Drops Bubbles and Capillary Rise

Introduction

Every matter in the universe is composed of tiny particles called molecules. They attract each other with some attractive force. There exists an intermolecular force of attraction between molecules. The matter is classified into five categories based on the force of attraction between the molecules. They are solid, liquid, gas, plasma, and Bose-Einstein. Solids are the matter in which the distance between the molecules is very small and they are tightly bound to each other. Liquids are matter having molecules at a small distance and they bound less tightly than solids.

What is Surface Tension?

Surface tension is the molecular behavior of liquid. The liquid tries to shrink to attain a small surface area. This phenomenon is called surface tension.

The molecules on the surface of the liquid are attracted towards the center to get reduced into smaller areas. There is an inward and tangential force that acts between the molecules. The tangential force that acts between the molecules is called the surface tension. It helps the liquid molecules to shrink. The net force on the inside molecule is zero as the forces in all directions cancel each other. The surface molecule has some net force. Surface tension is defined as the force per unit length or energy per unit area. The unit for surface tension is $\mathrm{jm^{-2}}$.

$$\mathrm{surface\:tension(T)=\frac{Force(F)}{Length(L)}}$$

Dimensional surface tension formula for surface tension is $\mathrm{MLT^{-2}}$.

Some Practical Examples for Surface Tension

• Some insects like water striders can walk on the surface of the liquid. Due to its less weight, it is not penetrated through the liquid.

• Needle or paper clips are denser than water. Even Though they float on the liquid due to the surface tension.

• During winter clothes are washed using hot water. Because they have lower surface tension. So they are used for easy wetting.

Adhesive and Cohesive Force

There are two types of attractive forces between the molecules of the liquid. They are an adhesive force and a cohesive force.

• Adhesive Force − The force of attraction that occurs between molecules of two different substances is called the adhesive force. Generally, this force is used to bind two objects together. Painting on the wall and butter on the bread are some examples of adhesive force.

• Cohesive Force − The force of attraction that occurs between molecules of the same substance is called cohesive force. The water molecules exert a cohesive force between them to combine.

Capillary and Capillary Rise

The phenomenon of liquid flow through a narrow space without any external force is called a capillary. Capillary action occurs because of the force of attraction between liquid and the surrounding solid surface. As the diameter of the tube is small, surface tension and adhesive force combine and rise the liquid into the tube. The distribution of water to all parts of the plants is due to the capillary action of the stem. The ink that spills to write in a nib of a pen is due to the capillary action.

The Formula for Capillary Rise

There is a rise or fall of liquid inside the capillary called capillarity. Let's consider a capillary tube of radius r is immersed in a liquid the rise of liquid inside the capillary is h. Let the density of the liquid be $\mathrm{\rho}$. Surface tension is a tangential force that acts at the point of contact between the capillary and the liquid. It makes an angle $\mathrm{\theta}$ with the walls of the capillary. The tangential force that acts at the point of contact is resolved into two components $\mathrm{T\:sin\theta}$ in the horizontal and $\mathrm{T\:cos\theta}$ in the vertical direction. The horizontally component $\mathrm{T\:sin\theta}$is canceled out by all the molecules at the surface. Thus the only force is a vertical component.

Thus the total upward force is $\mathrm{F=circumference\times force}$

$$\mathrm{F=2\pi r(Tcos\theta )}$$

The downward force is $\mathrm{F=mg}$

g is the acceleration due to gravity.

$$\mathrm{density(\rho )=\frac{mass(m)}{volume(v)}}$$

$$\mathrm{m=\rho V}$$

Volume of the liquid is $\mathrm{V=\pi r^{2}h}$

$$\mathrm{m=\rho \pi r^{2}h}$$

The downward force $\mathrm{F=\rho \pi r^{2}hg}$

At equilibrium the upward force and downward force are equal.

$$\mathrm{2\pi r(Tcos\theta )=\rho \pi r^{2}hg}$$

$$\mathrm{2Tcos\theta =\rho rhg}$$

$$\mathrm{T=\frac{\rho rhg}{2 cos\theta }}$$

This is the expression for surface tension.

What is Drop?

A small liquid column that is completely bounded by free surfaces is called a drop. Drop is formed when the liquid is allowed to gather at the lower end of the tube. Vapour condensation is also responsible for the formation of drops. By dividing the drop into half and the upwards force due to the surface tension is

$$\mathrm{F=P\pi r^{2}}$$

Equal and opposite downward force over the circumference of the surface is

$$\mathrm{F=T(2\pi r)}$$

At equilibrium $\mathrm{P\pi r^{2}=T(2\pi r)}$

$$\mathrm{P=\frac{2T}{r}}$$

What is a Bubble?

It is thin soapy water. To attain the least energy the sphere shape is preferred.

The pressure inside the Drop and Bubble

The pressure inside the Drop

Lets us assume a liquid drop whose radius is r. Due to surface tension, there is a resultant inward force experienced by the surface molecules. Inside pressure is greater than the outside pressure. There is an equivalent outward force formed by the excess pressure to balance the inward force due to surface tension.

By dividing the drop into half and the upwards force due to the surface tension is

$$\mathrm{F=P\pi r^{2}}$$

Equal and opposite downward force over the circumference of the surface is

$$\mathrm{F=T(2\pi r)}$$

At equilibrium $\mathrm{P\pi r^{2}=T(2\pi r)}$

$$\mathrm{P=\frac{2T}{r}}$$

This is the expression for pressure inside the drop.

Pressure inside the Bubble

There are two surfaces in the soap bubble that are in contact with air. The inner side of the bubble and the outer side of the bubble. As there are two flat surfaces the force is $\mathrm{2(2\pi r)T}$. Thus at the state of equilibrium,

$$\mathrm{P\pi r^{2}=2(2\pi rT)}$$

$$\mathrm{P=\frac{4T}{r}}$$

Both the pressure inside the drop and bubble depend inversely on the radius of the drop.

Conclusion

In this tutorial, we study how the liquid rise in capillary and capillarity action. Cohesive and adhesive forces play a role in raising the liquid in the capillary. Drop and bubble are looking similar but the bubble contains air whereas the drop contains liquid. The pressure inside the bubble is two times more than a drop.

FAQs

Q1. Give some properties of the liquid.

Ans. Liquids are incompressible and take the shape of a container. It has a definite volume. While heating the liquid changes into a gaseous state.

Q2. What are the differences between adhesive and cohesive force?

Ans.

Adhesive Force	Cohesive Force
This force occurs between molecules of different substances.	It occurs between molecules of the same substance.
When it is strong it makes the liquid spread over the surfaces.	It forms water droplets when it is strong.

Q3. What are the methods used to measure the surface tension?

Ans. Some of the methods that are used to measure surface tension are the spin drop method, pendant drop method, capillary rise method, and bubble pressure method.

Q4. What are the factors that affect the surface tension?

Ans. The surface tension of the liquid inversely depends on temperature. It is zero at critical temperature and maximum at freezing point. If oil or dust is on the surface of the water then its surface tension will decrease.

Q5. How does oil float on the water?

Ans. The surface tension of oil is lesser than the surface tension of water. That is why the oil floats on the surface of the water.