# Bodenstein number

Bodenstein number | |
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Derivations from other quantities | |

Dimension | dimensionless |

The **Bodenstein number** (abbreviated *Bo*, named after Max Bodenstein) is a dimensionless parameter in chemical reaction engineering, which describes the ratio of the amount of substance introduced by convection to that introduced by diffusion. Hence, it characterises the backmixing in a system and allows statements whether and how much volume elements or substances within a chemical reactor mix due to the prevalent currents. It is defined as the ratio of the convection current to the dispersion current. The Bodenstein number is an element of the *dispersion model of residence times* and is therefore also called the *dimensionless dispersion coefficient*.

Mathematically, two idealized extreme cases exist for the Bodenstein number. These, however, cannot be fully reached in practice:

- corresponds to full backmixing, which is the ideal state to be reached in a continuous stirred-tank reactor.
- corresponds to no backmixing, but a continuous through flow as in an ideal flow channel.

Control of the flow velocity within a reactor allows to adjust the Bodenstein number to a pre-calculated desired value, so that the desired degree of backmixing of the substances in the reactor can be reached.

## Determination of the Bodenstein number

The Bodenstein number is calculated according to

where

- : flow velocity
- : length of the reactor
- : axial dispersion coefficient

It can also be determined experimentally from the distribution of the residence times. Assuming an open system:

holds, where

- : dimensionless variance
- : variance of the mean residence time
- : hydrodynamic residence time