Quantum Hydrodynamics of the Bingham Fluid Addressing the CNT Enhanced Fluid Flow

Abstract The superflow of water at nanoscale remains an open problem. Classical hydrodynamics predicts flow rates that are 2 to 5 orders of magnitude lower than those observed experimentally. Therefore, it is natural to question the validity of such models while exploring alternative approaches. In this work, we investigate the behavior of viscoplastic fluids, particularly Bingham fluids, from the perspective of de Broglie–Bohm quantum mechanics, incorporating the effects of a quantum potential (quantum hydrodynamics). We phenomenologically assume that the physics behind these unexplained experimental results might be associated to an effective quantum potential which properties that can be associated to an effective anti-dissipative hydrodynamical term in the classical approach. We combine a theoretical approach with its numerical solutions to understand the interplay between the Navier–Stokes-Bingham hydrodynamical system and the quantum hydrodynamics. Our results indicate that the quantum potential can be directly associated with the increased flow velocity, reinforcing that quantum effects may play a significant role in the dynamics of fluids confined within nanotubes. Moreover, well-behaved solutions for the system’s wavefunction were identified even in the exotic case of anti-dissipative fluid flow. This evidence provides a possible theoretical explanation for the superflux phenomenon, reinforcing the hypothesis that quantum effects may underlie the discrepancies relative to classical hydrodynamic predictions.