Nanomedicine, Volume I: Basic Capabilities
© 1999 Robert A. Freitas Jr. All Rights Reserved.
Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999
184.108.40.206 Nanoflight and Gravity
In addition to forward progression through the medium, atmospheric flight requires active and continuous support against the pull of gravity. For small spherical objects of radius R = Rnano in the laminar flow (low NR) regime, the rate of fall in a still medium is approximated by Stokes Law for Sedimentation (Eqn. 3.10).* For nanorobots near the Earth's surface that are falling in air, with g = 9.81 m/sec2, rparticle ~ 1000 kg/m3, rfluid = rair and h = hair, then terminal velocity vt = 1.2 x 108 Rnano2 (m/sec). An Rnano = 1 micron nanorobot falls at vt = 120 microns/sec; an Rnano = 10 micron nanorobot falls at vt = 1.2 cm/sec, requiring a rather modest power expenditure of only Pnano/e% = (0.5 pW)/e% to remain aloft (Eqn. 9.74).
* In sea level pressure dry air, particles of 100 nm diameter will fall about twice as fast as estimated by Eqn. 3.10; 10-nm diameter particles fall about 12 times as fast as Stokes' sedimentation formula predicts.1572
Note also that in free atmosphere only the largest particles ever settle out by gravity alone. Thermal and dynamic turbulence keeps most of the smaller particles in suspension long beyond the period indicated by Eqn. 3.10. For example, nanorobot thermal velocity vthermal (Eqn. 3.3) exceeds nanorobot terminal velocity vt (Eqn. 3.10) for a nanorobot radius Rnano <~ 2 microns in sea level air at 20°C with rnano ~ 1000 kg/m3. The energy required to raise a 1-micron nanorobot a height of ~1 micron in a 1 g gravity field equals ~kT. Random indoor atmospheric eddies of 1-10 cm/sec caused by the movements of people, animals, doors, and heating and air conditioning systems equal or exceed the Stokes terminal velocity for particles of R <~ 10-30 microns.
Last updated on 22 February 2003