Lubrication Force Saturation Matters for the Critical Separation Size of the Non-Colloidal Spherical Particle in the Deterministic Lateral Displacement Device

Zhaosheng Yu,Yutian Yang,Jianzhong Lin

doi:10.3390/app12052733

Zhaosheng Yu, Yutian Yang + Show 1 more

Open Access

https://doi.org/10.3390/app12052733

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Journal: Applied sciences	Publication Date: Mar 7, 2022
Citations: 2	License type: CC BY 4.0

Affiliation: Zhejiang University

Abstract

Deterministic lateral displacement (DLD) is a popular technique for separating micro-scale and nano-scale particles continuously. In this paper, an efficient three-dimensional fictitious domain method is developed for the direct numerical simulation of the motion of a non-colloidal spherical particle in the DLD device (i.e., cylinder array), based on substantial modification of our previous FD method. A combination of the fast Fourier transformation (FFT) and a tri-diagonal solver is developed to efficiently solve the pressure Poisson equation for a DLD unit with a shifted periodic boundary condition in the streamwise direction. The lubrication force correction is adopted in the fictitious domain method to correct the unresolved hydrodynamic force when the particle is close to the cylinder with the gap distance below one mesh, and the lubrication force is assumed to saturate at a smaller critical gap distance as a result of the surface roughness effect. The proposed method is then employed to investigate the effect of the critical gap distance of the lubrication force saturation on the motion mode (i.e., separation size) of the particle in the DLD device. Our results indicate that the lubrication force saturation is important to the particle critical separation size, and a smaller saturation distance generally makes the particle more prone to the zigzag mode.

Highlights

With the rapid development of micro-electromechanical systems (MEMS), several continuous flow separation methods have been proposed in microfluidic devices
Our results show that the lubrication force saturation is important to the particle critical separation size, and a larger saturation distance generally makes the particle more prone to the lateral displacement mode
We have developed the direct-forcing fictitious domain (DF/FD) method [29] for the direct numerical simulation of particle-laden flows, based on the modification of the original distributed-Lagrange-multiplier-based FD method of Glowinski [30]

Summary

Introduction

The separation of particles is an important process in the medical laboratories and biomedical industries. The critical particle diameter for the separation or two motion modes is a key fundamental issue for the DLD separation technique, and has been investigated theoretically, numerically, and experimentally. We intend to develop a novel and efficient three-dimensional fictitious domain method specified for the DLD problem and examine the effect of the lubrication force saturation on the motion mode of a non-colloidal spherical particle in the cylindrical post array. Our results show that the lubrication force saturation is important to the particle critical separation size, and a larger saturation distance generally makes the particle more prone to the lateral displacement mode.

Flow Model

Fictitious Domain Method

Pressure Poison equation

Lubrication Force Correction

Mesh Convergence Test

Results and Discussion

Conclusions