Sensitivity analysis and study of the mixing uniformity of a microfluidic mixer

Abstract: We consider a microfluidic mixer based on hydrodynamic focusing, which is used to initiate the folding process of individual proteins. The folding process is initiated by quickly diluting a local denaturant concentration, and we define mixing time as the time advecting proteins experience a specified to achieve a local drop in denaturant concentration. In previous work, we presented a minimization of mixing time which considered optimal geometry and flow conditions, and achieved a design with a predicted mixing time of 0.10 $\mu$s. The aim of the current paper is twofold. First, we explore the sensitivity of mixing time to key geometric and flow parameters. In particular, we study the angle between inlets, the shape of the channel intersections, channel widths, mixer depth, mixer symmetry, inlet velocities, working fluid physical properties, and denaturant concentration thresholds. Second, we analyze the uniformity of mixing times as a function of inlet flow streamlines. We find the shape of the intersection, channel width, inlet velocity ratio, and asymmetries have strong effects on mixing time; while inlet angles, mixer depth, fluid properties, and concentration thresholds have weaker effects. Also, the uniformity of the mixing time is preserved for most of the inlet flow and distances of down to within about 0.4 $\mu$m of the mixer wall. We offer these analyses of sensitivities to imperfections in mixer geometry and flow conditions as a guide to experimental efforts which aim to fabricate and use these types of mixers. Our study also highlights key issues and provides a guide to the optimization and practical design of other microfluidic devices dependent on both geometry and flow conditions.