Froude number

Definition

The Froude number (symbol Fr) is a dimensionless parameter that describes the ratio of inertial forces to gravitational forces in a flow. In mixing technology, it relates to the motion of the mixing tool and is calculated from the tool’s circumferential velocity v, the tool radius r and the acceleration due to gravity g:

Fr = v² ÷ (g · r)

Alternatively, it can be expressed in terms of the rotational frequency n. Crucially, this parameter compares two competing forces: the acceleration with which the tool moves the material being mixed, and the force of gravity that pulls it back.

Significance for mixing technology

The Froude number characterises the motion regime of the bulk material. At low values, gravity dominates; the product slides and rolls. As the Froude number increases, the mixture is increasingly thrown about and loosened, until the energy input is so high that particle damage, segregation by density or undesirable heating may occur. The appropriate range for a given task depends on the product and the process objective and is determined experimentally.

Scope of application and limitations

The Froude number applies to rotating free-fall, drum and toss mixers, as well as to systems with horizontally mounted mixing elements. For vertical mixers with forced recirculation, it is not a design or scale-up criterion. The decisive factor here is that the mixing principle remains the same across all sizes and that the recirculation covers the entire mixing chamber regardless of the filling level; transferability is verified in the pilot plant using the original product.

Application in scale-up

Within its scope of application, the Froude number is frequently kept constant during a scale-up to achieve comparable flow conditions. As the impeller radius increases, the permissible rotational frequency decreases. Extending the mixing time in proportion to the volumes is, by contrast, not a viable approach, as it does not allow the flow pattern to be accurately represented.

Limitations

The Froude number describes only the ratio of two forces. Shear stress, residence time distribution, adhesive forces between fine particles, moisture and heat transfer are not taken into account. It is therefore a guideline for design, not a substitute for mixing trials on a sufficiently large scale.