Anisotropic permeability in deterministic lateral displacement arrays

Abstract

We uncover anisotropic permeability in microfluidic deterministic lateral displacement (DLD) arrays. A DLD array can achieve high-resolution bimodal size-based separation of microparticles, including bioparticles, such as cells. For an application with a given separation size, correct device operation requires that the flow remains at a fixed angle to the obstacle array. We demonstrate via experiments and lattice-Boltzmann simulations that subtle array design features cause anisotropic permeability. Anisotropic permeability indicates the microfluidic array's intrinsic tendency to induce an undesired lateral pressure gradient. This can cause an inclined flow and therefore local changes in the critical separation size. Thus, particle trajectories can become unpredictable and the device useless for the desired separation task. Anisotropy becomes severe for arrays with unequal axial and lateral gaps between obstacle posts and highly asymmetric post shapes. Furthermore, of the two equivalent array layouts employed with the DLD, the rotated-square layout does not display intrinsic anisotropy. We therefore recommend this layout over the easier-to-implement parallelogram layout. We provide additional guidelines for avoiding adverse effects of anisotropy on the DLD.

A Review on Deterministic Lateral Displacement for Particle Separation and Detection

“…However, this DLD model of binary separation is incomplete due to the existence of the intermediate displacement mode of separation. This intermediate displacement mode is caused by the uneven pressure between the lateral and downstream direction that disrupts the flow streamline, which is called as the anisotropic permeability effect [20,[26][27][28][29].…”

Rational design protocols for size-based particle sorting microdevices using symmetry-induced cyclical dynamics

“…When obstacles sizes do not satisfy this condition, the hydrodynamics of the system cannot be disregarded and can significantly alter the observed phenomena in comparison to our model. These sources of discrepancies include the development of lateral pressure gradients as described by [12], edge effects at the interface between different chained lattices, and differences in particle advection trajectories post-collision due to the now non-trivial flow perturbation induced by the obstacles. However, work by Risbud & Drazer [5] [8] has identified that in systems with arbitrary obstacle sizes relative to the colloidal particles, the interaction dynamics between particles and obstacles are essentially identical to those described in Section II B except that the "output" displacements are ±b c , a parameter depending on the hydrodynamics of the microdevice and the particle/obstacle sizes, rather than ±r.…”

“…Having described a mathematical framework for understanding the collision frequencies and lateral displacements per length of particles advecting through chained obstacle lattices, we now discuss how we can use "chained" obstacle lattices to solve the inverse design problem of approximating a desired size-dependent lateral displacement or collision frequency function. For the purposes of the following analyses, we will focus specifically on the rotated square lattices described in Section 2.1.1 and Section 2.5.1, as this family of lattices exhibits isotropic fluid permeability (see [12]) which minimizes performance degradation due to induced lateral pressure gradients.…”

Sorting same-size red blood cells in deep deterministic lateral displacement devices

“…We found out that if we just remove those pillars, the empty spaces result in less hydraulic resistance and hence induces a lateral pressure gradient. This breaks the homogeneity of the flow and introduces significant errors in the cell trajectories [35,58]. Therefore, we decided to replace the circular pillars crossing the walls with elliptical pillars in such a way that they maintain the same vertical spacing with the neighboring pillars.…”