Brain drain is one of numerous dynamics highly similar to Gresham's law, though with subtle implications. Goods movements, where mobile, follows direct reward.
Brain-drain may be for economic, technological, social, and cultural reasons. It's not uncommon for talent flows to be at least nominally bidirectional, though with different and distinct motivating factors. The flight of intellectual (and especially Jewish) European talent to the US before, during, and after WWII contrasts with black American's migration from the US, particularly though not just the South, to Europe. Contrast Fermi and Einstein against James Baldwin and Nina Simone. Both oppression (negative driver) and economic opportunity (positive) existed for each.
Within the British Commonwealth, substantial migratoon supported by some cultural and political commonality (even where other strong differences existed) facilitated vast human flows, generlly toward London, thpugh also other centres.
Similar dynamics exist within countries as well, often (per Jane Jacobs) at the urban regional level, particularly contrasted with rural regions. And hub formation / centres of excellence tend to accelerate such consolidation (a point Edward Glaeser argues relatively well, though with flaws).
Economic goods tend to move toward reward, and away from punishment or restraint, though the dynamic once in flow tends to be self-sustaining, at least for a time. There's much focus on positive network effects and growth, less on decline. But the immigration surces of migration toward first the U.S. Atlantic seaboard, and later the Western US, came from what had been earlier. priods' dynamic hubs. Why those declined should be instructive study.