Effects of heat conduction and sample size on ultrasonic absorption measurements

The absorption coefficient of a material can be determined by measuring the heating which occurs as a result of ultrasonic irradiation. When narrow focused beams are used to heat a sample, or when the available volume of a material is restricted to small dimensions, then the effect of heat conduction to surrounding unheated regions becomes significant, complicating the relation between measured temperatures and acoustic parameters. In this paper new analytical expressions, which account for radial and axial heat flow in a medium, are derived for the case of Gaussian-shaped ultrasonic beam patterns in thin or semi-infinite absorbing materials. Solutions are given for temperature histories resulting from an ultrasonic impulse (pulse decay method) or a step input (rate of heating method). The use of these equations in absorption measurements is discussed, and experimental results are given. These expressions provide flexibility in choice of laboratory ultrasonic parameters, and the results are especially useful for many biomedical measurements where the volume of tissue available is restricted.