Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| Beide Seiten der vorigen RevisionVorhergehende ÜberarbeitungNächste Überarbeitung | Vorhergehende Überarbeitung | ||
| en:grundlagenhandbuch:berechnung_der_dispergierguete [2026/05/28 09:34] – deppe2 | en:grundlagenhandbuch:berechnung_der_dispergierguete [2026/05/28 09:35] (aktuell) – [Agglomerate Disintegration] deppe2 | ||
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| Zeile 37: | Zeile 37: | ||
| In addition to the power, the stresses to which a sphere is subjected in a shear flow are considered in the next step, analogous to [[en: | In addition to the power, the stresses to which a sphere is subjected in a shear flow are considered in the next step, analogous to [[en: | ||
| - | $$\omega = \frac{1}{2} \dot{\gamma} | + | $$\omega = \frac{1}{2} \dot{\gamma} |
| The power at the sphere’s surface, as shown in Figure 10.2, is formulated as follows according to Raasch [[en: | The power at the sphere’s surface, as shown in Figure 10.2, is formulated as follows according to Raasch [[en: | ||
| Zeile 117: | Zeile 117: | ||
| Due to the high pressures occurring in continuous mixers, shear failures are more than likely to occur. From this follows: | Due to the high pressures occurring in continuous mixers, shear failures are more than likely to occur. From this follows: | ||
| - | $$\tau_{Sch} = \frac{1}{2} \sigma_v = \sigma_3 - \sigma_1 | + | $$\tau_{Sch} = \frac{1}{2} \sigma_v = \sigma_3 - \sigma_1 \tag{23}$$ |
| With σ1 and σ3 being the maximum principle stresses. We assume the hoop stress σv to be almost equal to the tensile strength σz, which we predict using Rumpf' | With σ1 and σ3 being the maximum principle stresses. We assume the hoop stress σv to be almost equal to the tensile strength σz, which we predict using Rumpf' | ||
| - | $$\tau_{Sch} = \frac{1}{2} \sigma_z = \frac{(1 - \varepsilon_A) \overline{F_{adh}}}{2\pi \cdot d_p^2} \tag{11} \tag{24}$$ | + | $$\tau_{Sch} = \frac{1}{2} \sigma_z = \frac{(1 - \varepsilon_A) \overline{F_{adh}}}{2\pi \cdot d_p^2} \tag{24}$$ |
| Inserting the agglomerate strength according to Rumpf (eqn. (11) results in the following differential equation for the agglomerate rupture: | Inserting the agglomerate strength according to Rumpf (eqn. (11) results in the following differential equation for the agglomerate rupture: | ||
| - | $$\frac{\partial \bar{d}}{\partial t} = \frac{5}{64} \cdot \frac{\tau_{Fluid} \cdot \dot{\gamma}}{\tau_{Sch} \cdot \pi} \cdot \bar{d} \tag{12} \tag{25}$$ | + | $$\frac{\partial \bar{d}}{\partial t} = \frac{5}{64} \cdot \frac{\tau_{Fluid} \cdot \dot{\gamma}}{\tau_{Sch} \cdot \pi} \cdot \bar{d} \tag{25}$$ |
| ==== Erosion ==== | ==== Erosion ==== | ||