© 2004 Robert A. Freitas Jr. and Ralph C. Merkle. All Rights Reserved.

Robert A. Freitas Jr., Ralph C. Merkle, Kinematic Self-Replicating Machines, Landes Bioscience, Georgetown, TX, 2004.

B.4.4.3 Stable Cavitation

Small pre-existing bubbles surrounded by a liquid will resonate in synchrony with the acoustic field, with the liquid acting as the oscillating mass and the gas serving as the compliant component. If the bubbles are pure acetylene gas, an oscillating compression that commonly reaches P_max = 3 atm might produce some decomposition which can occur in acetylene via slow deflagration above 2 atm at room temperature [3141]. Resonating bubbles have been reported in medical ultrasound beams at power intensities as low as 6800 W/m² at 0.75 MHz [3258], which is slightly higher than I_acoustic ~ 6100 W/m². Pyrolysis of acetylene in argon bubbles in aqueous solution has also been observed at 20,000 W/m² and 1 MHz (Section B.4.1), but much higher intensities should be required to initiate bubble resonance at higher frequencies (e.g., at n_acoustic = 10 MHz). This expectation should be verified experimentally, and it would be prudent to ensure that no preexisting acetylene microbubbles are present in the n-octane feedstock solution.

Bubble size is also an important factor. Minnaert [3259] showed that under adiabatic conditions the resonant frequency n_resonant of a bubble of gas of radius R_bubble with ratio of specific heats g_gas in a liquid of density r_liquid and absolute liquid pressure P_liquid is given by n_resonant = (3 g_gas P_liquid / 4 p² r_liquid)^1/2 / R_bubble ~ 3.67 / R_bubble for acetylene gas bubbles in liquid n-octane at STP, taking g_gas ~ 1.23, P_liquid ~ 1 atm (1.013 x 10⁵ N/m²), and r_liquid ~ 702.5 kg/m³. The largest possible reaction chamber-sized bubble with R_bubble = L_chamber / 2 = 1 micron resonates at n_resonant ~ 3.7 MHz, a frequency only somewhat below n_acoustic. However, such colloidal bubbles may have lifetimes on the order of msec [3260]. In particular, acetylene bubbles ~0.1 micron or smaller have a higher gas concentration inside the bubble than in solution, hence shrink rapidly (e.g., <8 msec) via diffusion and redissolution. Since the assembler solvent bath is an ultrapure liquid with no nucleation sites, and since the acoustic wavelength in n-octane at 10 MHz is ~100 microns >> 2-micron reaction chamber width (suggesting isotropic pressure throughout the chamber), cavitation bubbles should be difficult to initiate.

Note that the natural acoustic resonance frequencies for the assembler structure itself are many orders of magnitude higher, on the order of n_resonance > (~ v_sound / L) = 50 GHz taking v_sound ~ 17,300 m/sec for diamond structures of dimension L ~ X_ext = 343.572 nm. (Acoustic frequencies of 8 GHz were reported experimentally in liquid helium in the 1980s [3261]; frequencies up to 50 GHz can be used to see crystal defects in very good crystalline samples at liquid helium temperatures, and ultrasound in water is possible up to a few GHz [3262].)

Last updated on 13 August 2005