On the Three-Dimensional Structure of the Flow through Deterministic Lateral Displacement Devices and Its Effects on Particle Separation

Valentina Biagioni,Stefano Cerbelli,Alessandra Adrover

doi:10.3390/pr7080498

Valentina Biagioni, Stefano Cerbelli + Show 1 more

Open Access

https://doi.org/10.3390/pr7080498

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Journal: Processes	Publication Date: Aug 1, 2019
Citations: 5	License type: CC BY 4.0

Affiliation: Sapienza University of Rome

Abstract

Experiments have shown that a suspension of particles of different dimensions pushed through a periodic lattice of micrometric obstacles can be sorted based on particle size. This label-free separation mechanism, referred to as Deterministic Lateral Displacement (DLD), has been explained hinging on the structure of the 2D solution of the Stokes flow through the patterned geometry, thus neglecting the influence of the no-slip conditions at the top and bottom walls of the channel hosting the obstacle lattice. We show that the no-slip conditions at these surfaces trigger the onset of off-plane velocity components, which impart full three-dimensional character to the flow. The impact of the 3D flow structure on particle transport is investigated by enforcing an excluded volume approach for modelling the interaction between the finite-sized particles and the solid surfaces. We find that the combined action of particle diffusion and of the off-plane velocity component causes the suspended particles to migrate towards the top and bottom walls of the channel. Preliminary results suggest that this effect makes the migration angle of the particles significantly different from that obtained by assuming a strictly two-dimensional structure for the flow of the suspending fluid.

Highlights

The inherently laminar regime characterizing momentum transport at microfluidic scales makes it possible to accurately design a priori device geometries and operating conditions able to perform specific tasks as regards the transport of chemical species or even of mesoscopic objects suspended in a carrier fluid
We find that the combined action of particle diffusion and of the off-plane velocity component causes the suspended particles to migrate towards the top and bottom walls of the channel
An excluded-volume model inspired by that used in Hydrodynamic Chromatography, explicitly accounting for particle diffusion, has been put forward by one of these authors and co-authors in a series of recent articles [32,33,34,35,36] for tackling transport of finite-size particles in Deterministic Lateral Displacement (DLD) devices

Summary

Introduction

The zero net flux condition expressed by Equation (12) implies that a gradient of the cumulative particle number density C must develop at those points of the effective boundary where the normal velocity component is opposedly oriented to the local vector n normal to the surface (i.e., at points where the approaching velocity would cause the center of the particle to enter the excluded-volume region). At fixed fluid dynamic conditions, it is expected that such concentration gradient will become steeper and steeper at increasing values of Pe p , as already observed in two-dimensional implementations of the excluded-volume approach (see, e.g., Reference [34]) For this reason, a tailored discretization of the effective transport domain Ωeff , constructed so as to capture the thin boundary layer developed by C (x, t), must be enforced at those effective boundaries where the local fluid velocity possesses a sizeable normal component oriented towards the exterior of Ωeff. The modelling approach described above is used to determine the features of particle transport in the 3D geometry, with specific focus on the average migration angle, θ p , which primarily impacts upon separation performance of DLD-based microfluidic separators

System Geometry

Stokes Flow of the Suspending Fluid

Excluded-Volume Approach for Particle Transport

Results

Particle Transport

Conclusions