Publications

A Cartesian-octree adaptive front-tracking solver for immersed biological capsules in large complex domains Permalink

Published in Journal of Computational Physics, 2023

We present an open-source adaptive front-tracking solver for biological capsules in viscous flows. The membrane elastic and bending forces are solved on a Lagrangian triangulation using a linear Finite Element Method and a paraboloid fitting method. The fluid flow is solved on an octree adaptive grid using the open-source platform Basilisk. The Lagrangian and Eulerian grids communicate using an Immersed Boundary Method by means of Peskin-like regularized Dirac delta functions. We demonstrate the accuracy of our solver with extensive validations: in Stokes conditions against the Boundary Integral Method, and in the presence of inertia against similar (but not adaptive) front-tracking solvers. Excellent qualitative and quantitative agreements are shown. We then demonstrate the robustness of the present solver in a challenging case of extreme membrane deformation, and illustrate its capability to simulate inertial capsule-laden flows in complex STL-defined geometries, opening the door for bioengineering applications featuring large three-dimensional channel structures. The source code and all the test cases presented in this paper are freely available.

Recommended citation: Huet, Damien P., Wachs, Anthony. "A Cartesian-octree adaptive front-tracking solver for immersed biological capsules in large complex domains." Journal of Computational Physics 492 (2023): 112424. https://www.sciencedirect.com/science/article/pii/S0021999123005193?via%3Dihub

Numerical methods for biological flows laden with deformable capsules and solid particles Permalink

PhD thesis published in 2023

Computer simulations are an indispensable tool to understand and predict the behavior of many complex natural and industrial processes. In particular, complex flows such as rockfalls or flowing blood through microcirculation rely heavily on numerical tools as they are described by equations mathematicians cannot solve by hand. In this thesis, we develop improved numerical methods in order to simulate such complex flows. We first focus on granular flows composed of entangled particles. We study their complex intrication behavior as a step forward in the modeling of complex granular media, which are very common in industrial processes. Then we develop an efficient method to simulate highly deformable biological cells such as red blood cells. This method allows us to study the behavior of deformable cells in large and complex geometries, and therefore constitutes a valuable tool for biologists developing lab-on-chip devices used for instance to provide cheap and fast diagnoses.

Recommended citation: Huet, Damien P. "Numerical methods for biological flows laden with deformable capsules and solid particles" (2023)

Motion and deformation of capsules flowing through a corner in the inertial and non-inertial regimes Permalink

Submitted to Physical Review Fluids, 2023

We investigate the inertial and non-inertial dynamics of three-dimensional elastic capsules flowing through a square channel presenting a sharp corner. Our study analyzes the trajectory, area, velocity and membrane stress of the capsules in the case of a single capsule, a system of two interacting capsules and a train of ten capsules released upstream of the corner. The channel Reynolds number $Re$ ranges from 0.01 to 50 and the Capillary number $Ca$, which measures the ratio of the viscous and elastic stresses, ranges from 0.075 to 0.35. We find that in the inertial regime, the membrane stretch and stress increase dramatically as compared to the non-inertial case, and that the velocity overshoot inside the corner is also enhanced. The maximum capsule deformation is observed to depend nearly linearly on $Ca$ and $Re$. Additionally, we report a repelling mechanism between two confined capsules when their initial interspacing distance $d$ is smaller than a critical value $d_c$. The deformation of the leading capsule is found to be mitigated by the presence of the following capsule. In the case of multiple capsules flowing through the corner, we observe that the increase in the maximum areas of the trailing capsules eventually saturate at the tail of the train. Moreover, we find that the corner tends to separate the capsules regardless of their upstream interspacing distances $d$. This study contributes to the elaboration of practical guidelines for controlling capsule breakup and predicting throughput in both inertial and non-inertial microfluidic experiments.

Recommended citation: Huet, Damien P.; Morente, Antoine; Gai Guodong; Wachs, Anthony. "Motion and deformation of capsules flowing through a corner in the inertial and non-inertial regimes." https://arxiv.org/abs/2305.04129, 2023. https://arxiv.org/abs/2305.04129

Granular avalanches of entangled rigid particles Permalink

Published in Physical Review Fluids, 2021

In granular mechanics, the shape of grains plays a critical role in the overall dynamics and significantly affects the macroscopic properties of the system. Using a dam break setup, granular collapses of nonconvex (cross-shaped) plastic particles assumed quasirigid are conducted experimentally and simulated numerically for a wide range of aspect ratios $a = H_0/L_0$ , with $H_0$ the initial height of the column and $L_0$ its initial length. We report avalanche dynamics such as the top-driven collapse and the buckling collapse, as well as an intermittent flow behavior where reproducibility is lost and where the stability of the column is determined by the random initial configuration of the assembly of entangled particles. While counterintuitive and despite fundamentally different dynamics, we find that the runout distance $L_\infty$ and the final height $H_\infty$ of our granular collapses of crosses agree with those of spherical particles both experimentally and numerically. Our discrete element method simulations are able to reproduce all flow behaviors observed experimentally and they show excellent quantitative agreement with the experimental data. In the simulations, extra care is given to adopting a tangential friction force model based on the cumulative tangential displacement at the contact point, critical to represent stable cases, and to determining the contact model parameters. The analysis of (i) the force network via the average probability density function of contact force magnitude and (ii) the fabric anisotropy suggests that the stability of the column is a complex problem determined by mesoscale properties that we could not reliably identify at that point.

Recommended citation: Huet, Damien P., et al. "Granular avalanches of entangled rigid particles." Physical Review Fluids 6.10 (2021): 104304. https://link.aps.org/doi/10.1103/PhysRevFluids.6.104304

Accurate static contact law and high-order temporal schemes for computations of granular flow dynamics Permalink

Master thesis published in 2019

The smooth Distinct Element Method (DEM) is a numerical simulation technique used in the study of granular materials. The applications are numerous in the industry and in academia, especially in the life sciences field. Smooth DEM implies specifying inter-particles contact forces that are involved during the explicit numerical integration of the Newton’s laws of motion. In this thesis, we implement a tangential contact force accounting for a memory effect and leading to static behaviors that are known to show improved accordance with experiments. However, the validation procedure was tainted by what is believed to be the effect of an inaccurate rolling friction model. Simultaneoulsy, a multi-step higher order scheme was implemented, allowing the use of larger time steps at almost no additional computation cost. Validation of this scheme was successful in some ideal cases, while the effect on error scaling of time discretization itself is extensively discussed.

Recommended citation: Huet, Damien P. "Accurate static contact law and high-order temporal schemes for computations of granular flow dynamics." (2019) https://www.diva-portal.org/smash/record.jsf?pid=diva2%3A1380639&dswid=-4409

Damien Huet