Numerical design of a T-shaped microfluidic device for deformability-based separation of elastic capsules and soft beads

We propose a square cross-section microfluidic channel with an orthogonal side branch (asymmetric T-shaped bifurcation) for the separation of elastic capsules and soft beads suspended in a Newtonian liquid on the basis of their mechanical properties. The design is performed through three-dimensional direct numerical simulations. When suspended objects start near the inflow channel centerline and the carrier fluid is equally partitioned between the two outflow branches, particle separation can be achieved based on their deformability, with the stiffer ones going “straight” and the softer ones being deviated to the “side” branch. The effects of the geometrical and physical parameters of the system on the phenomenon are investigated. Since cell deformability can be significantly modified by pathology, we give a proof of concept on the possibility of separating diseased cells from healthy ones, thus leading to illness diagnosis.

Figure 1

Schematic representation of the T-shaped channel with a capsule suspended on its centerline. (a) Zoom of the section of the capsule in the $xy$ plane at $z=0$. (b) Zoom of the smoothed corners with curvature radius $R_f=0.1H$ between the main and the side channel.

Figure 2

Steady-state deformed shape of the external surface of a capsule at the centerline of a square section straight channel for $\beta =0.9$ and Ca = 0.02. Solid line: our numerical simulations; symbols: results from Hu et al. [30].

Figure 3

Dashed lines: trajectories of a capsule in the T-shaped device. Symbols: positions of the capsule center of volume at $t=0.3,0.8,1.4,2.4$. Solid lines: capsule shapes at $t=0.3,0.8,2.4$. $\beta =0.4$, Ca ranging from 0.01 to 0.05.

Figure 4

Deformed shapes of a capsule with $\beta =0.4$ and Ca between 0.01 and 0.05 at $t=0.3,0.8,1.4,2.4$. For the legend, refer to Fig. 3.

Figure 5

Temporal trends of the $x$ component $u_{p,x}$ (a) and of the $y$ component $u_{p,y}$ (b) of a capsule velocity at $\beta =0.4$ and Ca between 0.01 and 0.05. The symbols on each curve mark the time values $t=0.3,0.8,1.4,2.4$.

Figure 6

Upper row: von Mises stress ${\sigma }_{\text{VM}}$ on the external surface of a capsule with $\beta =0.4$ at $t=0.3,0.8,2.4$ for Ca = 0.01 (a), 0.05 (b). Lower row: ${\sigma }_{\text{VM}}$ in the intersection between the capsule membrane and the $xy$ plane at $z=0$ for $\beta =0.4,t=2.4$, Ca = 0.01 (c), 0.05 (d).

Figure 7

Critical capillary number for an elastic capsule ${\text{Ca}}_c$ as a function of the confinement ratio $\beta$. Inset: ${\text{Ca}}_c$ as a function of the particle initial position $y_{p0}$ at $\beta =0.6$.

Figure 8

Upper row: von Mises stress ${\sigma }_{\text{VM}}$ on the external surface of an elastic bead with $\beta =0.4$ at $t=0.3,0.8,2.0$ for Ca = 0.01 (a), 0.05 (b). Lower row: ${\sigma }_{\text{VM}}$ in the intersection between the particle and the $xy$ plane at $z=0$ for $\beta =0.4,t=2.0,{\text{Ca}}_e=0.01$ (c), 0.05 (d).

Figure 9

Critical elastic capillary number for an elastic bead ${\text{Ca}}_{e,c}$ as a function of the confinement ratio $\beta$.