© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

7.2.1.5 Continuous Stationary Source in Stationary Medium

Consider a source of message molecules emitting continuously at the constant rate 'Q_message (message molecules/sec) into the idealized stationary medium described in Section 7.2.1.3. 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 R_max = 'Q_message / (4 p D c_min). The time for the expanding detectable concentration sphere to reach a radius R = f_R R_max (where 0 <~ f_R <~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 t_rec ~ (1.1 f_R 'Q_message / 8 p c_min (1 - f_R) D^3/2)² for 0.1 < f_R <~ 1, using D from Eqn. 7.4 and c_min from Eqn. 7.5. Thus for simple messages (I_message = 100 bits) with R_max = 100 microns and R = 50 microns (f_R = 0.5), then 'Q_message ~ 4 x 10⁴ message molecules emitted per second and t_rec ~ 140 sec ('I ~ 1 bit/sec). For complex messages (I_message = 10⁹ bits), 'Q_message ~ 10 message molecules emitted per second and t_rec ~ 8.4 hours ('I ~ 3 x 10⁴ bits/sec).

Last updated on 18 February 2003