Dynamics of Elastic Capsules in constricted Microfluidic Channels
Park, Sun Young
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In this dissertation, we investigate computationally the transient dynamics of an elastic capsule in a square microchannel with two different types of constriction (i.e., a square or a rectangular constriction), and compare them with those owing to a droplet passing. The confinement and expansion dynamics of the fluid flow results in a rich deformation behavior for the capsule, from an elongated shape at the constriction entrance, to a flattened parachute shape at its exit. Larger capsules are shown to take more time to pass the constriction and cause higher additional pressure difference, owing to higher flow blocking. Our work highlights the effects of two different mechanisms for non-tank-treading transient capsule dynamics. The capsule deformation results from the combined effects of the surrounding and inner fluids normal stresses on the soft particles interface, and thus when the capsule viscosity increases, its transient deformation decreases, as for droplets. However, the capsule deformation is not able to create a strong enough inner circulation (owing to restrictions imposed by the material membrane), and thus the viscosity ratio does not affect much the capsule velocity and the additional pressure difference. In addition, the weak inner circulation results in a positive additional pressure difference even for low viscosity capsules, in direct contrast to low-viscosity droplets which create a negative. In addition, we focus on the hydrodynamic forces exerted on the constriction owing to the capsule passing by considering different capsule sizes, flow rates and viscosity ratios. As the capsule size increases, the forces increase owing to the higher flow blocking. The hydrodynamic forces on the constriction are only weakly affected by the viscosity ratio. For low-viscosity capsules, the additional hydrodynamic forces on the constriction are positive in direct contrast to low-viscosity droplets which create negative additional hydrodynamic forces on the constriction due to their strong inner circulation. Finally, we investigate the effects of the constriction type for the transient capsule dynamics. In the square constriction, the capsule is more deformed owing to the larger flow changes associated with the smaller cross-section area of this constriction. The higher flow blocking results in an increase of the capsule velocity, the additional pressure difference and the hydrodynamic forces exerted on the constriction owing to the capsule passing. Our findings suggest that the high cytoplasmatic viscosity, owing to the protein hemoglobin required for oxygen transport, does not affect adversely the motion of non-tank-trading erythrocytes in vascular capillaries.