Numerical simulations of elastic capsules with nucleus in shear flow

Abstract

The shear-induced deformation of a capsule with a stiff nucleus, a model of eukaryotic cells, is studied numerically. The membrane of the cell and of its nucleus are modelled as a thin elastic material obeying a Neo-Hookean constitutive law. The fluid–structure coupling is obtained using an immersed boundary method. The variations induced by the presence of the nucleus on the cell deformation are investigated when varying the viscosity ratio between the inner and outer fluids, the membrane elasticity and its bending stiffness. The deformation of the eukaryotic cell is smaller than that of the prokaryotic one. The reduction in deformation increases for larger values of the capillary number. The eukaryotic cell remains thicker in its middle part compared to the prokaryotic one, thus making it less flexible to pass through narrow capillaries. For a viscosity ratio of 5, the deformation of the cell is smaller than in the case of uniform viscosity. In addition, for non-zero bending stiffness of the membrane, the deformation decreases and the shape is closer to an ellipsoid. Finally, we compare the results obtained modelling the nucleus as an inner stiffer membrane with those obtained using a rigid particle.

Keywords:

• Capsule
• nucleus
• shear flow
• immersed boundary method

Acknowledgements

The authors acknowledge computer time provided by SNIC (Swedish National Infrastructure for Computing) and the support from the COST Action MP1305: Flowing matter. Dr. Lailai Zhu is thanked for the help with the implementation of the membrane module.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the European Research Council [grant number ERC-2013-CoG-616186]; TRITOS; Swedish Research Council (VR);; SNIC [grant number SNIC 2016/10-36].