In the experiments considered, water flows through very smooth carbon nanotubes. Water molecules have a diameter of .3 nm. The radius of the nanotube varies in the range [20,100] nm. A small friction has been measured. The surprising finding is that the resistance increases with the radius of the nanotube although large tubes are as smooth as small tubes.
In classical hydro-dynamics the wall is just a wall. Now one must define this notion more precisely. The wall is made of mono-atomic graphene layers. Layers are smooth, which reduces drag and water molecules are not adsorbed on the walls. Therefore the friction is very small but non-vanishing.
The reason is that the electrons of graphene interact with polar water molecules and form bound states and follow the flow. Catching the flow takes however some time which causes resistance. In Born-Oppenheimer approximation this is not taken into account and electrons are assumed to adapt to molecular configurations instantaneously. For thin nanotubes the graphene layers are not so well-ordered due to the geometric constraints and the number layers and therefore also of co-moving electrons is smaller. This reduces the friction effect.
Could TGD help to understand the findings?
- I wrote some time ago an article about quantum hydrodynamics in TGD Universe some time ago (see this). The model for turbulence would involve the notion of dark matter as phases of ordinary matter with effective Planck constant heff= nh0>h even in macroscales. heff would characterize the "magnetic body" (MB) associated with the flow.
- The quantum scale L associated with the flow is proportional to heff and could characterize the MB. L could be larger than the system size but would be determined by it. One could say that MB to some degree controls the ordinary matter and its quantum coherence induces ordinary coherence at the level of the ordinary matter. Quantum effects at the level of MB are suggested to be present even for the ordinary hydrodynamic flow. The detailed mechanism is however not considered.
- The outcome is the prediction that kinematic viscosity is proportional to heff/m, where m is the mass of the unit of flow, now a water molecule.
- What could be the quantum scale L now? The scale of classical forced coherence would be the radius R of the pipe or, as the study suggests, the size scale of the system formed by water flow and the ordered graphene layers. The scale L of quantum coherence associated with MB could be larger. The larger the number of layers, the larger the size L of MB.
From L ∝ heff, one has ν ∝ ℏeff/m ∝ L. In conflict with the classical intuitions, the friction would be proportional to L and decrease as the pipe radius decreases. This conforms with the proposal if the magnetic body associated with the electron system is the boss.
For a summary of earlier postings see Latest progress in TGD.