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

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

6.3.3 Acoustic Energy Conversion Processes

Most clearly useful for medical nanorobots are acoustomechanical transducers (Section 4.5.1) that can directly apply motive power to internal nanomechanical manipulator and computational systems. Drexler¹⁰ has described a simple transducer that can function as a pressure-driven actuator, which is abstractly modeled as a constant-force spring that resists the motion of a piston moving between two limit stops (Fig. 6.1). Such a device which experiences a cyclical volumetric change of DV in response to aboveambient pressure pulses of amplitude DP at a frequency n_p converts acoustic pulse energy into the mechanical energy of piston motion with almost 100% thermodynamic efficiency when the expansion is isothermal and reversible (e.g., when thermal equilibration time t_EQ << n_p^-1, which should always hold for n_p <~ 1 GHz).

Recognition of four additional restrictions on the net mechanical power (P_n) available from a pistontype transducer produces a very conservative power estimate:

{Eqn. 6.13}

The product of DP, the change in pressure during a stroke, and DV, the change in piston volume, is the change in Gibbs free energy per cycle.¹⁰ The piston energy lost to friction may be estimated from Eqn. 6.4 using the observation that interface velocity v ~ 2 n_p L for a piston of dimension ~L³, thus E_friction ~ 10^-25 n_p L^0.6; for E_friction < kT, L < 0.05 micron for n_p = 1 GHz, L < 5000 microns for n_p = 1 MHz. The energy lost in overcoming piston inertia ~ 1/2 mv² where m = r_p L³, so E_inertia ~ 2 r_p n_p² L⁵ for a piston of density r_p; for E_inertia < kT, L < 4 nm for n_p = 1 GHz, L < 60 nm for n_p = 1 MHz. Fluid viscous drag occurs when the piston must push itself through a viscous external aqueous medium in which the pressure pulses are traveling. However, if L << l = v_sound/n_p then the range of piston motion is far smaller than one wavelength and E_drag ~ 0 for submicron transducers: at n_p = 1 GHz, l = 1.5 microns in water at 310 K. Finally, E_heat ~ kT because useful work may not be extracted from an isothermal medium. L_min is the size of the receiver piston for which P_n < 0.

Of course, this is a very conservative approach because much depends upon how predictable the acoustic source is. J. Soreff notes that in the case of externally supplied, constant frequency, constant amplitude pressure waves, both E_inertia and E_heat are negligible because the capture of energy from the piston can be phase locked to the incoming waves, and the piston spring constant can be tailored to put the kinetic energy of the piston into a potential energy store at the end of its travel. Phase locking still requires an energy expenditure of kT for sensing, but this sensing could be spread over many cycles, given a source with a long coherence time.

Table 6.3, with values computed using Eqn. 6.13 and acoustic pressure estimates from Section 4.9.1, shows that a modest amount of acoustic energy is available from normal physiological processes within the human body, which are assumed to generate planar traveling waves. Path length is not important here because of the weak attenuation at such low frequencies (Section 4.9.1.3). For a single (~1 micron)³ transducer, usable received acoustic power up to P_n ~ 0.004 pW is regularly available from continuous sources. Intermittent or sporadic usable power sources up to P_n ~ 5 pW are also available. In many cases these sources would be in phase with the biothermal transducer described in Section 6.3.1.

Large epidermally-placed nanorobots may convert the force of wind resistance into usable energy. In theory, nanorobots may receive P_n = (1/2) e% r_air A v_run³ ~ 1 pW for efficiency e% = 0.30(30%), STP air density r_air = 1.29 kg/m³, and transducer area A = 1 micron² for a person walking or running at v_run = 1.8 m/sec (~4 mph). However, as a practical matter much less power is available to micron-size nanorobots because there is a near-skin boundary layer of relatively still air.

External sources of acoustic energy can also be employed (Section 6.4.1). Power pulse cycling depends on sensor design. For example, to avoid damaging the aforementioned acoustic sensor devices with large acoustic pulses intended to provide power, power pulses should be shaped with a slow initial amplitude rise sufficient to gently "peg" all sensor pistons to their distal stops, followed by a sharp upramp to peak amplitude, then a shallow decline sufficient to gently return sensor pistons to their proximal stops, followed by a sharp decline in pulse amplitude, thus safely completing the power cycle. An acoustic-powered legged microrobot ~1 mm in size with resonant actuators has been fabricated and tested.^352,559

The Space Thermoacoustic Refrigerator (STAR) developed by Steven L. Garrett for NASA in the early 1990s uses 160 dB sound waves in a confined space to create a spatial thermal gradient in a working fluid, an example of acoustothermal energy conversion.³⁴⁴⁶ Sonoluminescence caused by focused high-frequency sound waves in water provides an example of acoustophotonic power transduction.^543,716 Acoustochemical processes are well-known in the field of sonochemistry,^{625,1084,1085,1523} including ultrasonic depolymerization. Acoustomechanical fluid-driven microturbines ~250 microns in diameter have been fabricated and operated at ~KHz frequency with lifetimes of ~10⁸ revolutions.¹²¹⁸

Last updated on 18 February 2003