Short Answer

Stokes’ law explains the force of viscous drag acting on a small spherical object moving through a fluid. According to this law, the viscous force depends on the radius of the sphere, the velocity of the sphere, and the viscosity of the fluid.

Stokes’ law is used to understand how objects fall through liquids, how raindrops move, and how particles settle in fluids. It helps scientists measure viscosity and study the motion of small particles in liquids and gases.

Detailed Explanation :

Stokes’ law

Stokes’ law is a fundamental principle in physics that describes the force of viscosity acting on a small spherical object when it moves through a fluid. A fluid can be either a liquid or gas, and viscosity is the internal friction that resists flow. When a small object, like a tiny ball or droplet, moves through a fluid, the fluid opposes its motion. This opposing force is called viscous drag.

Stokes’ law helps us calculate this viscous drag force. It is especially useful for studying the motion of small particles moving slowly through a fluid. The law is named after the scientist Sir George Gabriel Stokes, who proposed it in 1851.

Meaning of Stokes’ law

Stokes’ law states that:

The viscous force acting on a small sphere moving through a fluid is directly proportional to the fluid’s viscosity, the radius of the sphere, and the velocity of the sphere.

This means:

• If the fluid is thicker (more viscous), the drag force increases.
• If the sphere is larger, the drag increases.
• If the sphere moves faster, the drag force becomes larger.

Stokes’ law applies only under special conditions:

• The object must be small and spherical.
• The flow of fluid around the object must be smooth (called laminar flow).
• The speed must be low.

When these conditions are met, Stokes’ law accurately predicts the drag force.

Why viscous force acts on a moving sphere

When a sphere moves through a fluid:

• Layers of the fluid slide over the surface of the sphere.
• Due to viscosity, these layers create friction.
• This friction slows down the motion of the sphere.

The sphere continuously pushes the fluid aside, and the fluid pushes back. This opposing push is the viscous force described by Stokes’ law.

Factors affecting viscous force according to Stokes’ law

The viscous drag depends on:

1. Radius of the sphere
   Larger radius → more surface area → greater viscous force.
2. Velocity of the sphere
   Faster motion → more fluid resistance → greater drag.
3. Viscosity of the fluid
   Thick fluid (like honey) → strong viscous force
   Thin fluid (like water) → weak viscous force

These three factors determine how strongly the fluid opposes the motion.

Applications of Stokes’ law

Stokes’ law is used in many scientific and practical fields:

1. Settling of particles in liquids
   Helps calculate how fast particles like dust, sand, or pollen settle in water.
2. Rainfall formation
   Used to study how raindrops fall through air and how their speed changes.
3. Measuring viscosity
   Scientists determine viscosity by observing the motion of a sphere in the fluid.
4. Blood flow analysis
   Helps understand the flow of blood cells through blood plasma.
5. Oil and chemical industries
   Used in designing separators and purifiers for liquids.
6. Sedimentation processes
   Applied in wastewater treatment plants to remove solid particles.
7. Ink and paint production
   Used to control particle movement and settling.

Terminal velocity and Stokes’ law

When a sphere falls through a fluid, three forces act on it:

• Gravity (pulling it down)
• Buoyant force (pushing it up)
• Viscous drag (opposing motion)

At some point, these forces balance each other, and the sphere falls with a constant speed called terminal velocity. Stokes’ law helps calculate this terminal velocity.

Small particles like pollen grains and dust settle slowly because viscous drag quickly balances gravity.

Conditions where Stokes’ law fails

Stokes’ law does not apply when:

• The particle is not spherical
• The fluid flow becomes turbulent
• The sphere moves very fast
• The particle is too large
• The fluid is not uniform

Thus, the law works best for tiny particles moving slowly in smooth-flowing fluids.

Real-life examples related to Stokes’ law

1. Oil droplets rising in water
   The speed of rising depends on viscous drag.
2. Cream separating from milk
   Fat globules move upward under buoyancy and drag.
3. Dust settling in a room
   Very small particles settle slowly due to high viscous drag.
4. Water purification
   Stokes’ law helps remove suspended impurities.

These examples show how widely Stokes’ law applies in nature and daily life.

Conclusion

Stokes’ law describes the viscous drag acting on a small spherical object moving through a fluid. The drag force depends on the viscosity of the fluid, the size of the sphere, and its velocity. This law is useful in understanding the settling of particles, movement of droplets, rainfall formation, and many scientific processes. Stokes’ law helps predict terminal velocity and plays an important role in industries, environmental science, medicine, and fluid mechanics.