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.

$$t_1 = \sum_i (t_1)_i \tag{7}$$