of molecules on the surface of the film or given liquid will experience a net force on the surface greater than the force that occurs inside the liquid. The excess pressure will occur just inside the surface of the liquid rather than on the outer surface.

Expression for excess pressure inside a soap bubble

The excess pressure within a soap bubble is inversely proportional to the surface tension. For a soap bubble with a radius r, the excess pressure is expressed as P = 4𝝈/r, where 𝝈 represents the surface tension, r represents the radius of the soap bubble, and p represents the pressure exerted in the bubble.

Excess pressure 𝝙P = Pi – Po, where Pi is the internal pressure while Po is the external pressure.

We know that the force due to pressure = force due to surface tension, so because of the excess pressure inside the bubble drop, the remaining free surfaces are supposed to experience the net force in the outward direction. Under isothermal conditions, the free space will be displaced by dR. Therefore, here the excess pressure will do some work in displacing the surface process, and this work can be stored as potential energy.

The work done is represented by the product of force and displacement.

dW = force x displacement

       = excess pressure x surface area x displacement in the surface

          = P x 4𝞹R2 x dR ——— (1)

If the potential energy of the system is increased, then we get the formula as

dU = surface tension x increase in the area of the free surface region.                      

                      = T [ 2 {4𝞹 (2RdR) } ] ———— (2)

 By equating the equation (1) and (2) we can obtain,

                 P x 4𝞹R2 x dR = T [ 2 {4𝞹 (2RdR) } ]     

                           P = (4T) / R

Relation between the excess pressure and surface tension

One major relation is that the force due to the surface tension is equal to the force due to the excess pressure. The force exerted by the pressure difference must balance the force exerted by the surface tension. One of the main examples of these relations are liquid drops or a soap bubble.

A spherical soap bubble, which is already in contact with air, consists of two liquid surfaces. One is inside the surface, and the other is outside the surface. And one of the very important things is that the pressure inside the surface will always be greater than the pressure outside the surface. Basically, if we increase the surface pressure, then automatically, the surface tension will increase.

Excess pressure and surface tension importance

The surface tension phenomenon was determined by the behaviour of liquids by using a number of processes and methodology. Some of them are wetting and wettability.  

In a water molecule, the surface tension is very important to attain a proper shape of the drop and maintain the structure.

The excess pressure will do some work upon the surfaces, and this work can be stored in the form of potential energy within the system.

Conclusion

Both the excess pressure and surface tension have a lot of applications. They play an essential vital role in our day to day life. Surface tension has its application in the field of physics and chemistry, and it has a major role in human body metabolism. In plant growth, the surface tension helps the water to move through the xylem tissues without any resistance.

Recently, researchers have revealed that the forces generated from surface tension play a vital role in rearranging the positions of the body cells.