Inertial migration of a deformable capsule in an oscillatory flow in a microchannel

Dynamics of a deformable capsule in an oscillatory flow of a Newtonian fluid in a microchannel has been studied numerically. The effects of oscillation frequency, capsule deformability, and channel flow rate have been explored by simulating the capsule within a microchannel. In addition, the simulation captures the effect of the type of imposed pressure oscillations on the migration pattern of the capsule. An oscillatory channel flow enables the focusing of extremely small biological particles by eliminating the need to design impractically long channels. The presented results show that the equilibrium position of the capsule changes not only by the addition of an oscillatory component to the pressure gradient but it also is influenced by the capsule deformability and channel flow rate. Furthermore, it has been shown that the amplitude of oscillation of capsules decreases as the channel flow rate and the rigidity of the capsule increases.

Figure 1

(a) Schematic of the problem setup and (b) an example of the capsule discretization.

Figure 2

Evolution of the capsule motion for different cases by illustrating the time-dependent progress in its trajectory (a) versus the flow direction for $\text{Re}=10$ and $\text{La}=10$, (b) versus time, (c) the equilibrium position versus the frequency, and (d) on the channel cross section with the same legend as that of (b).

Figure 3

Hysteresis loop at two different frequencies for $\text{La}=10$ and $\text{Re}=10.$

Figure 4

Deformation of the capsule at three different frequencies for $\text{La}=10$ and $\text{Re}=37.8.$

Figure 5

Deformed shape of the capsule at $\text{La}=10, \text{Re}=37.8$, and ${\omega }^{*}=0.1$ in one cycle close to its focal point when flow is (a) from left to right, (b) changing direction, (c) from right to left, and the corresponding dimensionless averaged velocity profile along the flow direction when flow is (d) from left to right, (e) changing direction, (f) from right to left.

Figure 6

Flow field around the capsule on its frame of reference at $t^{*}=3269.87$ for $\text{La}=10, \text{Re}=37.8$, and ${\omega }^{*}=0.1$ on the $xy$ plane.

Figure 7

Distance of the capsule focusing position from the center at various La numbers for ${\omega }^{*}=0.1$ and $\text{Re}=10.$

Figure 8

Distance of the capsule focusing position from the center at various Re numbers for ${\omega }^{*}=0.1$ and $\text{La}=10.$

Figure 9

Evolution of the capsule motion for two types of oscillatory functions with ${\omega }^{*}=0.1$ and their comparison with the steady case at $\text{La}=10$ and $\text{Re}=10.$