Observation:
All the details you could observe about the mixer blades, the hood, and the flow during mixing are important when making a smoothie, as the device performs two functions simultaneously. On the one hand, the fruits are to be chopped, and on the other hand, the chopped fruits are also to be mixed.
If you cut the fruits before mixing, the blade of the knife surely pointed in the direction you pressed, right? For chopping the fruits when mixing or pureeing, it should also be sufficient if the blades of the mixer or immersion blender are straight. But the blades are angled. Why? When cutting fruit, if you held the knife at an angle and pressed the same way as before, you would push the fruit away on the side with the acute angle (Please do not try this, risk of injury if the knife slips!). Due to the angled blades, exactly the same thing happens in your device. The chopped pieces are pushed away. With an immersion blender, the chopped pieces are pushed into the hood and deflected sideways by the round shape. If the hood has holes on the side, the pureed fruit can flow out of the hood without coming into significant contact with the unpureed fruit.
These flows are particularly important in a stand mixer, as it has to catch all the unpureed pieces without manual guidance. For this, it is important that the mixer creates a flow through the blades. The flow is usually directed downwards at the blades, is deflected at the bottom towards the walls, and then flows back in the middle at the top towards the blades.
What is important in any case is a high speed of the blades and the flow. The high speed means turbulence for the flow. Turbulence is a completely chaotic flow within the main flow. This turbulence is important for mixing the chopped fruits in the smoothie.
And what does this have to do with process engineering or engineering sciences?
Did the topic of flow guidance and chopping interest you? Flows are covered in lectures on fluid dynamics or fluid mechanics. Suitable fields of study could be process engineering or mechanical engineering.