to work every row should be insulated from all the others. in your design hot vapours travel horizontally, then up in the next row, and again
horizontally but in the opposite direction. to work as a column there should be an equilibrium between liquid and vapour, and this thanks to the
thermal equilibrium with the column. if the cooler vapour travels back where hot vapour is touching the walls it's going to warm again, so in the end
the temperature will drop vertically, not horizontally, this would be like having a really wide condenser, not a tall one
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