Estimation of heat distribution in the acoustic lens of an ultrasonic microscope with the carrier frequency of 1 GHz

Abstract

The propagation of heat was analyzed in the lens of an acoustic microscope used for testing of living cells at the frequency of 1~GHz. Information concerning the propagation of heat is necessary for determination of thermal boundary conditions which influence the temperature increase in the tested samples representing acoustical properties of water. The time of temperature propagation from water, heated due to high absorption, to the sapphire body of the lens was estimated to be 0.77 ms. To carry out these calculations the derivations of Carslow and Jaeger [2] and of Tautz [6] were adjusted. On the other hand the propagation time of the acoustic wave in the sapphire body equalled 0.0093 [ampersand]mu;s only. The time of image formation in the microscope is rather long being equal from one to several seconds due to mechanical inertia of the support vibrating together with the tested sample. The heat capacities of the water volume and the sapphire body were found to be comparable. However, if the heat capacity of the water volume would be many time smaller then the time of the finally attained temperature would be elongated. This effect can be neglected since the time of image formation is 3 orders of magnitude longer than the time of penetration of the sapphire body by the heat supplied by water. As the result a temperature equilibrium will be obtained with the average boundary temperature of water. In such a case no heat flux will penetrate the boundary water - sapphire and the condition of the thermal insulation at the boundary will be fulfilled. This thermal boundary condition makes it possible to determine the real temperature increase in biological specimens.