A density-based threshold model for evaluating the separation of particles in heterogeneous mixtures with curvilinear microfluidic channels

Particle separation techniques play an important role in biomedical research. Inertial focusing based microfluidics using nonlinear channels is one of the promising label-free technologies for biological applications. The particle separation is achieved as a result of the combination of inertial lift force (F_L) and Dean drag force (F_D). Although the mathematical expressions of F_L and F_D have been well derived in prior studies, they are still complicated, which limits their popularity in practice. Recent studies modified these expressions through experiments and proposed a threshold model, which assumes that only particles larger than the threshold will be well focused. Although this threshold model has been used in recent studies, two varying versions of the threshold model (TM1 and TM2) prevents standardisation in practice. In addition, both models were developed with regular low-density particles and may not be applicable to samples with higher density or samples with irregular shapes. Here, we evaluated the threshold models with samples of different densities. Based on these evaluations, we derived a modified model (TM4), which additionally considers the factor of particle density to improve the accuracy of existing models. Our results demonstrated that TM4 could more reliably predict the sorting efficiency of samples within a wider density range.