Theoretical calculation and experimental study on the third-order nonlinearity parameter C/A for organic liquids and...

In the present paper we deal with calculating and measuring the third-order nonlinearity parameter C/A for organic liquids and biological fluids. For the organic liquids, the second-order derivative of sound speed with respect to pressure at constant entropy is discussed in terms of thermodynamic parameters, and a formula for calculating C/A is established. Calculated results of C/A for various organic liquids demonstrate that omitting the second-order derivative of sound speed with respect to sound pressure in an isentropic process, could overestimate the value of C/A about 20%-30%. For measuring C/A, the finite-amplitude insert substitution technique is employed. A theoretical description of the sound pressure amplitude for the third-order harmonics is obtained using the perturbation method, in which the sound pressure amplitude of the third-order harmonics is shown approximately as a parabolic function of the propagation distance in the medium. By measuring and comparing the sound pressure amplitudes of the third-order harmonics when inserting a test sample, the reference liquid, and a comparative liquid, respectively, the value of C/A for the sample liquid is determined with reference to known C/A values of reference and comparative liquids. An experimental setup is developed, and the measured values of C/A for the organic liquids agree with the predicted ones calculated by the thermodynamic methods. Furthermore, the finite-amplitude method is extended to measure the C/A parameter for biological fluids, and the measured values of C/A for several biological fluids are also presented.