Froude number

Froude number applied to powder mixing applications

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Section summary
1. Froude number calculation
2. Froude number references for common powder mixers

Section summary

1. Froude number calculation

2. Froude number references for common powder mixers

1. Froude Number calculation

What is the Froude number formula ?

Powder mixing is based on the movement of the particles part of the recipe to be mixed. The movement can be of different types, and different designs of mixers will correspond to different mixing principles.

Mixers are often classified thanks to the Froude number. Froude number significance : this adimensional number will define the regime of mixing depending on its value.

Froude number is defined in equation 1 [Perry]:

Froude number for bulk powder blending

Equation 1 : Froude number formula

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 (agitator) 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

What is Froude number used for?

What is the Froude number ? Froude number is comparing 2 forces :

Fr = (forces other than gravity, mainly centrifugal) / gravity

If Fr < 1 it means that the gravity forces will be stronger than the centrifugal forces, the powder will remain settled in the mixer, moved, but not in a cloud
If Fr > 1 it means that the centrifugal forces will tend to be stronger than the gravity force : the powder will have a tendency to be lifted and suspended in air in the mixer.

2. Froude Number references of common mixers

Key Froude number application : mixing regime in powder dry mixers

Among the common mixers used industrially for powder mixing, the table below is proposing a classification according to Froude number

Table 1 : Mixer classified according to their Froude number and mixing principle

Fr	Mixing class	Mixer type	Pros	Cons
< 1	Diffusion	Type free fall mixers V Blenders Double Cone blenders Bin blenders Drums blenders	Very simple Low energy required Gentle mix No mixing elements in the equipment Reliability Access for cleaning	Long mixing Cannot achieve good mixing for powders of very different particle sizes Segregation effects can be experienced
< 1	Convection	Type thrust mixer Ribbon Blenders Screw Blenders	Achieve generally better mixing results than diffusion blenders Low energy inputs Generally less expensive than paddle or plough share mixers	Long mixing Mechanical complexity Access for cleaning Can damage product at long mixing time
> 1	Convection	Paddle Mixers Pneumatic mixers	Short mixing time Gentle mixing Low energy input Good access for cleaning (some design can be with extractible shafts For paddle mixers, exist in continuous mixing execution For padlle mixers, a liquid injection can be foreseen	Cost compared to diffusion tumblers / ribbon blenders If liquid injection, prone to agglomeration - then needs some additional mixing elements at higher shear For pneumatically generated fluid bed, attention must be given to risks of segregation due to fines "floating" at the top of the mixer
>> 1	Convection Shearing	Plough Share Mixers High shear mixing elements	Short mixing time Reduce risks of powder agglomeration Exist in continuous mixing execution	Higher powder breakage High energy input Cost

Another type of classification could be proposed depending on the type of process where mixers are integrated : Batch or Continuous. If batch mixers probably represent the majority of the industrial applications, some types of mixers (paddle mixers) can be used in a continuous mode, which can be useful for some kind of processes.

3. Froude number calculator

You can open a free Excel calculator for the Froude number here : Froude Excel Calculator