Computer Science – Sound
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufmsa31a1602h&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #SA31A-1602
Computer Science
Sound
0310 Airglow And Aurora, 0317 Chemical Kinetic And Photochemical Properties, 3359 Radiative Processes
Scientific paper
Laboratory sound absorption measurements provide much of what we know about the vibrational kinetics of air mixtures, forming the core basis for retrieving the altitude profile of water in the mesosphere from infrared emissions between 6.3 and 6.9 μm. Here we show that sound-absorption and laser-excitation experiments follow exactly the same kinetics, reflect the same underlying reaction rates, and can be vulnerable to similar ambiguities. This has not been obvious because the literature lacks a consistent prescription for calculating the sound absorption frequency spectrum from the reaction rate coefficients. We have developed the first general theoretical formalism for calculating the absolute magnitude of sound absorption per-unit-length, versus sound frequency, for any number of collisional excitation, relaxation, and energy transfer processes, for any mixture of atomic and molecular gases. This new formalism, and the computer code that implements it, provide the first systematic means for inferring collisional rate coefficients from sound absorption measurements in which more than one rotational or vibrational mode is active, such as N2/O2/H2O/CO2 gas mixtures in the laboratory and the atmosphere. When a sound wave travels through a gas, the alternating compression and expansion cycles heat and cool the gas. If the acoustic frequency roughly matches the rate of vibrational relaxation, then the effective vibrational temperature lags behind the translational temperature and the energy in the sound wave is attenuated. The measured frequency of maximum absorption is proportional to the vibrational relaxation rate. In the simplest laser-based experiment, we excite a single molecular level and record its exponential time decay, with the vibrational relaxation rate being proportional to the decay frequency. In both experiments we derive the relaxation rate coefficient from the linear graph versus gas pressure. The technical problem is that any mixture of molecular gases will have more than one relaxation time constant. Thus we write the chemical kinetics master equation as (1) (d/dt) Nm = Σnpq [ - kmn→pq Nm Nn + kpq→mn Np Nq ] which has the well-known time-dependent solution given by (2) Nm(t) = Σn Cmn exp(-λn t) where the λn values are the decay frequencies and the Cmn coefficients depend on how the gas was initially excited. What we have contributed is the frequency-dependent sound absorption solution to Equation (1): (3) cvint(ω) = Σnk Wn / (1 + i ω/λn) where cvint(ω) is the complex heat capacity (per molecule), ω is the circular sound frequency, 2πf, the λn are the calculated decay frequencies [as in Equation (2)] and k Wn is the real effective heat capacity for decay mode n. As pointed out by Landau and Teller [Phys. Z. Sowjet. 10, 34-43 (1936)], for a simple case when the decay modes correspond to vibrational modes, Wn is the ordinary heat capacity of the vibrational mode. In the more complicated case involving one or more reversible energy-transfer steps, e.g., water and oxygen, the vibrational modes and the decay modes do not correspond to each other, and we need to use the rate coefficients in Equation (1) to calculate both λn and Wn.
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