Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications

Red blood cells flowing through capillaries assume a wide variety of different shapes owing to their high deformability. Predicting the realized shapes is a complex field as they are determined by the intricate interplay between the flow conditions and the membrane mechanics. In this work we construct the shape phase diagram of a single red blood cell with a physiological viscosity ratio flowing in a microchannel. We use both experimental in vitro measurements as well as 3D numerical simulations to complement the respective other one. Numerically, we have easy control over the initial starting configuration and natural access to the full 3D shape. With this information we obtain the phase diagram as a function of initial position, starting shape and cell velocity. Experimentally, we measure the occurrence frequency of the different shapes as a function of the cell velocity to construct the experimental diagram which is in good agreement with the numerical observations. Two different major shapes are found, namely croissants and slippers. Notably, both shapes show coexistence at low ( 3 mm s-1) while in-between only croissants are stable. This pronounced bistability indicates that RBC shapes are not only determined by system parameters such as flow velocity or channel size, but also strongly depend on the initial conditions.

https://orbilu.uni.lu/bitstream/10993/37368/1/numerical%20-%20experimental%20observation%20of%20shpa%20bistability%20of%20red%20blood%20cells%20flowng%20in%20a%20microchannel.pdf

Numerical-experimental observation of shape bistability of red blood cells flowing in a microchannel.

Efficacy of injectable rib height on the heat transfer and entropy generation in the microchannel by affecting slip flow

Vessel bifurcation is a place where many diseases start, such as the atherosclerosis, because the flow in this place is complex involving secondary flow and/or stagnation regions, and the cells are often blocked to aggregate together. A numerical study has been conducted to analyze three-dimensional motion, deformation, and aggregation of multiple red blood cells (RBCs) in a microvessel bifurcation. A smoothed dissipative particle dynamics model is used to simulate the fluids inside and outside of the RBCs. The RBC membrane is modeled as a triangular network, associated with a deformation potential energy and an aggregation potential energy to describe the RBC deformation and aggregation, respectively. The interaction between the fluid and the RBCs is modeled by the immersed boundary method. The numerical models are first validated by examining the rheology of multiple RBCs in a cylindrical tube. Then, we investigate the effect of number of RBCs, mechanical properties, and interaction strength on their motion, deformation, and aggregation. The simulation results showed that the leading RBC has more deformation, compared with subsequent RBCs. The larger the RBC number, the easier the RBCs aggregate. The RBC deformation has an obvious effect on the RBC aggregation, whereas the RBC aggregation has a slight effect on the RBC deformation. Both the RBC deformation and aggregation can cause the RBC centroid to deviate at the apex of bifurcation, and this determines which branch the RBCs move into.

Motion, deformation, and aggregation of multiple red blood cells in three-dimensional microvessel bifurcations

An overview of the smoothed dissipative particle dynamics (SDPD) method is presented in a format that tries to quickly answer questions that often arise among users and newcomers. It is hoped that the status of SDPD is clarified as a mesoscopic particle model and its potentials and limitations are highlighted, as compared with other methods.

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Everything you always wanted to know about SDPD ⋆ ( ⋆ but were afraid to ask)

In biofluid flow systems, often the flow problems of fluids of complex structures, such as the flow of red blood cells (RBCs) through complex capillary vessels, need to be considered. The smoothed dissipative particle dynamics (SDPD), a particle-based method, is one of the easy and flexible methods to model such complex structure fluids. It couples the best features of the smoothed particle hydrodynamics (SPH) and dissipative particle dynamics (DPD), with parameters having specific physical meaning (coming from SPH discretization of the Navier-Stokes equations), combined with thermal fluctuations in a mesoscale simulation, in a similar manner to the DPD. On the other hand, the immersed boundary method (IBM), a preferred method for handling fluid-structure interaction problems, has also been widely used to handle the fluid-RBC interaction in RBC simulations. In this paper, we aim to couple SDPD and IBM together to carry out the simulations of RBCs in complex flow problems. First, we develop the SDPD-IBM model in details, including the SDPD model for the evolving fluid flow, the RBC model for calculating RBC deformation force, the IBM for treating fluid-RBC interaction, and the solid boundary treatment model as well. We then conduct the verification and validation of the combined SDPD-IBM method. Finally, we demonstrate the capability of the SDPD-IBM method by simulating the flows of RBCs in rectangular, cylinder, curved, bifurcated, and constricted tubes, respectively.

Hybrid smoothed dissipative particle dynamics and immersed boundary method for simulation of red blood cells in flows.

The changes in the mechanical properties of a cell are not only the cause of some diseases, but can also be a biomarker for some disease states. In recent times, microfluidic devices with built-in constrictions have been widely used to measure these changes. The transit time in such devices, defined as the time that a cell takes to pass through a constriction, has been found to be a crucial factor associated with the cell mechanical properties. Here, we use smoothed dissipative particle dynamics (SDPD), a particle-based numerical method, to explore the relationship between the transit time and mechanical properties of a cell. Three expressions of the transit time are developed from our simulation data, with respect to the stenosed size of constrictions, the shear modulus and bending modulus of cells, respectively. We show that a convergent constriction (the inlet is wider than the outlet), and a sharp-corner constriction (the constriction outlet is narrow) are better in identifying the differences in the transit time of cells. Moreover, the transit time increases and gradually approaches a constant as the shear modulus of cells increases, but increases first and then decreases as the bending modulus increases. These results suggest that the mechanical properties of cells can indeed be measured by analyzing their transit time, based on the recommended microfluidic device.

Relationship between transit time and mechanical properties of a cell through a stenosed microchannel.

The study of red blood cells (RBCs) flowing through rectangular microchannels has attracted an increasing interest, because most of the current microfluidic chips are designed as rectangular microchannels for the purpose of easy fabrication. In this paper, we numerically investigate the 3D motion and deformation of a RBC in rectangular microchannels, by using the smoothed dissipative particle dynamics to model the fluid flow and coupling the immersed boundary method to treat the fluid-RBC interaction. We have considered several fundamental questions concerned in experiments, including the effect of the mechanical properties of RBC, the initial position and orientation of RBC, as well as the asymmetry of the microchannel. In addition, we have demonstrated the differences among the fully 3D, axisymmetric, and 2D simulations of a RBC in microchannels.

Numerical studies of a red blood cell in rectangular microchannels

Thrombus formation is a complex, dynamic and multistep process, involving biochemical reactions, mechanical stimulation, hemodynamics, and so on. In this study, we concentrate on its two crucial steps: (i) platelets adhered to a vessel wall, or simply platelet adhesion, and (ii) platelets clumping and arrested to the adherent platelets, named platelet aggregation. We report the first direct simulation of three modes of platelet adhesion, detachment, rolling adhesion and firm adhesion, as well as the formation, disintegration, arrestment and consolidation of platelet plugs. The results show that the bond dissociation in the detachment mode is mainly attributed to a high probability of rupturing bonds, such that any existing bond can be quickly ruptured and all bonds would be completely broken. In the rolling adhesion, however, it is mainly attributed to the strong traction from the shear flow or erythrocytes, causing that the bonds are ruptured at the trailing edge of the platelet. The erythrocytes play an important role in platelet activities, such as the formation, disintegration, arrestment and consolidation of platelet plugs. They exert an aggregate force on platelets, a repulsion at a near distance but an attraction at a far distance to the platelets. This aggregate force can promote platelets to form a plug and/or bring along a part of a platelet plug causing its disintegration. It also greatly influences the arrestment and consolidation of platelet plugs, together with the adhesive force from the thrombus.

Huixin Shi

Papers

Hybrid smoothed dissipative particle dynamics and immersed boundary method for simulation of red blood cells in flows.

Relationship between transit time and mechanical properties of a cell through a stenosed microchannel.

Numerical studies of a red blood cell in rectangular microchannels

The key events of thrombus formation: platelet adhesion and aggregation

Numerical design of a microfluidic chip for probing mechanical properties of cells.