Numerical Modeling of Hydrodynamic Flow Focusing in a Microfluidic Device for Time-Resolved Serial Crystallography

Serial femtosecond crystallography (SFX) with an X-ray free-electron laser (XFEL) has enabled the determination of protein structures and protein reaction intermediates in millisecond to microsecond time resolutions. Mix-and-Inject crystallography (MISC) at XFELs enables fast mixing in the magnitude of milliseconds in order to achieve desired reaction time points. For these experiments, numerical simulations of a hydrodynamic flow mixer capable of fast mixing by diffusion has been developed using both COMSOL Multiphysics 5.6 and QuickerSims Computational Fluid Dynamics (CFD) Toolbox for MATLAB. These simulation programs were compared by calculations of mixing times and concentration flow profiles. Mixing times in the range of 1-10 ms were calculated in COMSOL under certain flow rate conditions whereas mixing times in the range of 6-15 ms were calculated with QuickerSims. From these mixing times, reaction intermediates can be varied from sub-millisecond to several hundred millisecond time points for a MISC experiment. Explanations for the discrepancies between the two models were attributed to variations in parameter definitions and meshing. Further analysis on the mixing characteristics were investigated by calculating an analytical solution to the convection-diffusion equation for fluid flow in a two-dimensional rectangular channel. The concentration profile along the width of the channel for the analytical solution was compared with the numerical solution obtained with COMSOL and QuickerSims. Upon comparison, it was determined that the diffusion coefficient may not be a significant factor for the disagreement between the two hydrodynamic flow models.