Evaluation of the third order nonlinear parameter C/A for glycerol from measurements of ultrasonic velocity versus temperature and pressure

Our purpose in the present study is to evaluate the C/A values for glycerol by using a thermodynamic method. It is assumed in the developed model that the thermal conductivity of the analyzed fluid is low and the Taylor development of the state equation is extended up to the third order. The theoretical expression of the C/A parameter is developed on the basis of some thermodynamic considerations. C/A parameter is not only function of ultrasonic velocity, density, B/A parameter but also on a second partial derivation term which is obtained from the equation of ultrasonic velocity versus pressure for a given temperature. The temperature and pressure dependence of the third order nonlinear parameter for glycerol has been estimated from 10 to 100°C and from 0.1 to 100 MPa, respectively. C/A parameter is essentially determined from measurements of glycerol ultrasonic velocity versus temperature and pressure by using a high pressure measurement cell equipped with temperature and pressure monitoring and control instrumentation. A time of flight method is exploited to measure, under high pressure, the glycerol ultrasonic velocity at different temperatures. The experimental data of glycerol ultrasonic velocity combined with measurements of density and those of B/A parameter at each considered temperature and pressure are used to evaluate, under high pressure, the third order nonlinear parameter versus temperature. The present investigation shows that the third order nonlinear parameter C/A is a decreasing function of pressure. C/A values vary from positive values at low pressures to negative values above 60 MPa. The third order nonlinear parameter C/A is found to be highly dependent upon hydrostatic pressure. The accuracy of the measured C/A values is estimated at about 10%.