Stokes law and sedimentation parameters

Stokes' Law describes the settling velocities of small spherical particles in a fluid medium. It is a fundamental principle in fluid dynamics and sedimentation. The law is named after George Gabriel Stokes, who derived the mathematical relationship in 1851. The formula for Stokes' Law is:

$v=\frac{2}{9}\frac{r^2({\rho }_p-{\rho }_f)g}{\eta }$

where:

• $v$ is the terminal velocity of the particle,
• $r$ is the radius of the spherical particle,
• ${\rho }_p$ is the density of the particle,
• ${\rho }_f$ is the density of the fluid,
• $g$ is the acceleration due to gravity,
• $\eta$ is the dynamic viscosity of the fluid.

Key Parameters in Sedimentation:

1. Particle Radius ($r$): The radius of the particle, which directly affects its settling velocity. Larger particles settle faster.

2. Particle Density (${\rho }_p$): The density of the particle. Denser particles settle faster in a fluid.

3. Fluid Density (${\rho }_f$): The density of the fluid. A denser fluid slows down the settling of particles.

4. Gravitational Acceleration ($g$): The acceleration due to gravity, typically $9.81{\text{m/s}}^2$ on Earth.

5. Dynamic Viscosity ($\eta$): The viscosity of the fluid, which resists the motion of the particles. Higher viscosity fluids slow down the settling of particles.

6. Terminal Velocity ($v$): The constant velocity a particle reaches when the gravitational force is balanced by the drag force and buoyancy force.

Applications:

Stokes' Law is used in various fields, including:

• Sedimentation and centrifugation processes in laboratories.
• Designing sedimentation tanks and clarifiers in water and wastewater treatment.
• Understanding the settling of aerosols and pollutants in the atmosphere.
• Soil and sediment analysis in geology and environmental science.