Unterschiede

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--- en:grundlagenhandbuch:verweilzeitberechnung [2026/05/21 22:33] – [Analysis of the Residence Time Distribution] neelest
+++ en:grundlagenhandbuch:verweilzeitberechnung [2026/05/24 18:07] (aktuell) – [Analysis of the Residence Time Distribution] neelest
@@ Zeile 97: / Zeile 97: @@
   * characteristic values of the distribution profiles have to fit in with the experimental results. Characteristic values are e.g. the value for $\Theta = 1$ and the position of the maximum of the probability density function [[en:grundlagenhandbuch:verweilzeitberechnung#references |[PA90]]], [[en:grundlagenhandbuch:verweilzeitberechnung#references |[PA90]]], [[en:grundlagenhandbuch:verweilzeitberechnung#references |[Eng87]]].
-  * the distribution function has to take into account the case of a pure plug flow with the boundary conditions:
+  * The distribution function must account for pure block flow with the boundary conditions
-$$F(\Theta) = \begin{cases} 0, & \text{für: } \Theta < 1 \\ 1, & \text{für: } \Theta \geq 1 \end{cases} \tag{13}$$
+$$F(\Theta) = \begin{cases} 0, & \text{for: } \Theta < 1 \\ 1, & \text{for: } \Theta \geq 1 \end{cases}\tag{13}$$
-$$\bar{\Theta} = \Theta_1 = 1 \tag{14}$$
+,
-  * the distribution function has to take into account the case of the so called ideal mixer with $\Theta_1 = 1$ using the parameters $c_1 = c_2 = 1$.
+  * Furthermore, for pure block flow, the following applies: $\bar{\Theta} = \Theta_1 = 1$,
-  * the variance $\sigma^2$ of the probability function:
+  * the distribution function must describe the limiting case of the so-called ideal mixer with $\Theta_1 = 0$ via $c_1 = c_2 = 1$,
+  * the variance $\sigma^2$ of the probability density function
-$$\sigma^2 = \int_{\Theta_1}^{\infty} (\Theta - 1)^2 f(\Theta)d\Theta \tag{15}$$
+$$\sigma^2 = \int_{\Theta_1}^{\infty} (\Theta - 1)^2 f(\Theta)d\Theta\tag{14}$$
-has to decrease with the minimum dimensionless residence time and has to take the following values:
+must decrease monotonically as a function of the shortest dimensionless residence time $\Theta_1$ and take the value 0 for $\Theta_1 = 1$ or the value 1 for $\Theta_1 = 0$,
-$$\sigma^2(\Theta_1 = 1) = 0 \tag{16}$$
+  * for physical reasons relating to the solid content, the variance $\sigma^2$ of the probability density function must always be smaller than that of a melt extruder. The melt extruder was discussed in [[en:grundlagenhandbuch:verweilzeitberechnung#references |[PL85]]].
-$$\sigma^2(\Theta_1 = 0) = 1 \tag{17}$$
-  * the variance of the probability function has to be smaller for plasticating extruders than for melt extruders due to the amount of solid particles present. More information referring to melt extruders can be found in [[en:grundlagenhandbuch:verweilzeitberechnung#references |[PL85]]].
 ===== References =====