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--- en:grundlagenhandbuch:verweilzeitberechnung:kuerzeste_verweilzeit [2025/06/22 10:53] – deppe2
+++ en:grundlagenhandbuch:verweilzeitberechnung:kuerzeste_verweilzeit [2026/01/27 15:42] (aktuell) – gelöscht deppe2
@@ Zeile 1: / Zeile 1: @@
-====== Minimum Residence Time ======
-===== Minimum Residence Time =====
-The minimum residence time $t_1$ is defined as the period between the entrance and the first exit of the material at the screw tip. In a rectangular channel there is a section where no rotational flow occurs, regardless of the type of the flow. In the case of a Newtonian fluid the area is always located at $y/h = 2/3$. Particles moving on this particular streamline are exhibited to the minimum residence time. Based on this observation, the results presented by Bigg and Middleman [1] Lappe [2, 3] proposed the following equation to calculate the minimum residence time:
-$$\Theta_1 = \frac{3}{4}\pi_v^{0.23(1-n)} \tag{1}$$
-where $\Theta_1$ is the dimensionless minimum residence time, namely the ratio of the minimum residence time to the average residence time, $\pi_v$ is the dimensionless throughput and n the power law index. In the figure one can see the influence of the power law index on the minimum dimensionless residence time.
-**Figure:** Influence of the Power Law index on the minimum dimensionless residence time [3-5]
-$\Theta_1$ decreases for constant dimensionless throughputs $\pi_v < 1$ with decreasing power law index n. One can see that the ratio of minimum and average residence time for a Newtonian fluid is always 0.75. This means that one cannot influence the dimensionless residence time by changing machine or processing parameters.
-In order to calculate the minimum residence time one has to distinguish the following cases:
-**I. Conveying elements (right handed screw elements, conveying kneading blocks, etc.):**
-  * 1. Solids Conveying Section
-    * Case 1: f < 1 (partially filled)
-$$\Theta_1 = \frac{1}{2} \tag{2}$$
-    * Case 2: f = 1 (fully filled)
-$$\Theta_1 = 1 \tag{3}$$
-  * 2. Melt Conveying Section
-    * Case 1: f < 1
-$$\Theta_1 = \frac{1}{2} \tag{4}$$
-    * Case 2: f = 1
-$$\Theta_1 = \frac{3}{4}\pi_v^{0.23(1-n)} \tag{5}$$
-**II. Reconveying Elements (left handed screw elements, reconveying kneading blocks, etc. as well as neutral elements):**
-$$\Theta_1 = 1 \tag{6}$$
-The overall minimum residence time is calculated by totalling the calculated minimum residence times in all sections of constant geometry.
-$$t_1 = \sum_i (t_1)_i \tag{7}$$