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Froude Number (Mixing)

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Section summary
1. Definition
2. Calculation of Froude Number
3. Application of Froude number in powder mixing

1. Definition - What is the Froude number ?

Froude number is an adimensional number. It is comparing 2 forces, : Fr = (forces other than gravity - mainly centrifugal) / gravity and give an indication of the dynamics of the flow of particles in a mixer.

2. Froude number calculation

Froude number for bulk powder blending

Equation 1 : Froude number

With
R = mixer radius or mixer agitator radius
ω = angular velocity

It can be expressed in a more convenient form for powder mixers having a mixing element in equation 2:

Froude number for bulk powder blending

Equation 2 : Froude number calculation for blender equipped with a mixing tool (ribbon, paddles...)

With
u = tip speed mixing element
D = diameter of mixing element

3. Application

The Froude number is used to caracterize how particles will be mixed in a dry-mixer.

If Fr < 1, gravity forces are higher than the inertial forces due to agitation or movement of the mixer, thus the mixing is done in dense phase, with particles rolling over each others. Free fall mixers (tumblers) or Ribbon blenders typically work in this range.

If Fr = 1, it is the tipping point, where the inertial forces and gravity forces balance. The particles agitated can be put in suspension by the mixer and fluidization happen. Double shaft paddle mixers, using a fluidization zone for mixing, typically work in the range Fr = 1 to 1.1

If Fr > 6-7, the powder is actually centrifugated and form an annular on the wall of the mixer. It is typically what happens with shear mixers (which can also work in the fluidized zone with Fr in between 2 to 6).