Elasticity Number

on . Posted in Dimensionless Numbers

Elasticity number, abbreviated as El, a dimensionless number, is the ratio of elastic force to internal force in viscoelastic flow.  This dimensionless parameter helps characterize the relative importance of elastic and viscous effects in the flow behavior of viscoelastic materials.  The elasticity number is particularly relevant in understanding the flow of materials that exhibit both elastic and viscous behavior, such as certain polymers.

The elasticity number is a useful parameter for predicting the flow behavior of viscoelastic fluids in different flow regimes.  When Elis much greater than 1, elastic effects dominate, and the material exhibits more elastic behavior.  When El is much less than 1, viscous effects dominate, and the material behaves more like a viscous fluid.  Understanding the elasticity number is crucial in designing and analyzing processes involving viscoelastic materials, such as polymer processing and certain types of fluid flows in industrial applications.

Elasticity Number formula

$$El \;=\; t \; \eta \;/\; \rho \; r^2$$     (Elasticity Number)

$$t \;=\; El \; \rho \; r^2 \;/\; \eta$$

$$\eta \;=\; El \; \rho \; r^2 \;/\; t$$

$$\rho \;=\; t \; \eta \;/\; El \; r^2$$

$$r \;=\; \sqrt{ t \; \eta \;/\; El \; \rho }$$

Symbol English Metric
$$El$$ = elasticity number $$dimensionless$$
$$t$$ = relaxation time $$sec$$ $$s$$
$$\eta$$  (Greek symbol eta) = viscosity $$lbf - sec \;/\; ft^2$$ $$Pa - s$$
$$\rho$$   (Greek symbol rho) = density $$lbm \;/\; ft^3$$ $$kg \;/\; m^3$$
$$r$$ = pipe radius $$in$$ $$mm$$