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Abstract Capillary flow is the spontaneous wicking of liquids in narrow spaces without the assistance of external forces. Examples of capillary flow can be found in numerous applications ranging from controlling and transporting fuel in spacecrafts to printed electronics manufacturing. Open rectangular microchannels often appear in these applications, with the lack of a top resulting in a complex free-surface morphology and evaporation. Here, we present a brief overview of this topic and discuss some recent advances.