A front-tracking method for the flow of a capsule in a Newtonian fluid

This study examines the deformation dynamics of elastic capsules in viscous flows through a fully coupled fluid–structure interaction framework. Skalak (Sk) and Neo-Hookean (NH) membrane models are employed to describe thin elastic shells subjected to planar simple shear and hyperbolic flows. The incompressible Navier–Stokes equations are solved using the front-tracking method for a capsule with a specific constitutive law. The membrane is represented by a Lagrangian grid enabling accurate modeling of large deformations. The influence of the capillary number on capsule deformation, normal load distribution, and equilibrium shape is systematically analyzed. In planar hyperbolic flow, distinct differences are observed between the Sk and NH models in both capsule shape and normal load distribution. With increasing capillary number, the Sk model predicts elongated shapes with sharp edges, whereas the NH model exhibits concave regions near the capsule ends. These contrasting responses arise from their different sensitivities to surface area variation: the Sk model resists area dilation, producing non-uniform stresses and sharp features, while the NH model allows larger area changes and smoother deformations. The results emphasize the key role of membrane constitutive behavior in stress and normal load localization, providing insights relevant to microfluidic design, cell mechanophenotyping, and biomedical encapsulation.