Enhancing the Photophoretic Lift Force at Low Reynolds Numbers using Three-Dimensional Porous Structures

It is well documented that the lift force of hovering micro aerial vehicles can be enhanced by increasing their air-flow velocities. This is commonly accomplished using nozzles and other flow-manipulating geometries with Reynolds numbers above order 100. [1,2] However, the effects of nozzles and other geometries are not well characterized for lower Reynolds numbers within the Stokes’ regime. In general, controlled flight in low-Reynolds number conditions using conventional propulsion methods such as propellers is difficult. Instead, levitation at ultra-low Reynolds number conditions has been accomplished through other means, including photophoretically as demonstrated recently by Cortes et al. [3] and Azadi et al. [4]. These works levitated planar materials without macroscale geometric enhancements and relied strictly on the lift force created through a temperature or accommodation coefficient difference across the planar structure. In the current work, we numerically explored the feasibility of multi-scale structures operating at low-to-moderate Reynolds numbers that pair microscale photophoretic gas pumping with macroscale jet-inducing nozzles.

We used ANSYS Fluent to simulate the lift forces in centimeter-scale porous membrane discs (no macroscale enhancements) and in conical nozzles created from porous membranes. Our results indicate that porous conical nozzles provide an order of magnitude lift enhancement relative to flat discs with inlet velocities as low as 10^-6 m/s. In addition, we developed a semi-analytical flow model and found good agreement with the simulations. We are currently fabricating mylar structures analogous to the simulation geometries, laser machined to create porosity and adhered to lightweight frames to maintain their shape. The multi-scale structures we create will be of critical importance for exploring low-pressure environments such as Earth’s mesosphere and the Martian atmosphere.

References:

[1] Benedict, Moble, et al. "Experimental investigation of micro air vehicle scale helicopter rotor in hover." International Journal of Micro Air Vehicles3 (2015): 231-255.

[2] Seddon, John M., and Simon Newman. Basic helicopter aerodynamics. Vol. 40. John Wiley & Sons, 2011.

[3] Cortes, John, et al. "Photophoretic levitation of macroscopic nanocardboard plates." Advanced Materials16 (2020): 1906878.

[4] Azadi, Mohsen, et al. "Controlled levitation of nanostructured thin films for sun-powered near-space flight." Science Advances7 (2021): eabe1127.