# Bodenstein Number

on . Posted in Dimensionless Numbers

Bodenstein number, abbreviated as Bo, a dimensionless number, is used in chemical engineering and fluid dynamics.  The Bodenstein number relates the rate of chemical reaction to the rate of diffusion in a system.  The Bodenstein number is particularly relevant when considering the kinetics of chemical reactions in cases where the reaction rate is limited by the transport of reactants to the reaction site.  It helps to determine whether a reaction is more controlled by reaction kinetics or by the transport of reactants.

### Key points about Bodenstein number

• If the number is high (Bo >> 1)  -  The reaction rate is limited by diffusion and reactants are not reaching the reaction site quickly enough.
• If the number is low (Bo << 1)  -  The reaction rate is fast compared to diffusion and the reaction is mainly controlled by the kinetics.

The Bodenstein number is a useful tool for understanding the interplay between reaction rates and diffusion rates in chemical systems, and it's often employed in the design and analysis of chemical reactors and other chemical processes.

### Bodenstein number formula

$$Bo = v \; l \;/\; D_a$$     (Bodenstein Number)

$$v = Bo \; D_a \;/\; l$$

$$l = Bo \; D_a \;/\; v$$

$$D_a = v \; l \;/\; Bo$$

Symbol English Metric
$$Bo$$ = Bodenstein number $$dimensionless$$
$$v$$ = velocity $$ft \;/\; sec$$ $$m \;/\; s$$
$$l$$ = reaction length $$ft$$ $$m$$
$$D_a$$ = effective axial diffusivity $$ft^2 \;/\; sec$$  $$m^2 \;/\; s$$