Rational Design Protocols for Size-Based Particle Sorting Microdevices Using Symmetry-Induced Cyclical Dynamics

TL;DR

This paper develops a unified theoretical framework and design algorithms for size-based particle sorting microfluidic devices using symmetry-induced cyclical dynamics, enabling precise control of particle displacement.

Contribution

It introduces novel methods to describe particle-obstacle interactions for arbitrary lattice geometries and provides algorithms to design microdevices that accurately achieve desired particle displacements.

Findings

Validated design algorithms match target displacements with high accuracy

Designed devices outperform existing methods in size, accuracy, and complexity

Mathematically proven methods ensure reliable device performance

Abstract

In this paper, we describe the unification and extension of multiple kinematic theories on the advection of colloidal particles through periodic obstacle lattices of arbitrary geometry and infinitesimally small obstacle size. We focus specifically on the particle displacement lateral to the flow direction (termed "deterministic lateral displacement") and the particle-obstacle interaction frequency, and develop novel methods for describing these as a function of particle size and lattice parameters for arbitrary lattice geometries for the first time in the literature. We then demonstrate design algorithms for microfluidic devices consisting of chained obstacle lattices of this type that approximate any lateral displacement function of size to arbitrary accuracy with respect to multiple optimization metrics, prove their validity mathematically, and compare the generated results favorably to designs in the literature with respect to metrics such as accuracy, device size, and complexity.