Numerical Modelling of Mixing in a Microfluidic Droplet Using a Two-Phase Moving Frame of Reference Approach

Droplets generated in microfluidic channels are effective self-contained micromixers and micro-reactors for use in a multiplicity of chemical synthesis and bioanalytical applications. Droplet microfluidic systems have the ability to generate multitudes of droplets with well-defined reagent volumes and narrow size distributions, providing a means for the replication of mixing within each droplet and thus the scaling of processes. Numerical modelling using computational fluid dynamics (CFD) is a useful technique for analysing and understanding the internal mixing in microfluidic droplets. We present and demonstrate a CFD method for modelling and simulating mixing between two species within a droplet travelling in straight microchannel, using a two-phase moving frame of reference approach. Finite element and level set methods were utilised to solve the equations governing the coupled physics between two-phase flow and mass transport of the chemical species. This approach had not been previously demonstrated for the problem of mixing in droplet microfluidics and requires less computational resources compared to the conventional fixed frame of reference approach. The key conclusions of this work are: (1) a limitation of this method exists for flow conditions where the droplet mobility approaches unity, due to the moving wall boundary condition, which results in an untenable solution under those conditions; (2) the efficiency of the mixing declines as the length of the droplet or plug increases; (3) the initial orientation of the droplet influences the mixing and the transverse orientation provides better mixing performance than the axial orientation and; (4) the recirculation inside the droplet depends on the superficial velocity and the viscosity ratio.