Geometry-Influenced Slippage on a Bubble Mattress in Microfluidics

Hydrodynamic slippage is advantageous for drag reduction and it has been achieved with hydrophobic microstructures. Such substrates can provide soft gas/liquid interfaces with shear-free boundary condition, thereby slippage. The establishment of stable soft-interfaces is crucial for the slippage; however, it has been a challenge. In this study, we design and fabricate hydrophobic microfluidic devices, allowing stable two-phase flow with controllable micro-bubbles at the boundary of the micro-channels. We experimentally and numerically exam the geometric effect of the micro-bubbles on the slippage. The effective slip length is measured for a wide range of protrusion angles, $\theta$, using micro-particle image velocimetry. Our measurements reveal a maximum effective slip length approximately at $\theta$ = 10 degrees. In addition, the experimental results show a decrease in slip length with increasing protrusion angles when $\theta > 10^\circ$. The transverse laminar flow over micro-bubbles has also been numerically studied with finite element methods. The experimental results show a good agreement with the numerical results quantitatively.