Microfluidic sorting of deformable particles finds many applications, for example, medical devices for cells. Deterministic lateral displacement (DLD) is one of them. Particle sorting via DLD relies only on hydrodynamic forces. For rigid spherical particles, this separation is to a great extend understood and can be attributed to size differences: large particles displace in the lateral direction with respect to the flow while small particles travel in the flow direction with negligible lateral displacement. However, the separation of non-spherical deformable particles such as red blood cells (RBCs) is more complicated than rigid particles. For example, is it possible to separate deformable particles that have the same size but different mechanical properties? We study deformability-based sorting of same-size RBCs via DLD using an in-house integral equation solver for vesicle flows in two dimensions. Our goal is to quantitatively characterize the physical mechanisms that enable the cell separation. To this end, we systematically investigate the effects of the interior fluid viscosity and membrane elasticity of a cell on its behavior. In particular, we consider deep devices in which a cell can show rich dynamics such as taking a particular angular orientation depending on its mechanical property. We have found out that cells moving with a sufficiently high positive inclination angle with respect to the flow direction displace laterally while those with smaller angles travel with the flow streamlines. Thereby, deformability-based cell sorting is possible. The underlying mechanism here is cell migration due to the cell's positive inclination and the shear gradient. The higher the inclination is, the farther the cell can travel laterally. We also assess the efficiency of the technique for dense suspensions. It turns out that most of the cells in dense suspensions does not displace in the lateral direction no matter what their deformability is. As a result, separating cells using a DLD device becomes harder. • We investigate the cell dynamics in DLD flow, i.e., we study cell's inclination angle and lateral velocity in Sections 3.1 and 3.2. • We compare these cell-in-DLD dynamics with simple flows such as a free shear and a confined Poiseuille flows in Sections 4.1 and 4.2. • In order to quantify migration, we compute a new quantity in Section 4.3, which we call the "pseudolift", that turns out to be an indicative measure of migration. • Lastly, we present phase diagrams for the transport modes in Section 3.3 and investigate the separation in dense RBC suspensions in Section 3.4 for different viscosity contrasts, capillary numbers and device configurations. The efficiency of DLD for dense suspensions in deep devices has not been studied experimentally and numerically. However, it is essential to investigate the dense suspension regime because the deep devices with dense suspensions provide higher throughput than the shallow devices with dilute suspensions. Methodology. We use a standard 2D mechanical model for RBCs [33, 40, 43] . We model an RBC as a vesicle with a reduced area of 0.65 which resists deformation due to bending and tension. It is impermeable to flow and locally inextensible. Since RBCs and vesicles share similar dynamical properties and the
We refer the reader to REF for the review of related work on deformability-based cell sorting and the details of our numerical scheme for cell flow simulations.
Sorting same-size red blood cells in deep deterministic lateral displacement devices
Physics