Abstract
A theoretical analysis is given of a solion pressure detector which has a direct current output proportional to the logarithm of the acoustic pressure input. An approximate method is used which avoids the necessity for solving the Navier-Stokes equation describing the fluid flow and the convection diffusion equation for calculating the current. The calculation consists of (1) solving the zero flow “transient” diffusion equation for the reducible component in the electrochemical redox system, (2) using this transient solution to calculate the output current with the time spent inside the detector orifice as the independent variable, and (3) relating this time to the pressure by using the known acoustic impedance of the detector orifice. The calculated results show that the logarithmic response is obtained through a combination of diffusion and hydrodynamic effects. For the ideal case of piston flow, the logarithmic response is degraded.
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