# Ericksen Number

on . Posted in Dimensionless Numbers

Ericksen number, abbreviated as Er, a dimensionless number, is used in the field of liquid crystal physics to describe the ratio of elastic forces to viscous forces in a liquid crystal material.  Liquid crystals are a state of matter that exhibits properties of both liquids and crystals.  They have anisotropic properties, meaning that their properties vary depending on the direction.  The Ericksen number is specifically used to characterize the behavior of liquid crystal flows, especially in situations where the material is subjected to shear or deformation.

The Ericksen number helps describe the relative importance of elastic and viscous effects in liquid crystal flows.  A high Ericksen number suggests that the elastic properties of the material dominate, while a low Ericksen number indicates that viscous forces play a more significant role.

In liquid crystal physics, the behavior of liquid crystals is influenced by their molecular structure, orientation, and response to external stimuli like shear forces.  The Ericksen number is a crucial parameter for understanding and predicting the behavior of liquid crystals in various applications, including display technologies and other devices that utilize their unique properties.

### Ericksen Number formula

$$Er \;=\; \eta \; v \; l \;/\; E$$     (Ericksen Number)

$$\eta \;=\; Er \; E \;/\; v \; l$$

$$v \;=\; Er \; E \;/\; \eta \; l$$

$$l \;=\; Er \; E \;/\; \eta \; v$$

$$E \;=\; \eta \; v \; l \;/\; Er$$

Symbol English Metric
$$Er$$ = Ericksen number $$dimensionless$$
$$\eta$$  (Greek symbol eta) = viscosity $$lbf - sec\;/\;ft^2$$ $$Pa - s$$
$$v$$ = velocity of bulk fluid $$ft\;/\;sec$$ $$m\;/\;s$$
$$l$$ = length $$ft$$ $$m$$
$$E$$ = elasticity $$lbf\;/\;in^2$$  $$Pa$$

Tags: Force