# Excess pressure inside a Liquid drop

• Vivek98phyboy
In summary, the conversation discusses the concept of excess pressure inside a liquid drop due to surface tension and the conditions for equilibrium. It also raises questions about the role of surface tension and the behavior of a drop with zero surface tension.
Vivek98phyboy
While studying about the effects of surface tension i came across the excess pressure inside a liquid drop.
Here they considered a hemisphere ABCDE from the drop and listed out the conditions for it to be in equilibrium.

The forces acting on them are taken as

F1= 2πRS
F2= P1×(Projection of hemispherical surface on ABCD)
=>F2=P1×πR²
F3=P2×πR²

For equilibrium we take
F1+F2=F3

But what role does the surface tension (T) has in maintaining the equilibrium for a hemisphere.
My doubts are:
1. Isn't the pressure due to Atmosphere and the pressure inside the hemispherical drop enough to balance each other. Why do we need a surface tension here?
2. When i referred some other sources, it said that the surface tension holds the drop from bursting. If it is so, the force due to T we calculates here acts only along the base periphery of the hemisphere. What effect would it have on the curved surface?

Hope this won't come under Homework help

The surface tension of the bubble is due to the attraction of molecules with their neighbors thus pulling them closer and causing the surface area to shrink. This naturally will increase the pressure inside until an equilibrium situation is produced.

In the analysis three forces are identified. That due to the outside pressure pushing on the surface (P0πr2) that due to the surface tension acting in the surface on the circumference (2π rσ) which act together and that due to the inside pressure (P πr2) countering the other two to produce the equilibrium situation. where r is the radius and σ is the surface tension

The pressure in the bubble is constant throughout . The splitting of the bubble into two hemispheres simplifies the analysis.

thus

P πr2 = P0πr2 + 2π rσ

or P = P0+ 2σ/r

gleem said:
The surface tension of the bubble is due to the attraction of molecules with their neighbors thus pulling them closer and causing the surface area to shrink. This naturally will increase the pressure inside until an equilibrium situation is produced.

In the analysis three forces are identified. That due to the outside pressure pushing on the surface (P0πr2) that due to the surface tension acting in the surface on the circumference (2π rσ) which act together and that due to the inside pressure (P πr2) countering the other two to produce the equilibrium situation. where r is the radius and σ is the surface tension

The pressure in the bubble is constant throughout . The splitting of the bubble into two hemispheres simplifies the analysis.

thus

P πr2 = P0πr2 + 2π rσ

or P = P0+ 2σ/r
What if the surface tension is zero?
How would the hemispherical part of the drop behave?

See comment #2 by @.Scott in the thread:

Zero surface tension: "It would signify that the molecules within the fluid have the same attraction to each other as to the atmosphere at the surface."

Last edited:

## What is excess pressure inside a liquid drop?

Excess pressure inside a liquid drop refers to the additional pressure that is present on the surface of a liquid drop due to its curvature. This pressure is caused by the cohesive forces between the molecules of the liquid and is inversely proportional to the radius of the drop.

## What causes excess pressure inside a liquid drop?

Excess pressure inside a liquid drop is caused by the surface tension of the liquid. The cohesive forces between the molecules of the liquid create a surface tension that pulls the molecules towards the center of the drop, resulting in a higher pressure on the surface.

## How is excess pressure inside a liquid drop measured?

Excess pressure inside a liquid drop can be measured using a device called a tensiometer. This instrument measures the force required to stretch a liquid surface and can calculate the excess pressure based on the surface tension and curvature of the drop.

## What is the relationship between excess pressure and surface tension?

Excess pressure and surface tension have an inverse relationship. This means that as the surface tension of a liquid increases, the excess pressure inside a drop decreases, and vice versa. This relationship is described by the Young-Laplace equation.

## What are the practical applications of understanding excess pressure inside a liquid drop?

Understanding excess pressure inside a liquid drop has many practical applications in various fields such as physics, chemistry, and engineering. It can help in the design of microfluidic devices, understanding the behavior of bubbles and droplets, and in the study of capillary action and surface tension. It also has implications in fields like medicine, where it is used to understand the behavior of fluids in the human body.

Replies
8
Views
1K
Replies
2
Views
1K
Replies
2
Views
1K
Replies
8
Views
410
Replies
3
Views
966
Replies
6
Views
809
Replies
18
Views
393
Replies
1
Views
3K
Replies
15
Views
4K
Replies
18
Views
2K