Excess Pressure in Water Drop and Soap Bubble and Applications

Because of the surface tension water drops always acquires spherical shape. In the process of acquiring a spherical shape all the molecules are pulled towards the Center of the sphere and hence an extra pressure is developed at the Center of that Sphere. The force due to the pressure always acts away from the center whereas the force due to the surface tension always acts towards the Center. When these two forces are equal in magnitude and opposite in direction we can acquire an equilibrium state as shown below.

Deriving equation for excess pressure in a soap bubble is also a similar exercise. The only difference is the soap bubbles inner surface as well as the outer surface are free surfaces and hence in the place of one length we have to take two lengths. Everything else is similar.

Applications of excess pressure

Two soap bubbles of different radius are kept in vacuum. At constant temperature find the ratio of the masses of the gases inside them.

In solving this problem we have to consider the ideal gas equation because the gas molecules that are present inside the sphere are supposed to be ideal gas molecules.

We can also calculate the radius of the interface when two bubbles of different radius are in contact as shown below. The bubble with a smaller radius will have an extra pressure than the bubble with a larger radius. The total effect to pressure is the higher pressure minus lower pressure.

We can also calculate resultant radius when two different drops are combined together under isothermal conditions to form a big drop.

In solving this problem we are simply depending on a concept that mass as well as the number of the moles are always conservative.