Interplay of deformability and adhesion on localization of elastic micro-particles in blood flow

Abstract

The margination and adhesion of micro-particles (MPs) have been extensively investigated separately, due to their important applications in the biomedical field. However, the cascade process from margination to adhesion should play an important role in the transport of MPs in blood flow. To the best of our knowledge, this has not been explored in the past. Here we numerically study the margination behaviour of elastic MPs to blood vessel walls under the interplay of their deformability and adhesion to the vessel wall. We use the lattice Boltzmann method and molecular dynamics to solve the fluid dynamics and particle dynamics (including red blood cells (RBCs) and elastic MPs) in blood flow, respectively. Additionally, a stochastic ligand–receptor binding model is employed to capture the adhesion behaviours of elastic MPs on the vessel wall. Margination probability is used to quantify the localization of elastic MPs at the wall. Two dimensionless numbers are considered to govern the whole process: the capillary number $Ca$, denoting the ratio of viscous force of fluid flow to elastic interfacial force of MP, and the adhesion number $Ad$, representing the ratio of adhesion strength to viscous force of fluid flow. We systematically vary them numerically and a margination probability contour is obtained. We find that there exist two optimal regimes favouring high margination probability on the plane $Ca{-}Ad$. The first regime, namely region I, is that with high adhesion strength and moderate particle stiffness; the other one, region II, has moderate adhesion strength and large particle stiffness. We conclude that the existence of optimal regimes is governed by the interplay of particle deformability and adhesion strength. The corresponding underlying mechanism is also discussed in detail. There are three major factors that contribute to the localization of MPs: (i) near-wall hydrodynamic collision between RBCs and MPs; (ii) deformation-induced migration due to the presence of the wall; and (iii) adhesive interaction between MPs and the wall. Mechanisms (i) and (iii) promote margination, while (ii) hampers margination. These three factors perform different roles and compete against each other when MPs are located in different regions of the flow channel, i.e. near-wall region. In optimal region I, adhesion outperforms deformation-induced migration; and in region II, the deformation-induced migration is small compared to the coupling of near-wall hydrodynamic collision and adhesion. The finding of optimal regimes can help the understanding of localization of elastic MPs at the wall under the adhesion effect in blood flow. More importantly, our results suggest that softer MP or stronger adhesion is not always the best choice for the localization of MPs.