Stokes' Law
Stokes' Law describes the sedimentation of particles in suspensions (fruit pulp in orange juice). It is also used to model the flotation of droplets in emulsions (creaming of milk fat).
Equation
The equation below describes the separation velocity ($v$) of particles with diameter $D$ in a solvent with viscosity $\mu$ when subject to acceleration due to gravity $g$. The $\Delta \rho$ means the difference ($\Delta$) between the density ($\rho$) of the particle and the solvent.
$$v = \frac{D^2 \cdot(\Delta \rho) \cdot g }{18 \cdot \mu}$$
Measurement of viscosity
The equation can be rearranged to solve for viscosity:
$$\mu = \frac{D^2 \cdot (\rho_{ball} - \rho_{liquid}) \cdot g }{18 \cdot v}$$
With a ball of known physical dimensions and a liquid of known density, the viscosity can be calculated based on measurement of the ball's velocity with a stopwatch and ruler.
This is known as the "falling ball" method.
Practical uses
The equation can be used to identify the key parameters that influence how a group of particles fall or rise due to gravity. This can be used to develop strategies to make the separation of a material from a liquid happen more quickly or slowly.
In manufacturing, some processes are designed to either promote or prevent the physical separation of particles from liquids, for example:
- Homogenisation: reduces the size of particles to prevent destabilisation, increasing the stability of a commercial beverage
- Flocculation: aggregates particles together to increase destabilisation, enabling the removal of impurities from water
Simulation
I developed a simulation in JavaScript for teaching Stokes' law.
In the simulation, you can use sliders to visualise the effect of adjusting the following parameters:
- Average particle size
- Solvent viscosity
- Density difference
- Centrifugal force
I published a paper on the simulation in The Journal of Chemical Education.
The paper is free to read and includes tips on using the simulation in the classroom and steps to embed it in your LMS.