Imagine, there is huge closed system in which water circulation happens ( such as cooling system ). Pumps circulate the water through different heat exchnagers.
Then, it is needed to add the chemical to the system. As you know , when you add some amount of chemical to the closed system , the some amount of time is needed in order to get the same concentration of mixture in all point of system ( when you take sample from system). It means that we should wait until 100% mixing happens and concentration of the chemical is the same through whole system (totally mixed)
I am asking about how to calculate this time. Are there any equations for calculation of that time?
Time or number of circulations. A number of factors will influence here. I will mention a few of them: type of pump, flow geometry, liquid velocity, liquid and mixture properties eg. viscosity. It is necessary to start with assumptions, for example, assuming the isothermal flow, the axially symmetrical flow, smooth wall of channal etc. Regards,
https://www.sciencedirect.com/search?qs=time%20calculation%20for%20complete%20mixing&show=25&sortBy=relevance
To make this calculation, you need to make a model of your system. Besides obvious information, like the system volume and pump flow rates, you will also need information on how the fluid is mixed up in your system. This can be approximated by models, such as an ideal stirred tank (CSTR) or a plug flow reactor (PFR). Real systems are typically described by a combination of CSTR's and PFR's in a certain configuration (e.g. parallel, series).
A more practical approach would be to do a tracer study. In this case you inject an easily traceable component into your system (like a colorful dye), and sample the fluid concentration at regular time intervals.
As a 'rule of thumb' the number of circulations could be a good indicator on the degree of mixing. But keep in mind that 'dead zones' may exist, which may require a long time to mix up with the bulk of the liquid.
I recommend you to characterize the mixing time of your system. You will need a tracer, whose concentrarion in time should be easily measured. Find attached a paper that describes this technique in a simple way. kind regards.
https://drive.google.com/file/d/1yU0PS2ONfuVkRxvyx_lA06irQo0vDAoz/view
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