Photophoretic flight of perforated structures in near-space conditions

Lightweight nanofabricated structures could photophoretically loft payloads in near-space. Proposed structures range from microscale engineered aerosols¹, to centimetre-scale thin disks with variations in surface accommodation coefficients^2,3, to sandwich structures with nanoscale thickness^4,5 that might be extended to metre-scale width^6,7. Quantitative understanding of how structural and surface properties determine photophoretic lofting forces is necessary to develop a practical flying device. Here we focus on thermal transpiration as the most promising photophoretic mechanism for lofting large devices⁸ and present a hybrid analytical-numerical model of the lofting force on a structure that consists of two perforated membranes spaced a small distance apart. We identify optimal structural parameters, including device size, membrane perforation density and distribution of the vertical ligaments that connect the two membranes, each as a function of atmospheric altitude. Targeting these optimal parameters, we fabricate structures with a heterogeneous ligament distribution, which efficiently compromises between structural rigidity and photophoretic performance. We measure how lofting forces generated by these structures depend on pressure using gases with three different molecular weights. We observed photophoretic levitation of a 1-cm-wide structure at an air pressure of 26.7 Pa when illuminated by 750 W m^-2, about 55% the intensity of sunlight. Lastly, we describe the preliminary design of a 3-cm-radius device with 10-mg payload capacity at 75-km altitudes and discuss horizontal motion control, overnight settling, and applications in climate sensing, communications and Martian exploration.