Two- and three-dimensional modeling and optimization applied to the design of a fast hydrodynamic focusing microfluidic mixer for protein folding

We present a design of a microfluidic mixer based on hydrodynamic focusing which is used to initiate the folding process (i.e., changes of the molecular structure) of a protein. The folding process is initiated by diluting (from 90% to 30%) the local denaturant concentration (initially 6 M GdCl solution) in a short time interval we refer to as mixing time. Our objective is to optimize this mixer by choosing suitable shape and flow conditions in order to minimize this mixing time. To this end, we first introduce a numerical model that enables computation of the mixing time of a mixer. This model is based on a finite element method approximation of the incompressible Navier-Stokes equations coupled with the convective diffusion equation. To reduce the computational time, this model is implemented in both full three-dimensional (3D) and simplified two-dimensional (2D) versions; and we analyze the ability of the 2D model to approximate the mixing time predicted by the 3D model. We found that the 2D model approximates the mixing time predicted by the 3D model with a mean error of about 15%, which is considered reasonable. Then, we define a mixer optimization problem considering the 2D model and solve it using a hybrid global optimization algorithm. In particular, we consider geometrical variables and injection velocities as optimization parameters. We achieve a design with a predicted mixing time of 0.10 μs, approximately one order of magnitude faster than previous mixer designs. This improvement can be in part explained by the new mixer geometry including an angle of π/5 radians at the channel intersection and injections velocities of 5.2 m s−1 and 0.038 m s−1 for the side and central inlet channels, respectively. Finally, we verify the robustness of the optimized result by performing a sensitivity analysis of its parameters considering the 3D model. During this study, the optimized mixer was demonstrated to be robust by exhibiting mixing time variations of the same order than the parameter ones. Thus, the obtained 2D design can be considered optimal also for the 3D model