Cavity two fluid Flow – Python? OpenFoam

I am trying to attack a personal project to simulate a channel flow that has a cavity. Inside the cavity there is a fluid stationary. At some instant, another fluid (miscible in the first one) starts to flow.

I am reading about typical cavity flow solutions in Python. It is no problem for me to understand and code those. However, I am not able to find a case where two fluids are present and/or the fluid in the cavity can “come out” into the channel, as well as can the fluid in the cannel “come into” the cavity.

Any ideas? Library or typical OpenFoam exemples so I can base on?

Thank you in advance

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