the best we can achieve is a transitional flow (basically a turbulent laminar flow) because we obviously can never get rid of the coffee and we would work at decreasing the Reynolds number which brings us closer to perfect laminar flow. if it was always laminar flow we would never get donut shots so obviously there are other things influencing the flow. but is laminar flow the best goal to aim for and are we not just asking for forms of channeling at the point of highest velocity (the center) and under-extracted coffee at the walls? the flow near the surface of the walls would be extracting through diffusion only and diffusion is going to be slower than the flow, so wouldn't it be better to have an even flow through the entire puck and work at eliminating the no-slip condition altogether?
The no-slip condition doesn't just work on stationary walls but also for moving walls. if the walls are moving (and there is no other influence) the flow relative to the surface of the walls would be zero (so would be moving with the walls) and the fluid next to those would slip a little bit more, then next to those a little bit more, etc... producing a reverse laminar flow. So at first, I thought how could you make a PF with moving walls to match the flow at the highest velocity and counteract the no-slip condition by controlling it? but a PF like that would be a bit ridiculous, essentially a long pipe that would be pressed through the PF and act as moving walls. Perhaps it could work as a sort of kick-starter hand press gizmo but I think an easier solution would be a superhydrophobic coating on the PF walls which would do a good job at eliminating the no-slip condition. Water wouldn't stick to the surface but rather bead up on the walls and immediately exit.
if there was no resistance at the walls it will have an effect at increasing the flow and probably have higher EY as the sides would be extracted at the same rate as the centre (no laminar flow effect). Typically this is an excuse to dose down and grind finer but in this case it may just be dosing down which would result in the same TDS in the cup as the extraction would be more efficient.
is the no-slip condition a problem in espresso that we just deal with and should we be looking at ways to reduce the no-slip? would a superhydrophobic coated PF be a solution to this? what do you think?