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Shear rate und shear deformation
Shear rate
The shear rate can, as a first approximation, be described by:
$$\dot \gamma = \frac{v_0}{h}$$ $$\text{with}$$ $$v_0 = \pi \cdot n \cdot D$$
and the channel height $h$. This equation is applied for shear and mixing sections. However, it only describes a simple drag flow of Newtonian fluids. For shear-thinning (pseudoplastic) fluids, the average shear rate is somewhat higher (also due to the superposition with pressure flow). As an approximation for conventional screw channels, the following relation applies:
$$\dot \gamma = \frac{exp(0,055 \cdot \pi_\dot m)}{cos(\varphi)} \cdot \frac{v_0}{h}$$
where $\pi_\dot m$ is the dimensionless throughput and $\varphi$ is the helix (flight) angle.
Shear deformation
The shear deformation $\overline{\gamma}$ describes the deformation of a volume element that is sheared due to a shear rate. Thus, shear deformation is the product of shear rate and residence time.
$$\overline{\gamma}= \dot \gamma \cdot \ t$$
This is integrated along the screw length. The cumulative shear deformation gradient is a measure of the laminar mixing effect.