Mixed indicators

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Graphical representation of the mixed key figures

REX/PSI provides both analytical mixing indicators and regression models based on numerical simulations of the mixing effect of different zone types.

Analytical mixed indicators

In theshort report and in the Mixture triangle three mixing ratios are displayed for the calculated screw.

Transverse mixing ratio

The transverse mixing ratio $\pi_{LSM}$ is calculated as follows: $$\pi_{LSM} = \left[ 1 + \left(c_0 \overline{\gamma} \right)^2 \right]^{-1/2}$$ $$\text{with}$$ $$\overline{\gamma} = \frac{2 \left(1.03 + 0.074n \right) L}{\cos\varphi \sin\varphi} \cdot \frac{1}{h_1 \, \pi_\dot{m}}$$ $$\text{and}$$ $$c_0 = c_1 \sqrt{\frac{h_1}{h_0}} \left(\frac{T_z}{T_0}\right)^{c_2} \frac{n^{c_3}}{\pi_\dot{m}}$$

with c1=0.08367, c2=0.7067 and c3=0.344

Longitudinal mixing ratio

The longitudinal mixing ratio $\sigma^2$ is calculated as follows

$$\sigma^2 = 1 + \exp(c_1 \Theta_{min}^{c_2}) - \exp(c_3 \Theta_{min})$$

with the dimensionless minimum residence time $\Theta_{min} = \frac{t_{min}}{\bar{t}}$ and

extruder type c1 c2 c3
melt extruder 0.2476 0.6014 0.8301
Conv. plasticising extruder -4.8828 2.1287 0.0028505
grooved barrel extruder -2.368 1.1268 0.1186

Agglomerate size reduction

The agglomerate size reduction ratio $Z$ is calculated as follows:

$$Z=\left[ 1+\left( \frac{t}{c_{31}}\right)^{c_{21}}\left( ln\left( \frac{\tau}{\tau_{min}}\right)\right)^{1/c_{11}}\right]^{-1}$$

with the current shear stress $\tau$, the minimum shear stress $\tau_{min}$ and the three decay constants $c$. The minimum shear stress and the three decay constants are Material parameters. REX offers default values at the push of a button.

Further topics

en/berechnungen/verweilzeitverteilung.1740686572.txt.gz · Zuletzt geändert: 2025/02/27 21:02