# Deborah Number

on . Posted in Dimensionless Numbers

Deborah number, abbreviated as De, a dimensionless number, is used in fluid dynamics to describe the relative importance of elastic and viscous effects in a viscoelastic material or fluid.  It characterizes the behavior of materials that exhibit both viscous (flow-like) and elastic (solid-like) properties.  The Deborah number helps to understand whether a material will behave more elastically or more viscously under a given set of conditions.

### Key points about the Deborah number

• When De ≪ 1  -  Elastic effects dominate, and the material behaves more like a solid, exhibiting elastic deformation.
• When De ≫ 1  -  Viscous effects dominate, and the material behaves more like a fluid, exhibiting flow behavior.
• When De is of the order of 1  -  The material exhibits both elastic and viscous behaviors, and the response is a combination of the two.

The Deborah number is commonly used in the study of polymers, gels, and other viscoelastic materials, as well as in various industrial applications such as the design of materials for controlled damping, vibration isolation, and other mechanical properties.

### Deborah Number formula

$$De \;=\; t_r \;/\; t_o$$     (Deborah Number)

$$t_r \;=\; De \; t_o$$

$$t_o \;=\; t_r \;/\; De$$

Symbol English Metric
$$De$$ = Deborah number $$dimensionless$$
$$t_r$$ = relaxation time of material $$sec$$ $$s$$
$$t_o$$ = time of observation $$sec$$ $$s$$