**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

**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 sphere^{703}
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 10^{4} message molecules emitted per second and t_{rec}
~ 140 sec ('I ~ 1 bit/sec). For complex messages (I_{message} = 10^{9}
bits), 'Q_{message} ~ 10 message molecules emitted per second and t_{rec}
~ 8.4 hours ('I ~ 3 x 10^{4} bits/sec).

Last updated on 18 February 2003