Abstract This paper deals with the design, analysis and optimization of micro-mixer for fluids having very low diffusivity (in the order of 10−12 m2/s) to be used in Lab on Chip (LOC) for medical diagnosis. As flow is laminar and the cross-sectional area is in microscale, the viscous forces are strong causing the fluids to be transported in streamline with minimum diffusion. The main objective in designing a micro mixer is to achieve complete mixing with minimum channel length and pressure drop. In this work a passive micro mixer with two inlets and one outlet (Y shaped passive micro mixer) with obstacles in various shapes and sizes is modelled, to study the effect of mixing. After a CFD analysis, Analysis of variance (ANOVA) of 3K design with 3 parameters as well as a 2K design with 4 parameters was performed to study the effect of parameters on mixing index (mixing length) and pressure loss. There is a negative correlation between the response obtained for mixing length and pressure loss while varying the parameters. This makes it difficult to predict the optimum configuration. Taguchi method is used to obtain an optimum configuration to overcome this negative correlatiozn.