Aerosol Transport – Inertia

:: Section 3

Newton's Resistance Law and Stokes's Law

II. Stokes's Law

When small particle size and low velocity are involved, the Reynolds number is small and the flow is laminar. Under this condition, inertial forces are negligible compared to viscous forces. Newton's Law is no longer valid and Stokes's Law shall be used, which has the following form:

In order to determine the drag coefficient in the Stokes's regime, we can compare the above equation to the Newton's resistance equation:

Then, we can get the drag coefficient in the laminar flow regime. It is inversely proportional to the drag coefficient Re_p as:

There are several assumption associated with the Stokes's Law:

• The fluid is incompressible.
• There is no other particle nearby that would affect the flow pattern.
• The motion of the particle is constant.
• The particle is spherical and rigid.
• The air velocity right at the particle surface is zero.

We should keep these assumptions in mind and verify if the assumptions are valid when we use the equation.

Which of the following condition(s) can the Stokes's Law be applied? (a) A particle with a diameter of 10 μm having a velocity of 1 m/s. (b) A particle with a diameter of 100 μm having a velocity of 10 m/s. (c) A particle with a diameter of 1 mm (1000 μm) having a velocity of 20 m/s.

To calculate the Re_p values, you can use the web-calculator below: