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

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

7.2.1.6 Continuous Mobile Source in Stationary Medium

Consider a mobile nanorobot traveling through a stationary aqueous medium at velocity v_n (m/sec), emitting message molecules continuously at the rate of 'Q_message (molecules/sec). The cigar-shaped molecular trail envelope has a maximum length X_fadeout = 'Q_message / 4 p D c_min, and at a distance X_max = X_fadeout / e behind the moving source the message molecules diffuse outward to a maximum detectable radius R_max = (0.342) ('Q_message / v_n c_min)^1/2 as measured from the motion axis; for distances >X_max the radius of the detectable message molecule envelope declines to zero at X_fadeout, with t_fadeout = X_fadeout / v_n. Thus, a nanorobot velocity v_n = 10 microns/sec and an X_fadeout = 1000 microns requires 'Q_message = 4 x 10⁵ molecules/sec for simple message molecules (I_message = 100 bits) giving R_max ~ 60 microns at X_max = 370 microns and t_fadeout = 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 7.2.1.7.

Last updated on 18 February 2003