A slip length analysis of microchannel flow with smooth and structured surfaces

One of the most significant challenges in microchannel design is the reduction of pressure drops within miniature fluidic pathways. A promising approach involves the manipulation of boundary conditions, mainly through the integration of structured hydrophobic surfaces. The mathematical characterization of these hydrophobic surfaces is achieved through the application of the Navier boundary condition, with the slip length identified as the critical parameter of interest. This paper delves into an in-depth exploration of how varying slip lengths impact the liquid flow dynamics within microchannels with a rectangular cross section. We consider a diverse range of microchannel hydraulic diameters 5–200 μm and aspect ratios from 1:1 to 1:20 for Reynolds numbers in the laminar range 10–1000. Three-dimensional calculations are performed on both conventional smooth microchannels and those equipped with air-filled groove-structured surfaces. The results are then compared with the analytical solution and experimental results. The application of a hydrophobic structure to a single microchannel surface is resulted in the friction factor reduction by over 30%, while the application of the hydrophobic structure to two opposing walls led to a reduction by over 60%. The maximum throughput is shown to be achieved for a bubble protrusion angle of approximately 0° for a microchannel with a single hydrophobic wall. The greatest reduction in the friction factor was achieved when the bubbles were positioned in a staggered configuration at bubble protrusion angles of approximately –25° for microchannel with two opposing hydrofobic walls.