In this work we use entropic and geometric quantifiers, such as fractal dimension to enable the quantification of the optimization process of mixing in laminar flow systems. As a case study we investigate the fluid flow in microchannels where the laminar characteristics are a result of the size of the channel and the fluid viscosity. In this respect the microfluidics and polymer melt flows in extruders are quite similar. The particular microchannel geometries for which we solve numerically the Navier-Stokes equation are: (i) the staggered herring bone (SHB) which consists of periodic grooves and ridges distributed along the channel length; (ii) a couple of fractal microchannels where by employing the Weierstrass function we generate non-periodic patterns of ridges on the channel bottom; and (iii) helical Dean channels that exploit the interplay between centripetal forces and mass conservation. In all cases in order to optimize the mixing the designer has to choose various geometric sizes for the channel, to fully exploit the counter-rotating transversal vortices that are generated. Once the flow fields are known, the mixing of advected light particles can be assessed. The quality of the mixing between two types of tracers is determined by using Shannon-Renyi entropic measures. To further understand and quantify the mixing we also compute fractal dimensions of Poincare plots along the channels and perform a multi-scale analysis of the Poincare images. For each image we considered 30 versions, starting with the original image, smallest scale of observation (largest number of pixels) 157,094 and ending at the largest scale of observation with only 180 pixels. A renormalization group process of local averaging of pixels transforms the n’th version into n+1’th version. The entropy is shown to grow logarithmically with the number of pixels. The slope of entropy vs. ln(number bins) determines the fractal dimension.