High throughput, automated prediction of focusing patterns for inertial microfluidics

Visual inspections for identifying focusing points in inertial microfluidic flows are prone to misinterpreting stable locations and focusing shifts in the case of non-trivial focusing patterns. We develop and deploy an approach for automating the calculation of focusing patterns for a general channel geometry, and thereby reduce the dependence on empirical/visual procedures to confirm the presence of stable locations. We utilize concepts from interpolation theory (to represent continuous force-fields using discrete points), and stability theory to identify "basins of attraction" and quantitatively identify stable equilibrium points. Our computational experiments reveal that predicting equilibrium points accurately requires upto $\times$10-20 times more refined force-maps that conventionally used, which highlights the spatial resolution required for an accurate representation of cross-sectional forces. These focusing patterns are validated using experimental results for a rectangular channel, and triangular channel with an apex angle of $90^\circ$. We then apply the approach to predict and explain focusing patterns and shifts for a $90^\circ$-isosceles triangular channel across a range of Reynolds numbers for $\frac{a}{H} = 0.4$ (particle-to-channel size ratio). We observe that the predicted focusing patterns match experiments well. The force-maps also reveal certain "clouds" of localized stable points, which aid in explaining the onset of bifurcation observed in experiments. The current algorithm is agnostic to channel cross-sections and straight/curved channels, which could pave way to generating a library of focusing patterns as a function of channel geometry, and $Re$, to assist in design of novel devices for tailored particle-streams.