What Is Dynamic Viscosity?

The complex viscosity can be used to characterize the viscoelasticity of the polymer melt ( * = -i). The real part of the complex viscosity, called dynamic viscosity, represents the contribution of viscosity.

Dynamic viscosity:

According to the complex stress and the complex strain rate, the complex viscosity can be obtained, that is:

= s / g = (so / igo) · e = so / igo · (cos + isin) =

so / go · sin-i · (so / go) · cos = -i

= so / igo · sin = G / is called dynamic viscosity , it is related to the loss modulus, and it represents the contribution of viscosity, which is the energy dissipation part of complex viscosity; = so / igo · cos = G / is called imaginary viscosity. It is related to the dynamic modulus and represents the contribution of elasticity. It is a measure of elasticity and energy storage. Viscoelastic properties of polymer fluids can be characterized using complex viscosities. ^[1]

Assuming a small amplitude, the material is a linear body, and a sinusoidal strain is applied to the material:

g = gosint

In the formula, go is a small amplitude, and is a peripheral frequency, that is, an angular frequency. When the cyclically varying strain expressed by a complex number is a complex strain g:

g = go · e

Complex strain rate:

g = dg / dt = igoe

For an ideal elastomer, its stress response is:

s = Egoe

Stress and strain are in phase.

For an ideal viscous body, the stress response is:

s = igoe = go

That is, the stress phase is advanced by 90 strain.

For an elastic viscous body, the stress response is:

s = soe

That is, the stress phase is ahead of the strain by .

Knowing s and g defines the complex modulus G

G = s / g = so / go · e = G + iG

In the formula, G = so / go · cos is called dynamic modulus or believer's modulus, which means the elastic part; G = so / go · sin is called dynamic loss or loss modulus, which means the viscosity part. ^[2]