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Inertial and non-inertial focusing of a deformable capsule in a curved microchannel
- Saman Ebrahimi, Prosenjit Bagchi
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- Journal:
- Journal of Fluid Mechanics / Volume 929 / 25 December 2021
- Published online by Cambridge University Press:
- 27 October 2021, A30
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- Article
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A computational study is presented on cross-stream migration and focusing of deformable capsules in curved microchannels of square and rectangular sections under inertial and non-inertial regimes. The numerical methodology is based on immersed boundary methods for fluid–structure coupling, a finite-volume-based flow solver and finite-element method for capsule deformation. Different focusing behaviours in the two regimes are predicted that arise due to the interplay of inertia, deformation, altered shear gradient, streamline curvature effect and secondary flow. In the non-inertial regime, a single-point focusing occurs on the central plane, and at a radial location between the interior face (i.e. face with highest curvature) of the channel and the location of zero shear. The focusing position is nearly independent of capsule deformability (represented by the capillary number,
$Ca$). A two-step migration is observed that is comprised of a faster radial migration, followed by a slower migration toward the centre plane. The focusing location progressively moves further toward the interior face with increasing curvature and width, but decreasing height. In the inertial regime, single-point focusing is observed near the interior face for channel Reynolds number
$Re_{C}\sim {O}(1)$, that is also highly sensitive to
$Re_{C}$ and
$Ca$, and moves progressively toward the exterior face with increasing
$Re_{C}$ but decreasing
$Ca$. As
$Re_{C}$ increases by an order, secondary flow becomes stronger, and two focusing locations appear close to the centres of the Dean vortices. This location becomes practically independent of
$Ca$ at even higher inertia. The inertial focusing positions move progressively toward the exterior face with increasing channel width and decreasing height. For wider channels, the equilibrium location is further toward the exterior face than the vortex centre.
Motion of a capsule in a curved tube
- Saman Ebrahimi, Peter Balogh, Prosenjit Bagchi
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- Journal:
- Journal of Fluid Mechanics / Volume 907 / 25 January 2021
- Published online by Cambridge University Press:
- 25 November 2020, A28
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Cross-streamline migration of deformable capsules is studied in three-dimensional curved vessels using a numerical model. Two geometries are chosen: torus vessels to study the effect of constant vessel curvature, and U-shaped vessels to study the effect of change in curvature. A wide range of inertia is considered to include a broad range of applications, from the microcirculation to inertial microfluidics. Vessel curvature and change in curvature are shown to affect capsule migration because of the way they affect the undisturbed flow. In toroidal vessels at negligible inertia, no secondary flow exists and the axial fluid velocity is shifted toward the inner surface of the vessel. In this limit, capsules settle at a location that is away from the vessel centreline, and between the location of the maximum fluid velocity and the innermost surface. Increasing the vessel curvature results in the equilibrium position being increasingly closer to the inner surface. The results suggest the presence of a curvature-induced migration that drives the capsule continuously toward the region of higher streamline curvature. The equilibrium locations are on the symmetry plane of the torus, and are stable equilibria when inertia is negligible. At finite inertia, capsules released on the symmetry plane first settle at an equilibrium located on this plane, which may either be stable or unstable. This equilibrium location depends on both capsule deformability (characterised by capillary number,
$Ca$) and the tube Reynolds number
$R{e_t}$. It is closer to the inner edge of the torus for smaller
$R{e_t}$ and larger
$Ca$, and toward the outer edge for larger
$R{e_t}$ and smaller
$Ca$. This dependence of the equilibria arises due to the secondary flow (or Dean's vortex), which opposes the curvature-induced inward migration. The equilibrium locations on the symmetry plane are unstable if the secondary flow is strong, in which case capsules depart the symmetry plane, and set on to a spiralling motion, eventually settling near the centres of the Dean's vortices. For the U-shaped vessels, the curvature change is shown to create a radial velocity component, even at small inertia, that can be of comparable magnitude to the axial velocity, and that increases with increasing curvature. This radial velocity causes a large and abrupt change in capsule trajectory toward the inner side of the vessel where the curvature increases, but toward the outer side where the curvature decreases.
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