ACOUSTIC NONLINEARITY OF LIQUIDS

Nonlinear elasticity in materials enables interesting technologies such as novel imaging techniques as well as "acoustic diodes," which can be important in communications.  This work focused on the determination of the parameter of nonlinearity (B/A) in several liquids using the "thermodynamic technique." In the thermodynamic technique, B/A is related to the derivatives of sound speed with respect to pressure and temperature along with several other thermodynamic properties of the material:

Where ρ is the mass density, β is the volumetric coefficient of thermal expansion, T is the temperature (in Kelvin), c is the sound speed, p is the pressure, and C_p is the specfic heat at constant pressure.  Using the high temperature/high pressure SFAI tool, we measured the sound speed in several liquids over a wide range of temperatures and pressures.  These measurements enabled the determination of the derivatives in the equation above.  Combined with the other thermodynamic properties, this allowed us to determine B/A in the fluids over a large temperature and pressure range.

Sound speeds in liquid water as a function of temperature along the liquid-vapor coexistence curve. Water is very unique among liquids in that its sound speed increases with temperature until ~70 °C before decreasing.	Sound speeds in Fluorinert FC-43 as a function temperature and pressure. Sound speeds are in m/s and black markers denote measurement points.
B/A (a dimensionless quantity) as a function of temperature and pressure in Fluorinert FC-43. With a B/A above 10 at laboratory ambient conditions, Fluorinert is highly nonlinear. Remarkably, this quantity is found to increase by a factor of 3 at higher temperatures.