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 ×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∘. We then apply the approach to predict and explain focusing patterns and shifts for a 90∘-isosceles triangular channel across a range of Reynolds numbers for aH=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.
Available at: http://works.bepress.com/baskar-ganapathysubramanian/78/