# What’s Surface Tension in Fluid Mechanics | Water Droplet & Soap Bubble Formula4 min read

## What’s Surface Tension?

The property of spreading tension of a liquid surface film is called surface tension. Surface tension is represented by the symbol “σ” and the unit of surface tension is Newton per meter N/m.

Surface tension is caused by the “cohesion” between the liquid particles and the surface. Whenever a liquid is in contact with other liquids or gases, or a solid surface, an interface develops that acts like a stretched elastic membrane, creating surface tension.

Cohesion: The force of attraction between the molecules of the same liquid.

Adhesion: The force of attraction between molecules of different liquids (or) between liquid molecules and the solid boundary containing the liquid.

Surface tension is also expressed as work done per unit surface area in J/m²

$\huge \sigma=\frac{W\ \left(or\right)\ E}{A}$

Two characteristics of this membrane are the contact angle, and the magnitude of the surface tension, (N/m). Both of these depend on the type of liquid and the type of solid surface (or other liquid or gas) with which it shares an interface, for example, the surface of a car will get wet when water is applied to the surface. If the surface of the car is waxed before applying water and then water is applied, then the surface of the car will not be wet.
This is due to the contact angle being smaller than 90°, greater than 90° because, in effect, the wax has changed the nature of the solid surface.

For liquids, surface tension decreases with increase in temperature. Due to this surface tension, the liquid droplets take the form of a sphere, which is the size for the minimum surface area.

Surface tension is a measure of a liquid’s tendency to take a spherical shape due to the mutual attraction of liquid molecules.

Some Important Values,

• Surface tension for air-water interface, σ= 0.073 N/m
• Surface tension for air-mercury interface, σ=0.480 N/m
• Contact angle for water-glass interface, θ= 0
• Contact angle for mercury-glass interface, θ= 130°

## Droplet, Soap bubble, and Liquid jet:

When a droplet is initially detached from the surface of the main body of the liquid, a net inward force is exerted on the entire surface of the droplet due to the face tension, which causes the droplet surface to dissipate from all droplets. contact occurs. side and result in an increase in the internal pressure within the droplet.

The droplet contraction continues until the inward force due to surface tension is in equilibrium with the internal pressure and the droplet forms a sphere that is the size for the minimum surface area.

The internal pressure within the jet of the liquid also increases due to surface tension.

The intensity of the internal pressure within a droplet and the intensity of the external pressure over a jet of liquid can be determined by the expressions below.

### 1. Pressure Intensity inside a droplet:

Consider a spherical droplet of radius r having internal pressure intensity “p” in excess of the outside pressure intensity.

If the droplet is cut into two halves, then the forces acting on one half will be those due to pressure intensity (p) on the projected area {πr^2} 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)

$\huge p=\ \frac{2\sigma}{r}\ OR\ \Delta p=\ \frac{4\sigma}{d}$

where d=diameter of droplet

The above equation indicates that the internal pressure intensity increase with the decrease in the size of the droplet.

### 2. Pressure intensity inside a soap bubble:

A spherical soap bubble in contact with air has two surfaces one inside and the other outside, each of which contributes an equal amount of tensile force due to surface tension as on a hemispherical section of a soap bubble of radius r, tensile The force due to surface tension is equal to 2σ(2πr).

However, the pressing force acting on the hemispherical section of a soap bubble is the same as in the case of a drop and is equal to p(πr^2). Thus equating these two forces for equilibrium, we get,

p(πr²) = 2σ(2πr)

$\huge p=\ \frac{4\sigma}{r}\ OR\ \Delta p=\ \frac{8\sigma}{d}$

where d=diameter of bubble

### 3. Pressure intensity inside a liquid jet:

Consider a jet of liquid of radius r, length l, and having internal pressure intensity p greater than external pressure intensity.

If the jet is cut into two halves, then the force acting on one half is the intensity p of the pressure on the projected area (2rl) and the tensile force (2l) due to surface tension (σ) acting along both sides Will be, For equilibrium both these forces will be equal and opposite and hence we have,

p(2rl) = σ(2l)

$\huge p=\ \frac{\sigma}{r}\ OR\ \Delta p=\ \frac{2\sigma}{d}$

where d=diameter of jet

Note: Air bubble raise in a liquid treated as air droplet, ΔP = 4σ/d

 FAQS Q. Temperature effect on surface tension? Ans. As temperature increases surface tension decreases. Q. What’s Surface Tension? Ans. The property of the liquid surface film to exert tension is called the Surface Tension. surface tension is denoted by the symbol of “σ” and the unit is surface tension is Newton per metre N/m. Q. What is Pressure Intensity inside a liquid droplet? Ans. $\huge p=\ \frac{2\sigma}{r}\ OR\ \Delta p=\ \frac{4\sigma}{d}$ Q. What is Pressure intensity inside a soap bubble? Ans. $\huge p=\ \frac{4\sigma}{r}\ OR\ \Delta p=\ \frac{8\sigma}{d}$ Q. What is Pressure intensity inside a liquid jet? Ans. $\huge p=\ \frac{\sigma}{r}\ OR\ \Delta p=\ \frac{2\sigma}{d}$