Finite element simulation of a viscoelastic cell entering a cylindrical channel: Effects of frictional contact

Abstract

Finite element method has been extensively used to simulate the process of single cells entering a narrow channel under a prescribed pressure. Yet an in-depth understanding on the effects of the frictional boundary condition in such simulations is lacking. The main challenge lies in the continuously evolving contact region between the deformed cell and the channel wall during the entry process, which makes it difficult to apply proper boundary conditions for the friction and pressure. In this work, we present an approach to continuously update the boundary condition according to the contact status during entry. Using this approach and modeling the cell as a visco-hyperelastic sphere, we study how the pressure boundary conditions and the friction coefficient affect the simulated cell entry process. Specifically, we compare two special cases of pressure boundary conditions: positive pressure at the trailing edge of the cell or negative pressure at the leading edge. It is found that the two cases produce the same result in terms of the cell entry length under frictionless contact, but give considerably different results under frictional contact. Effects of whether the pressure boundary is updated are then studied by considering more special cases. All these results are well explained by the pressure superposition principle, and further insights into the effects of pressure boundary condition and boundary update are also acquired. Finally, focusing on the case of positive pressure with boundary updates, we obtain simulation results revealing how the entry length depends on the pressure, time and friction coefficient. In particular, a larger friction coefficient can significantly reduce the entry length under a prescribed pressure or a certain entry time. Our results suggest that it is necessary to implement accurate pressure boundary conditions (e.g., pressure magnitudes at the two edges of cell and continuously updated pressure boundary regions) in order to faithfully capture the frictional contact between the cell and the channel wall. In addition, the simulation approach can be useful in modeling the general process of a viscoelastic sphere entering a cylindrical channel involving frictional contact.