Stokes Drag and Terminal Settling
Balance viscous drag against weight and buoyancy for a tiny settling sphere.
Free theory articleBalance viscous drag against weight and buoyancy for a tiny settling sphere.
Concept & interpretation
An isolated rigid sphere settling in an unbounded Newtonian fluid under gravity experiences viscous drag that opposes its motion. When creeping-flow assumptions apply (very low Reynolds numbers), this drag is described by Stokes' law. The balance between gravitational forces (weight and buoyancy) and viscous drag determines the sphere's terminal velocity.
Interactive Experiment
Use the Stokes Drag and Terminal Settling module to observe the balance of forces.
- Set the Radius (um) to 5,Particle density (kg/m^3) to 2000, and Viscosity (mPa*s) to 1. Observe that the particle settles downward with a terminal velocity of 5.45e-05 m/s.
- Change the Particle density (kg/m^3) to 1000. Notice that the particle becomes neutrally buoyant: the net gravitational force is zero, the terminal velocity is zero, and the motion is Neutral.
- Change the Particle density (kg/m^3) to 500. The net gravitational force becomes negative (buoyancy dominates weight), and the particle rises with a negative terminal velocity.
- Increase the Radius (um) to 10. Observe how the terminal velocity magnitude increases by a factor of 4 due to ther2 scaling relationship.