This paper presents an immersed boundary method (IBM) for deformable capsules in incompressible viscous flow. Unlike the conventional IBM, the present method utilizes an unstructured mesh coupled with the moving least squares method, which improves the performance for applications involving a complex geometry. We validate our method through independent studies on oscillation and deformation of spherical capsules in viscous flow. Our simulations on a deformable capsule flowing in an elbow channel show that the capsule capillary number affects its shape and deformation area significantly. The maximum deformation area is found to be linearly proportional to the capillary number. In addition, our simulation on soft capsule sorting using a pinched flow fractionation microfluidic device shows that smaller capsules tend to migrate toward the pinched wall region before streaming out in the expansion region. The result is that smaller capsules drift closer to the center plane of the device and can be efficiently separated from the larger ones using branching. For capsule sorting applications using Tjunction, we found that the fate of a capsule depends on the relative position of its center of mass and the dividing streamline. Larger capsules are diverted from the main stream toward the side outlet, leading to effective size fractionation.
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