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# Froude number

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

## 1. Froude Number calculation

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

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

Froude number is defined in equation 1 [Perry]:

Equation 1 : Froude number

With
ω = angular velocity

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

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 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 suspended in air in the mixer.

## 2. Froude Number references of common 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
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 mixer 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.