Particle migration in areas of constricted flow

TL;DR

The paper addresses how particle size and non-spherical shape influence margination and adhesion in a 2D constricted flow using Lattice-Boltzmann simulations with immersed boundary coupling. By comparing circular and rectangular particles across varying $R_{equiv}$ and occlusion levels, the study shows that rectangles marginate more strongly and earlier than circles, driven by enhanced drag and lift and modulated by wake dynamics. The authors quantify margination via mean-square displacement and define an adhesion probability $P$ that increases with certain geometric and shear conditions, highlighting potential design rules for vascular-targeted carriers. While the 2D model captures key qualitative trends, the work acknowledges dimensional limitations and suggests extending to 3D to refine migration and adhesion predictions for clinical applications.

Abstract

Cardiovascular diseases are a leading cause of death globally. Among them, some are linked to stenosis, which is an abnormal narrowing of blood vessels, as well as other factors. Smart drug delivery systems based on micro- and nanoparticles are a promising method to offer non/minimal-invasive therapeutic mechanisms. Here we investigate the propensity of particles with different shapes and sizes to drift laterally (marginate) towards an occlusion area in a two-dimensional (2D) parallel plate laminar flow using the Lattice-Boltzmann method (LBM). To verify the outcomes on both sides of the stenosis, a probability of adhesion to the borders was calculated. Analysis was done on the impact of wall-shear stress on both sides of the stenosis. Our results show that rectangular particles migrate in larger amounts and earlier than circular ones.

Figures (9)

• Figure 1: Representation of a single discretized circular particle (red dots) moving through the fluid lattice (white dots). Each particle boundary node is assigned a velocity $\bm{v_b}$. The corresponding fluid velocity at the same location, $\bm{u_b}$, is obtained via a four–neighbor interpolation, illustrated by the gray rectangle.
• Figure 2: Schematic of the 2D setup used in the simulations.
• Figure 3: Flow velocities and particles positions for different shapes; (a-b) circular, $R=10$ and (c-d) rectangular, $R_{equiv}=15.8$ ($l_1=10, \gamma=3$) at different times crossing the constriction zone. In every case, the initial positions of the particles were the same. The color bar shows the values of flow velocity. Set of parameters: $Re=400$ and $N=40$.
• Figure 4: Increasing rate of the MSD as a function of the equivalent radius for circles and rectangles. The rate was calculated as the slope of a log-log fitting of the MSD(t). Circle and square dots represent circular and rectangular particles, respectively. Percentage occlusion: 25%, and rest of parameters as in Fig. \ref{['fig:Fig1']}.
• Figure 5: Ratio of particles migrated to the lateral boundaries and mean residence time at the boundaries before (a,c) and after (b,d) the stenosis as a function of $R_{equiv}$. Blue-solid lines correspond to an occlusion of 25% and red-dashed lines to 50%. Circles and squares dots are for circles and rectangles particles, respectively. Set of parameters as in Fig. \ref{['fig:Fig1']}.