Excess pressure: definition, formula, examples

A soap bubble has two liquid surfaces which are in contact with air, one inside the soap bubble and the other outside the soap bubble. At equilibrium conditions, the air pressure inside the soap bubble is increased than the outside pressure, and the extra pressure is called excess pressure.    

What is excess pressure? 

When the free surface of any liquid changes and is curved, there is a change in pressure. This is the difference in pressure caused between the inner side of the surface and the outer side of the surface. This results in excess pressure. 

1. Suppose the surface of the liquid is plane, the forces that are caused due to surface tension act tangentially. These forces acting tangentially are in opposite directions of the liquid of the surface. The total results of the force on that molecule will be zero. In this case, the pressure on the vapour side will equal the pressure on the liquid side. 

2. If the surface of the liquid is curved, then every molecule will experience a force that is along the tangent to that surface. When the components of these forces are resolved, it is observed that horizontal forces cut each other, and vertical components add up. So, this resultant force is normal to the surface. The pressure on the concave side of the curve will be greater than the pressure on the convex side. 

Excess pressure inside a liquid drop 

Due to the surface tension force, the small bubbles and liquid drops are spherical. The pressure inside a liquid drop or a bubble is greater than the pressure outside it.

What is excess pressure inside a liquid drop? 

Let the radius of a liquid drop be R. let the surface tension of the liquid be T. Let p1 be the pressure inside the liquid drop. Let p2 be the pressure inside the liquid drop. The different kinds of forces that act on the liquid drop are:

a) The force is caused due to surface tension. Ft=2πRT (towards the right)

b) The force is caused due to outside pressure. F1=P1πR2 (towards the right)

c) The force is caused due to inside pressure. F2=P2πR2 (towards left)

The drop is in the state of equilibrium, so Ft=  F2 – F1

2πRT = P2πR2 – P1πR2

=>(P2 – P1) πR2 = 2πRT

=> excess pressure = P2 – P1 = 2T/R 

Excess pressure that is present inside a soap bubble 

Let the radius of a soap bubble be R. Let the soap bubble’s surface tension be T. Let p1 be the pressure inside the soap bubble. Let p2 be the pressure inside the soap bubble. 

A soap bubble consists of two liquid surfaces in contact with the air. So, the total force on the surface of the soap bubble that is caused due to surface tension will be 2 * 2πRT. The different kinds of forces that act on the soap bubble are:

a) A force that is caused due to surface tension. Ft=4πRT (towards the right)

b) The force is caused due to outside pressure. F1=P1πR2 (towards the right)

c) The force is caused due to inside pressure. F2=P2πR2 (towards left) 

The drop is in the state of equilibrium, so Ft=  F2 – F1

4πRT = P2πR2 – P1πR2

=>(P2 – P1) πR2 = 4πRT

=> excess pressure = P2 – P1 = 4T/R 

Excess pressure that is present inside an air bubble in a liquid 

Let the radius of an air bubble be R. Let the air bubble’s surface tension be T. Let p1 be the pressure inside the air bubble. Let p2 be the pressure inside the air bubble. The various kinds of forces that act on the air bubble are:

a) The force that is caused is due to surface tension. Ft=2πRT (towards the right)

b) The force that is caused is due to outside pressure. F1=P1πR2 (towards the right)

c) The force is caused due to inside pressure. F2=P2πR2 (towards left)

The drop is in the state of equilibrium, so Ft=  F2 – F1

2πRT = P2πR2 – P1πR2

=>(P2 – P1) πR2 = 2πRT

=> excess pressure = P2 – P1 = 2T/R 

Conclusion 

There is a difference in the outside pressure and inside pressure when the shape of the liquid is changed and it becomes curved. This difference in external and internal pressure results in excess pressure. There are many applications as well as uses of excess pressure. Excess pressure can easily be calculated in a liquid drop or an air bubble by the formula 2T/R. Excess pressure in a soap bubble can be found by the formula 4T/R. There are many applications of excess pressure in reservoirs. The excess pressure of any spherical drop or bubble depends on its radius. Excess pressure of any bubble or liquid drop is inversely proportional to the radius of the bubble or drop. The pressure in smaller air bubbles or liquid drops is higher than in larger air bubbles or liquid drops.