Draft proofing an indoors barn door



We have arrived very small entryway leading into a bigger hallway. Since this is an old house there are some draft issues. We have had av double curtain hung in the doorway between these two rooms. It is not av Great look but it works. Now my mind is set on replacing the curtain with a barndoor. But I am worried about all the air and draft running in between the door andre the Wall. IT is obviously not andre airtight solution, but is there anyway I can close it a little extra? Any good advise?

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Anyone find a good solution with pictures to this question? We want to use a sliding barn door to separate our living room from our all seasons porch. Want it to be insulated though.