**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
9.4.2.5). 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 9.4.1.2).
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 F_{viscous}/F_{inertial} = (12 h_{fluid}
/ C_{D} r_{fluid}) (1 / R_{nano}
v_{nano}) ~ 10^{-5} / (R_{nano} v_{nano}) in
310 K water. Given that the highest likely nanorobot swimming speed in vivo
is v_{nano} ~ 1 cm/sec (Section 9.4.2.6),
then F_{viscous}/F_{inertial} **>~** 100 for R_{nano}
<~ 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
bacteria^{3582} 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 others^{3615}
have been proposed).

Last updated on 17 February 2003