A numerical look at the deformation of capsule membranes in a flow

How elastic capsules and cells deform in a viscous flow is important for many biomedical and microfluidic applications, including drug delivery and next-generation diagnostic devices. Capsule dynamics have been well studied, both experimentally and numerically, yet researchers still do not completely understand how the capsule membrane affects deformation.

Mehrdad Najafian and Saeed Mortazavi numerically examined capsule membrane dynamics. They used the incompressible Navier-Stokes equation to calculate the motion of the fluids, treating the elastic membrane as a boundary coupling the internal fluid and surrounding fluid. They evaluated the results from two different constitutive models, the Skalak and Neo-Hookean models, which they used to describe the mechanical behavior of the membrane. The authors then compared capsule deformation, equilibrium shape, and normal-load distribution under simple shear and planar hyperbolic flows at different capillary numbers.

Their results showed different responses to increasing deformation between the two models. The Skalak model produced elongated shapes with sharp edges due to its resistance to area dilation. The Neo-Hookean model, which allowed for larger area variations, showed smoother deformation and concavities near the capsule ends.

“The most exciting result was the strikingly different behavior of the two membrane models, especially in planar hyperbolic flow,” Mortazavi said. “The contrasting morphologies directly reflect how the membrane constitutive law controls stress and normal-load localization, which is a key insight for interpreting capsule mechanics.”

The authors hope their findings can help improve predictions of capsule membrane mechanics in complex flows. They plan to continue studying more realistic flow conditions, including modeling Poiseuille flow and finite-Reynolds-number flows, to provide a more comprehensive understanding of capsule dynamics.

Source: “A front tracking method for the flow of a capsule in a newtonian fluid,” by M. Najafian and S. Mortazavi, Physics of Fluids (2026). The article can be accessed at https://doi.org/10.1063/5.0339991 .