6 



The significance of the indicial response function (1 - e~^^^) is readily apprehended. Equa- 

 tion [2] states that the response of the instrument to a suddenly occuring step change in the 

 concentration of dissolved gas in the incoming sample is not an immediate corresponding 

 step change in the pressure p but rather an asymptotic exponential approach to the new read- 

 ing with "response time" (i.e., time required for the reduction by a factor 1/e of the depar- 

 ture of the reading from the new equilibrium) equal to r . 



It is, of course, essential to the usefulness of the instrument that the response time 

 t(= V/QB-q), be made reasonably short. It is desirable, in fact, to make the rapidity of re- 

 sponse as great as possible. This can be accomplished by making the gas-space volume V 

 small and the flow rate Q and mixing efficiency jj high. Since the mixing efficiency cannot 

 be made greater than unity, the practical problem becomes one of maximizing the ratio of the 

 flow rate to the volume of the gas space while maintaining adequate exposure and mixing. 

 The desirable choices of gas-space volume, flow rate, and mixing efficiency militate against 

 one another in various ways so that it is difficult to determine the most suitable compromise 

 in design. Thus, an extremely small gas volume would make for rapid response, but a small 

 volume is somewhat incompatible with the combination of a high flow rate and a large area of 

 exposure. 



Equation [2] describes the response of the instrument for a case in which the change in 

 input involves only one gas. Where the response to a mixture of gases is required, a slightly 

 more general expression applies. Dalton's Law states that in a mixture of gases, each be- 

 haves independently of the others. In the experiments to be described, a step change in the 

 concentration of nitrogen and oxygen dissolved in water is simulated; the changes in equili- 

 brium pressures are approximately in the atmospheric proportions of 80 percent nitrogen to 20 

 percent oxygen. The expected indicial response for this case consists of a linear super- 

 position of the responses due to each gas separately, if it is assumed that the mixing effi- 

 ciency for one gas is not affected by the presence of the other. Accordingly, instead of Equa- 

 tion [2], the equation describing the approach to equilibrium for a mixture of oxygen and 

 nitrogen in atmospheric proportions after a sudden displacement from equilibrium is: 



P-Po + (P- Po)i^ - .8e-<^/'?^iV^)'-.2e-(^'/<?^o^)'') 



[3] 



Here p is the instantaneous value of the total gas pressure in the gas space, P is the total 

 equilibrium pressure corresponding to the new concentrations of nitrogen and oxygen in the 

 inflow, and |3„ and ^„ are the solubility coefficients for nitrogen and oxygen respectively. 

 For simplicity, the mixing efficiencies for the two gases are assumed to be equal and 



