Early turbulence and pulsatile flows enhance diodicity of Tesla’s macrofluidic valve
Nature Communications volume 12, Article number: 2884 (2021 ) Cite this article
Microfluidics has enabled a revolution in the manipulation of small volumes of fluids. Controlling flows at larger scales and faster rates, or macrofluidics, has broad applications but involves the unique complexities of inertial flow physics. We show how such effects are exploited in a device proposed by Nikola Tesla that acts as a diode or valve whose asymmetric internal geometry leads to direction-dependent fluidic resistance. Systematic tests for steady forcing conditions reveal that diodicity turns on abruptly at Reynolds number \({\rm{Re}}\approx 200\) and is accompanied by nonlinear pressure-flux scaling and flow instabilities, suggesting a laminar-to-turbulent transition that is triggered at unusually low \({\rm{Re}}\) . To assess performance for unsteady forcing, we devise a circuit that functions as an AC-to-DC converter, rectifier, or pump in which diodes transform imposed oscillations into directed flow. Our results confirm Tesla’s conjecture that diodic performance is boosted for pulsatile flows. The connections between diodicity, early turbulence and pulsatility uncovered here can inform applications in fluidic mixing and pumping.
From circulatory and respiratory systems to chemical and plumbing networks, controlling flows is important in many natural settings and engineering applications1,2,3,4,5. Perhaps the simplest means for directing flows is through the geometry of vessels, pipes, channels, and networks of such conduits. How geometry maps to flow patterns and distribution, however, is a challenging problem that depends on flow regime, as characterized by dimensionless quantities involving length- and time-scales and fluid material properties6. The field of microfluidics focuses on low Reynolds numbers in which small volumes are conveyed at slow speeds, and recent progress stems from advances in microscale manufacturing and lab-on-a-chip applications7. The flow physics at these scales is dominated by pressures overcoming viscous impedance, and the linearity of the governing Stokes equation enables theoretical and computational approaches that greatly aid in the design of microfluidic devices8. At larger scales and faster rates, the applications are as numerous and important2,3 but the flow physics quite different. The underlying Navier–Stokes equation is nonlinear, theoretical results are fewer, simulations are challenging, and the mapping between geometry and desired fluidic objectives all the more complex6. The phenomenology of high-Reynolds-number or inertia-dominated flows is well documented: Flows are slowed in boundary layers near surfaces and tend to separate in a manner sensitive to geometry to yield vortices, wakes, jets, and turbulence6,9. Such complexities are exemplified by the breakdown of reversibility: Running a given system in reverse, say by inverting pressures, does not in general cause the fluid to move in reverse but instead triggers altogether different flow patterns6.
