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
220.127.116.11 Continuous Mobile Source in Stationary Medium
Consider a mobile nanorobot traveling through a stationary aqueous medium at velocity vn (m/sec), emitting message molecules continuously at the rate of 'Qmessage (molecules/sec). The cigar-shaped molecular trail envelope has a maximum length Xfadeout = 'Qmessage / 4 p D cmin, and at a distance Xmax = Xfadeout / e behind the moving source the message molecules diffuse outward to a maximum detectable radius Rmax = (0.342) ('Qmessage / vn cmin)1/2 as measured from the motion axis; for distances >Xmax the radius of the detectable message molecule envelope declines to zero at Xfadeout, with tfadeout = Xfadeout / vn. Thus, a nanorobot velocity vn = 10 microns/sec and an Xfadeout = 1000 microns requires 'Qmessage = 4 x 105 molecules/sec for simple message molecules (Imessage = 100 bits) giving Rmax ~ 60 microns at Xmax = 370 microns and tfadeout = 100 sec.
These equations703 also apply to a continuous stationary source in a nonstationary medium, where the medium moves past the source with a slow, constant velocity with perfect laminar nonturbulent flow in the absence of nearby boundary surfaces, an idealized instance of the case described in Section 18.104.22.168.
Last updated on 18 February 2003