It is hard to imagine how you would set up a steady-state system to produce this effect. That being the case, all measurements would be transient. Spatial variability can be expected along with temporal. Experimental measurement would be illusive. I suspect that the answers you get from CFD would depend entirely on your assumptions and selection of calculations. This means that you might be able to get whatever answer you want by turning knobs on the CFD, which means you can't obtain a definitive answer via CFD for a problem like this. That takes us back to the original question: Why do you need to know this? Is it essential for the design or operation of an ammonia absorption cycle or something like that? If it is, there is operational data to provide guidance.

There exist several metal-amine complexes which are formed by the chemical bonding of aquaous ammonia to a metal ion, forming brightly coloured complexes. Perhaps you can use spectroscopy to determine the colour intensity of a liquid and the corresponding concentrations of such a complex.

As Dudley J Benton already idicated, obtaining detailed spatial and temporal resolutions will be challenging. Spectroscopy would only give you a spatially averaged signal.