The Logarithmic Dilution Method of Linearity Measurement

The logarithmic dilution method for detector calibration was introduced by Lovelock (3) for GC detectors and was further modified by Fowlis and Scott (1). The system provides a continuous flow of solvent containing solute, the concentration of which decreases logarithmically with time. 

Let the vessel have a volume V, and let the concentration of solute in the vessel be c after time t. Let a volume dv of pure solvent enter the vessel displacing a volume dv from the vessel. The mass of solute removed will be dm = c dv. Now the change in mass dm in the dilution vessel will result in a change of solute concentration dct, thus 

V is the volume passed thiou the system after time t k is the constant of integration. 

if the logarithm of the detector output is plotted against time, then for a truly linear detector a straight line will be produced having a slope of -Q/V. If the detector has a response index of r and the slope of the line is then 

the response index of the detector can be determined, but the accuracy of this determination will depend upon the constant nature of Q, the flow rate, and consequently, a good quality, constant flow pump should be employed. Manufacturers generally do not give the response index of their detectors, and, therefore, for highly accurate work its value needs to be determined. 

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