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
18.104.22.168 Continuous Stationary Source in Stationary Medium
Consider a source of message molecules emitting continuously at the constant rate 'Qmessage (message molecules/sec) into the idealized stationary medium described in Section 22.214.171.124. Such a source might be useful for status telemetry, navigational beacons, or periodic sampling monitors. If the source continues for a long time then the detectable threshold concentration sphere703 of message molecules around the point source asymptotically approaches a maximum radius Rmax = 'Qmessage / (4 p D cmin). The time for the expanding detectable concentration sphere to reach a radius R = fR Rmax (where 0 <~ fR <~1 is the fractional radial expansion of the message sphere), the exact solution for which involves the complementary error function, is approximated reasonably well by trec ~ (1.1 fR 'Qmessage / 8 p cmin (1 - fR) D3/2)2 for 0.1 < fR <~ 1, using D from Eqn. 7.4 and cmin from Eqn. 7.5. Thus for simple messages (Imessage = 100 bits) with Rmax = 100 microns and R = 50 microns (fR = 0.5), then 'Qmessage ~ 4 x 104 message molecules emitted per second and trec ~ 140 sec ('I ~ 1 bit/sec). For complex messages (Imessage = 109 bits), 'Qmessage ~ 10 message molecules emitted per second and trec ~ 8.4 hours ('I ~ 3 x 104 bits/sec).
Last updated on 18 February 2003