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 Diffusive Swimming

The second strategy for active diffusive intake is by swimming. Again, the nanodevice is equipped with suitable active propulsion equipment (Section 9.4) which enables it to move so as to continuously encounter the highest possible concentration gradient near its surface. Consider a spherical motile nanorobot of radius R propelled at constant velocity vswim through a fluid containing a desired molecule for which the surface of the device is essentially a perfect sink (Section 4.2.5). Applying the Stokes velocity field flow around the sphere to the standard diffusion equation, a numerical solution by Berg and Purcell337 found that the fractional increase in the diffusion current due to swimming is proportional to vswim2 for vswim<< D/R, and to vswim1/3 for vswim >> D/R.

Diffusive intake is doubled at a swimming speed vswim = 2.5 D/R, which for 1-micron devices is ~5000 microns/sec when absorbing small molecules, ~50 microns/sec for large molecules. The viscous frictional energy cost to drive the nanodevice through the fluid, derived from Stokes' law (Eqn. 9.73), requires an onboard power density of:

{Eqn. 3.8}

If h = 1.1 x 10-3 kg/m-sec, vswim = 2.5 D/R, R = 0.5 micron, D = 10-9 m2/sec for small molecules, then Pd ~ 5 x 105 watts/m3. For large molecules with D = 10-11 m2/sec, Pd ~ 50 watts/m3. Thus the energy cost of diffusive swimming appears modest for nanomechanical systems; gains in diffusion by swimming for nanodevices will be restricted primarily by the maximum safe velocity that may be employed in vivo (Section

In general, outswimming diffusion requires movement over a characteristic distance Ls ~ D/vswim.389 For bacteria moving at ~30 micron/sec and absorbing small molecules, then Ls ~ 30 microns, roughly the sprint distance exhibited by flagellar microbes such as E. coli. For micron-scale nanodevices moving at ~1 cm/sec (Section 9.4), Ls ~ 1-100 nm for large to small molecules.


Last updated on 7 February 2003