The golden-mean surface pattern to enhance flow mixing in micro-channel

Mixing of analytes and reagents in microfluidic devices is often crucial to the effective functioning of lab-on-a-chip. It is possible to affect the mixing in microfluidics by intelligently controlling the thermodynamic and chemical properties of the substrate surface. Numerous studies have shown that the phase behavior of mixtures is significantly affected by surface properties of microfluidics. For example, the phase separation between the fluids can be affected by heterogeneous patterns on the substrate. The patterned substrate can offer an effective means to control fluid behavior and in turn to enhance mixing. The golden mean is a ratio that is present in the growth patterns of many biological systems—the spiral formed by a shell or the curve of a fern, for example. The golden mean or golden section was derived by the ancient Greeks. Like “π” the golden mean ratio is an irrational number 1.618, or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\left( {\sqrt 5 + 1} \right)} \mathord{\left/ {\vphantom {{\left( {\sqrt 5 + 1} \right)} 2}} \right. \kern-\nulldelimiterspace} 2}$$\end{document}. It was found that the golden mean was an optimum ratio in natural convection heat transfer problem (Liu and Phan-Thien, Numer Heat Transf 37:613–630, 2000). In this study, we numerically studied the effect of optimum surface pattern on mixing in a micro channel and found that the flow oscillation and chaotic mixing were enhanced apparently when the ratio of hydrophobic and hydrophilic boundary follows the golden mean.