Axially Tapered Microchannels of High Aspect Ratio for Evaporative Cooling Devices

Abstract

Analytical solutions are derived for evaporating flow in open rectangular microchannels having a uniform depth and a width that decreases along the channel axis. The flow generally consists of two sequential domains, an entry domain where the meniscus is attached to the top corners of the channel followed by a recession domain where the meniscus retreats along the sidewalls toward the channel bottom. Analytical solutions applicable within each domain are matched at their interface. Results demonstrate that tapered channels provide substantially better cooling capacity than straight channels of rectangular or triangular cross section, particularly under opposing gravitational forces. A multiplicity of arbitrarily tapered channels can be microfabricated in metals using LIGA, a process involving electrodeposition into a lithographically patterned mold.