discussion of the manner in which the gas pressure in the chamber approaches the equilibrium 

 value. 



RESPONSE TO FLUCTUATIONS IN INPUT 



Considering first the case of a single gas dissolved in the inflowing sample, let the 

 instantaneous pressure of that gas in the gas space be denoted by p and let the equilibrium 

 pressure corresponding to the concentration of dissolved gas in the inflowing sample be P. 

 Denote by Q the volume flow rate of the liquid sample. The temperature will be considered 

 to be constant. The inflowing sample carries dissolved gas into the chamber at a rate such 

 that if it were completely extracted and added to the gas space of volume V, the rate of in- 

 crease in pressure would be PQ^/V. This follows from the definitions given for the flow rate 

 Q, solubility coefficient 6, and equilibrium pressure P. Similarly, if, in passing through the 

 chamber, the sample liquid is brought into complete equilibrium with the existing pressure p 

 in the gas space, there will be carried out from the chamber an amount of dissolved gas suffi- 

 cient to reduce the pressure in the gas space at the rate pQ^/V. The net rate of change of 

 pressure in the gas space will then be ($/3/F)(P-p). 



In general, however, the exchange of gas between the sample liquid and the gas space 

 will not be complete so that the actual rate of change of pressure will be given by an equa- 

 tion of the form 



dt -^^ '^' 



where r has been written for V/Q^jj. The factor r), which will be called the mixing efficiency, 

 has some value between zero and unity. Thus the mixing efficiency rj represents the actually 

 utilized fraction of the capacity of the flowing sample for carrying dissolved gas into or out 

 from the chamber. Its value depends upon the area of exposure, the intimacy of mixing, and 

 the degree of agitation as well as upon the molecular diffusivity in both the gaseous and 

 liquid phases. 



It is instructive to consider the case in which, at time t = 0, the pressure p in the gas 

 space has some arbitrary value p^ and the equilibrium pressure P remains constant for sub- 

 sequent time, .corresponding to some constant concentration of dissolved gas in the inflowing 

 sample. This condition may be recognized as corresponding to a sudden change (at time 

 « = 0) in the concentration of dissolved gas in the inflowing sample after previous establish- 

 ment of equlibrium. The time function describing the response to such a "step" change in the 

 input is sometimes called the indicial response^ and is a useful characterization of the be- 

 iBvior of an instrument with respect to fluctuations in the quantity being measured. In the 

 case being considered, the integral of Equation [1] gives the response: 



p = P^^{P-p^){l-e-'/^) [2] 



