A common-baseline semi-empirical resistance framework for symmetric obstacle arrays in deterministic lateral...

Deterministic lateral displacement (DLD) relies on controlled flow partitioning in obstacle arrays, yet existing resistance-based boundary design is largely established for circle pillars and is not readily extended to other symmetric obstacle geometries. Here, a common-baseline semi-empirical resistance framework is developed using the square obstacle as the reference. For circle, diamond, and I-shaped obstacles, the streamwise local-gap profile g_i(x) is reduced to a contour-derived geometric correction ψ_i, and a shape-specific response exponent γ_i, calibrated from numerical resistance data, maps ψ_i to the resistance relative to the square baseline. Independent validation of the final non-square resistance expressions gives an overall RMSPE of 4.93%. Applicable ranges are identified from the response behavior. For the I-shaped obstacle, whose contour combines curved groove segments with sharp transitions, the resistance relation is retained over 0.20 ≤M_L/W≤ 0.75, while groove-ratio assessment further identifies 0.20 ≤C/M_a≤ 0.35 for boundary design. Applying the resulting resistance relations to positive and negative boundary-gap design shows that corrected N = 8 and N = 12 I-shaped arrays preserve the intended first-flow-lane flux partitioning over most boundary rows at both groove-ratio bounds. Particle-trajectory comparisons near the positive boundary further show that the 3.2 and 3.4 μm particles maintain displacement migration after boundary correction, whereas both particles ultimately follow zigzag trajectories without correction. These results provide a quantitative hydrodynamic pathway linking obstacle contour, resistance prediction, and boundary-gap design in symmetric DLD arrays.