Fine-tuning molecular acoustic models: sensitivity of the predicted attenuation to the Lennard–Jones parameters

Abstract

In a previous paper [Y. Dain and R. M. Lueptow, J. Acoust. Soc. Am. 109, 1955 (2001)], a model of acoustic attenuation due to vibration-translation and vibration-vibration relaxation in multiple polyatomic gas mixtures was developed. In this paper, the model is improved by treating binary molecular collisions via fully pairwise vibrational transition probabilities. The sensitivity of the model to small variations in the Lennard-Jones parameters--collision diameter (sigma) and potential depth (epsilon)--is investigated for nitrogen-water-methane mixtures. For a N2(98.97%)-H2O(338 ppm)-CH4(1%) test mixture, the transition probabilities and acoustic absorption curves are much more sensitive to sigma than they are to epsilon. Additionally, when the 1% methane is replaced by nitrogen, the resulting mixture [N2(99.97%)-H2O(338 ppm)] becomes considerably more sensitive to changes of sigma(water). The current model minimizes the underprediction of the acoustic absorption peak magnitudes reported by S. G. Ejakov et al. [J. Acoust. Soc. Am. 113, 1871 (2003)].

Synthesizing Primary Molecular Relaxation Processes in Excitable Gases Using a Two-Frequency Reconstructive Algorithm

“…2), sound speed, and normalized attenuation, for the mixture of N 2 with the foreign gas-in this case, 5% molar fraction of methane (CH 4 ). The dashed lines represent the ''real'' behavior of the mixture (95%N 2 and 5%CH 4 , molar fractions) as predicted by the physical theoretical model [6,7]. The reconstructive algorithm predicts the main effective relaxation frequency to be 21.426 kHz, which is within 0.14% of the value 21.456 kHz predicted by the theoretical model.…”

A model for the vertical sound speed and absorption profiles in Titan’s atmosphere based on Cassini-Huygens data

“…The acoustic wave number is computed from first principles, using molecular collision dynamics. 9 Non-ideal gas interactions are modeled differently than in Ref. 5.…”

Relaxation Time Coupling Method for Ultrasonic Sensor Design

“…We can construct the matrix R by calculating the jj k and jk k as [6]: T is the equilibrium temperature. 10 ( ) k j and 10 01 ( , ) k j k are the V-T transition rate and the V-V transition rate respectively. They can be calculated by the Tanczos equation [1,3].…”

“…Over the years, some relaxation time theories have been proposed [7][8][9][10]. However, these theories did not provide an appropriate physical model to demonstrate the theoretical derivation.…”