The transverse acoustic impedance of an inhomogeneous viscous fluid

The transverse acoustic impedance Z of a fluid can be determined from measurements of the complex reflection coefficient of a transverse ultrasonic wave incident on a plane solid/fluid interface. Inhomogeneities in the fluid close to the solid surface may have a significant effect on the measured values of Z. We have derived the Riccati equation which determines Z in an inhomogeneous viscous fluid, using transmission line theory. This equation was integrated numerically to obtain the impedance of viscous films and for inhomogeneities due to healing lengths and van der Waals forces near the solid/fluid interface. The results show that the measurement of both the real and imaginary parts of Z can be a powerful technique for investigating any inhomogeneities which occur on a length scale comparable with the viscous penetration depth in the fluid.