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
5.2.2 Actively Swimming Nanodevices
Nanodevices of another class may swim rapidly through the bloodstream. It should be possible to navigate even the fastest-moving arterial flows if desired. This locomotive capability is risky to the patient if employed by large numbers of devices simultaneously (Section 9.4.1), and may not be necessary for many of the applications proposed in this book.
Bloodstream swimming by nanorobots is qualitatively dissimilar to surface swimming or to a submarine moving through the ocean at depth. Unlike these macroscale analogs where inertial forces prevail, in the microscale environment viscous forces dominate. Inertial and gravitational forces are almost irrelevant. Bloodstream swimming by simple reciprocal motions is not possible (Section 220.127.116.11). Rather, it is necessary to use deformation, helical, or other drive systems, all of which involve either a tubular shape to allow propulsed fluids to pass through the center of the device, or an axially symmetric form such as a conical-, egg- or teardrop-shaped spiral to minimize viscous drag while "drilling" through the fluid during locomotion. Red blood cells assume a biconcave shape only when in static equilibrium. In a flowing condition, lone erythrocytes deform into the shape of a bullet or slipper in the capillary blood vessels;362 at lower shear rates in the arteries, multiple cells aggregate into cylindrical rouleaux oriented roughly in the direction of flow (Section 18.104.22.168). Metamorphic surfaces may allow a nanodevice to configure all fluid contact planes to achieve minimum drag for every velocity vector employed and every fluid traversed.
Are conventional streamlined shapes necessary or useful for micron-scale swimmers? In the macroscopic world, a body traveling through water experiences the least resistance to forward motion (drag) if it is rounded in the front and tapers to a rear point in the familiar shape of a tuna or whale -- the animal thus shaped meets little drag, ~10 times less than would a sphere or a person of the same size.2022 However, streamlining and special hydrofoil shapes serve mainly
A. to reduce induced drag, which largely disappears in nonturbulent microscale flows; and
B. to reduce pressure drag, an inertial force which also becomes relatively unimportant at the microscale.
For example, the ratio of viscous drag to pressure drag may be computed from Eqns. 9.89 and 9.90 as Fviscous/Finertial = (12 hfluid / CD rfluid) (1 / Rnano vnano) ~ 10-5 / (Rnano vnano) in 310 K water. Given that the highest likely nanorobot swimming speed in vivo is vnano ~ 1 cm/sec (Section 22.214.171.124), then Fviscous/Finertial >~ 100 for Rnano <~ 10 micron. Thus at the microscale, viscous forces predominate. Viscous forces are determined by total surface area in contact with fluid, so the lowest drag on a moving mass is produced (all else being equal) by a shape that presents the minimum possible surface area to the fluid, that is, approximating a sphere. The drag even on extremely pointed shapes differs little whether the object is moving forward or sideways. For instance, experiments show that the most extreme needle-shaped bodies fall about half as fast sideways as they do end-on.1378 Note that natural micron-scale swimmers such as bacteria and small metazoans are typically ovoid or cylindrical, rather than fishlike, in shape.
An examination of 218 genera of free-floating and free-swimming bacteria3582 revealed that motile genera are less likely to be spherical and have larger axial ratios (typically 3:1) than nonmotile genera. Spherical shapes were found to produce the largest random dispersal by Brownian motion, and oblate spheroids were rare, possibly due to the increased surface area. Prolate spheroids provided a reduced sinking speed; elongation slightly favored swimming speed, but strongly improved the temporal detection of chemical stimulus gradients by any of three different mechanisms -- the probable explanation for the popularity of rod-like shapes in motile bacteria (though others3615 have been proposed).
Last updated on 17 February 2003