in acoustic ohms. Since the diaphragms are com- 

 pliant, this effect is considered as an acoustic 

 compliance, C, measured in acoustic farads. The 

 product of the acoustic resistance and compliance 

 determines the low frequency response of the 

 transducer . 



If the flow detector is connected to the 

 external electrical circuit shown in Fig. 3 and 

 if flow through the cathode elements is assumed 

 to be zero, the individual cathodic currents will 

 tend to a quasi background current as the iodine 

 ions in the neighborhood of the cathodes are 

 depleted. The background current is then deter- 

 mined by Eqn. (l) . If the two cathode electrodes 

 indicated in Fig. 3 are identical, their back- 

 ground or "no flow" currents will be identical. 

 The differential "output" will then read zero 

 or near zero volts, depending upon how nearly 

 identical the cathodes actually are. The iodine 

 ions contained in the volume in and around the 

 cathodes are reduced to near zero except for the 

 small amount of iodine diffusing into the region. 



Assume now that, with the cell connected to 

 the external bias, a net differential pressure 

 is developed between the compliant diaphragms. 

 A net hydraulic flow of the electrolyte solution 

 will commence from one chamber to the other 

 chamber. The amount of volume flow is determined 

 by the net differential pressure and the acoustic 

 resistance through the cathodes. This is illus- 

 trated by the classical relationship3 



04 0.6 0.8 



ELECTRODE BIAS -VOLTS 



Fig. h. Output characteristics of a typical 

 solion linear pressure detector. 



where I is the electrical current in the external 

 cathode circuit. From Eqn. (5) a substitution 

 for the volume flow rate gives 



FNI ££ 



10" 



(7) 



*»-*£ 



where Ap is the net differential pressure, R is 

 the acoustic resistance of the cathode and 

 2Y. is the volume flow rate. The volume flow 



rate is related to the pressure by R and can 

 be a linear or a nonlinear relationship depending 

 upon whether R is constant or some function of 

 p[R(p)] . At low frequencies (f<l cps), pressure 

 and volume flow rate are related by R, but at 

 higher frequencies the relationship must become 

 |Z| so as to include the acoustic inertance of 

 the fluid in the flow path. A linear flow 

 detector has a useful upper frequency response 

 in the 30 to 50 cps region. 



As flow commences through the cathode elec- 

 trodes, electrolyte at the bulk iodine concentra- 

 tion is forced into the region of the cathode 

 electrodes . The output current is not limited to 

 the diffusion currents of Eqn. (l) but increases 

 in relationship to the number of iodine ions per 

 unit time arriving at the cathode . If the 

 cathodes behave as linear detector electrodes, 

 all the iodine arriving at the cathodes is 

 reduced. The linear detector cathode, therefore, 

 furnishes an output current which is linearly 

 proportional to the volume flow rate. This is 

 shown by 



I = FN ^ x 10" 

 dt 



(5) During the flow cycle discussed the electrolyte 

 passing through the "upstream" cathode has been 

 depleted of its iodine ions and only dilute elec- 

 trolyte arrives at the "downstream" cathode. The 

 downstream cathode has its small background cur- 

 rent reduced even further since the dilute solu- 

 tion flowing through this cathode tends to over- 

 come the iodine diffusing in from the bulk 

 solution on the downstream side. The net effect 

 is to cause an increase in the external electrical 

 current associated with the upstream cathode, 

 while the electrical current associated with the 

 downstream cathode remains small or even decreases. 



The resulting voltage developed across the 2 

 resistors in the external load is such that one 

 output lead becomes positive with respect to the 

 other and, in the case described, this differen- 

 tial voltage is proportional to the applied dif- 

 ferential pressure and preserves the phase as 

 well as the amplitude. A return to zero differ- 

 ence pressure lets the output difference voltage 

 return to zero volts. A reversal of the pressure 

 causes a reversal in the polarity of the output 

 difference voltage . 



Output characteristics of a typical linear 

 detector are illustrated in Fig. k. The load 

 line has been adjusted so that at some hypotheti- 

 cal maximum pressure the voltage between the 

 cathode and anode is always greater than 0.1 volts. 

 (6) In this manner, the solion always operates in the 

 proper region as a constant current device. For 



165 



