Quantum hydrodynamics of the Bingham fluid and the CNT enhanced fluid flow

The superflow of water at nanoscale remains an open problem. Classical hydro-dynamics predicts flow rates that are 2 to 5 orders of magnitude lower than thoseobserved experimentally. Therefore, it is natural to question the validity of suchmodels while exploring alternative approaches. In this work, we investigate thebehavior of viscoplastic fluids, particularly Bingham fluids, from the perspectiveof de Broglie–Bohm quantum mechanics, incorporating the effects of a quantumpotential (quantum hydrodynamics). We assume that the physics behind theseunexplained experimental results might be associated to introducing an effectiveanti-dissipative term induced by the quantum potential. The study combinesa theoretical approach with its numerical solutions, and comparative analysis,employing the Navier–Stokes equations and the Bingham model. Our results indi-cate that the inclusion of the quantum potential is directly associated with theincreased flow velocity, reinforcing that quantum effects may play a significantrole in the dynamics of fluids confined within nanotubes. Moreover, well-behavedsolutions for the system’s wavefunction were identified even after the inclusionthe of effective anti-dissipative term. This evidence provides a possible theoret-ical explanation for the superflux phenomenon, reinforcing the hypothesis thatquantum effects may underlie the discrepancies relative to classical hydrodynamic predictions.