Rotational frequency

The terms mixing mechanism rotational frequency and mixing mechanism rotation describe the rotary motion of mixing tools. They do not only apply to mixers. The same kinematic relationships also apply to shredders, centrifuges, fans, centrifugal pumps, cutting rotors, knife heads and rotor-stator systems.

A key physical quantity is the circumferential velocity. It is calculated from the vector product of the angular velocity and the radius vector. In terms of magnitude, the relationship v = ω · r applies. The circumferential velocity describes the linear velocity of a point on the rotating tool.

The circumferential velocity is an important parameter for the efficiency of process engineering equipment. It is often used to describe mixing, conveying or comminution processes. In particular, it is a basic parameter for the scale-up of laboratory or pilot plants to large-scale equipment.

However, the circumferential velocity alone is not sufficient to fully describe rotational processes. This applies to mixing as well as to conveying, comminuting, impact stressing or deagglomerating bulk solids. A second decisive variable is the centripetal acceleration acting on the product.

Centripetal acceleration is calculated from the square of the angular velocity multiplied by the radius of rotation. The formula is a = ω² · r. This relationship is equivalent to a = v² / r. It describes the radial acceleration that forces the product into a circular path.

Centripetal acceleration significantly determines the forces acting on the mixture. It influences compaction, relative movement of the particles and contact forces between the product and the tool. It therefore has a direct influence on mixing intensity, segregation tendency and mechanical stress on the mixture.

For a safe and reliable scale-up, both the circumferential speed and the centripetal acceleration must be taken into account. Only the simultaneous consideration of both variables allows a physically consistent transfer of process conditions to larger apparatus.