Capsules In Shear Flow Research Articles

Fully Eulerian models for the numerical simulation of capsules with an elastic bulk nucleus

In this paper, we present a computational framework based on fully Eulerian models for fluid–structure interaction for the numerical simulation of biological capsules. The flexibility of such models, given by the Eulerian treatment of the interface and deformations, allows us to easily deal with the large deformations experienced by the capsule. The modeling of the membrane is based on a full membrane elasticity Eulerian model that is capable of capturing both area and shear variations thanks to the so-called backward characteristics. In the validation section several test cases are presented with the goal of comparing our results to others present in the literature. In this part, the comparisons are done with different well-known configurations (capsule in shear flow and square-section channel), and by deepening the effect of the elastic constitutive law and capillary number on the membrane dynamics. Finally, to show the potential of this framework we introduce a new test case that describes the relaxation of a capsule in an opening channel. In order to increase the challenges of this test we study the influence of an internal nucleus, modeled as a hyperelastic solid, on the membrane evolution. Several numerical simulations of a 3D relaxation phenomenon are presented to provide characteristic shapes and curves related to the capsule deformations, while also modifying size and stiffness parameter of the nucleus.

Isogeometric boundary element analysis of creasing of capsule in simple shear flow

Wrinkling and creasing of an elastic membrane are post-buckling processes induced by in-plane compression. When a hyperelastic capsule is suspended in a simple shear flow, its membrane forms several wavy patterns. To elucidate the post-buckling behavior of a capsule in a Stokes shear flow, we investigated the effects of the shear rate and membrane thickness on capsule deformation by performing numerical analysis to capture the wrinkling and creasing of the capsule membrane. The deformation of the capsule was formulated based on the Kirchhoff–Love shell theory and the Stokes flow was calculated using the boundary integral equation. The capsule shape was represented by a T-spline surface. The isogeometric boundary element analysis showed that the capsule in the shear flow formed wrinkles and creases. Whereas wrinkling occurred at low shear rates, both wrinkling and creasing occurred at high shear rates depending on the membrane thickness. Based on the geometrical consistency of the capsule surface, we suggest that the deformation type can be determined by mechanical and geometrical effects of the membrane thickness, that is, the bending rigidity and ease of self-contact, respectively. This approach will be useful for investigating the geometrical consistency for further understanding the post-buckling behavior of capsules in Stokes flows.

Oxygen transport across tank-treading red blood cell: Individual and joint roles of flow convection and oxygen-hemoglobin reaction.

Gas, especially oxygen, transport in the microcirculation is a complex phenomenon, however, of critical importance for maintaining normal biological functions, and the cytoplasm fluid in red blood cells (RBCs) is the major vehicle for transporting oxygen from lungs to tissues via the circulatory system. Existing theoretical and numerical studies have neglected the cytoplasm convection effect by treating RBCs as rigid particles undergoing a constant translation velocity. As a consequence, the influence and mechanism of the cytoplasm flow on oxygen transport are still not clear in microcirculation research. In this study, we consider a tank-treading capsule in shear flow, which is generated with two parallel plates moving in opposite directions: the top plate of a higher oxygen pressure (PO2) representing the RBC core in the central region of a microvessel and the bottom plate of a lower PO2 representing the microvessel wall. Numerical simulations are conducted to investigate the individual and combined effects of cytoplasm convection and oxygen-hemoglobin (O2-Hb) reaction on the oxygen transport efficiency across the tank-treading capsule, and different PO2 situations and shear rates are also tested. Due to the lower oxygen diffusivity in cytoplasm, the presence of the capsule reduces the oxygen transfer flux across the gap by 7.34% in the pure diffusion system where the flow convection and O2-Hb reaction are both neglected. Including the flow convection or the O2-Hb reaction has little influence on the oxygen flux; however, when they act together as in real microcirculation situations, the enhancement in oxygen transport could be significant, especially in the low PO2 and high shear rate situations. In particular, with the respective PO2 at 60 and 30mmHg on the top and bottom plates and a 400 s-1 shear rate, the oxygen flux reduction is only 0.02%, suggesting that the cytoplasm convection can improve the oxygen transport across RBCs considerably. The simulation results are scrutinized to explore the underlying mechanism for the enhancement, and a new nondimensional parameter is introduced to characterize the importance of cytoplasm convection in oxygen transport. These simulation results, discussion and analysis could be helpful for a better understanding of the complex oxygen transport process and therefor valuable for relevant studies.

Dynamic modes of a capsule under oscillating shear flow with finite inertia

Inertia may significantly influence the transient deformation process and the steady-state structure of a deformable capsule. The behavior of a two-dimensional deformable capsule in shear flow at finite Reynolds numbers (Re) is studied numerically. By simulating numerous cases with different Re and frequencies (f), we observed persistent oscillation, asymmetric oscillation, deflected oscillation, and stable modes. The phase diagram in the Re–f plane is presented. At low frequencies, a capsule shows a phase-lag phenomenon between the deformation and the applied shear. At moderate frequencies, the anomaly of decreasing maximum deformation with increasing Re is observed. The anomaly is attributed to the mode shift. In addition, a scaling law of the maximum deformation of the capsule as a function of Re and f is proposed. This study may shed some light on the identification and screening of cells in vitro as well as the transport and breakup of cells in vivo.

Lateral migration of viscoelastic capsules in tube flow

In this article, the lateral migration process of a viscoelastic capsule of spherical original shape in a tube flow is simulated. The capsule membrane follows the Skalak constitutive law for elasticity, and the membrane viscosity is modeled using the recently developed finite difference scheme. The methodology is validated carefully by simulating the tank-treading motion of an elastic capsule in shear flow. The lateral migration of viscoelastic capsules is then investigated in detail with various combinations of viscosity ratio, membrane shear viscosity, and capillary number. In general, the migration process starts with an initial transient phase, where the capsule deformation and migration velocity suddenly increase from zero to a maximum value. Following that, the deformation and migration velocity gradually reduce as the capsule moves toward the tube centerline. The capsule also performs continuous rotation during the migration, and the rotation gradually slows down with the capsule migration. The interior-exterior fluid viscosity contrast and the membrane viscosity have similar effects in reducing the capsule deformation and inclination angle to the flow direction; however, a strong membrane viscosity may introduce significant oscillations in the capsule deformation, inclination, and migration velocity. Due to the reduced capsule deformation, the migration velocity and capsule rotation become slower for capsules with higher viscosity contrast and/or membrane viscosity. Moreover, the influence of membrane viscosity on the migration dynamics intensifies at higher capillary number. Finally, empirical correlations are proposed for the migration velocity and rotation period, and the proposed relations match fairly well the simulation results, which cover wide ranges of system parameters. The discussions and analysis could be valuable for better understanding the complicated flow–capsule interaction and capsule dynamics in the migration process.

Unsynchronized motion of inner and outer membranes of compound capsules in shear flow

Despite its significance in understanding behaviors of biological cells with nucleus or designing functions of complex artificial capsules in applications, the dynamics of elastic capsules enclosing complicated internal structures in flow is still largely unexplored. In this study, by using our own three-dimensional front-tracking finite-difference model, we present a numerical investigation into the dynamics of a compound capsule in a simple shear flow whose inner and outer membranes have the same prolate ellipsoidal shape at the rest state. Particular interest is focused on the unsynchronized motion of the inner and outer membranes. Regarding the dynamical regime, both the inner and outer capsules can undergo either synchronized or unsynchronized dynamical regimes (i.e., swinging or tumbling), which strongly depends on the inner-to-outer capillary number ratio Cain/Caout, the inner-to-outer volume ratio ϕ, and the prolate aspect ratio a/b. Particularly, via establishing a phase diagram based on a/b and ϕ at Cain/Caout = 1, we find that the inner and outer membranes can exist simultaneously in different dynamical regimes, even if they have the same deformability and the same shape. More importantly, if the detailed oscillation behavior is also concerned besides the capsule’s dynamical regime, such as the transient shape and the oscillating period, unsynchronization is always obvious between the inner and outer capsules. Specifically, the inner capsule exhibits a slower oscillation than the outer capsule no matter if they lie in the swinging or tumbling regime.

Finite-difference and integral schemes for Maxwell viscous stress calculation in immersed boundary simulations of viscoelastic membranes.

The immersed boundary method (IBM) has been frequently utilized to simulate the motion and deformation of biological cells and capsules in various flow situations. Despite the convenience in dealing with flow-membrane interaction, direct implementation of membrane viscosity in IBM suffers severe numerical instability. It has been shown that adding an artificial elastic element in series to the viscous component in the membrane mechanics can efficiently improve the numerical stability in IBM membrane simulations. Recently Li and Zhang (Int J Numer Methods Biomed Eng 35:e3200, 2019) proposed a finite-difference method for calculating membrane viscous stress. In the present paper, two new schemes are developed based on the convolution integral expression of the Maxwell viscoelastic element. We then conduct several tests for the accuracy, stability, and efficiency performances of these three viscous stress schemes. By studying the behavior of a one-dimensional Maxwell element under sinusoidal deformation, we find that a good accuracy can be achieved by selecting an appropriate relaxation time. The twisting sphere tests confirm that, compared to the numerical errors induced by other components in capsule simulations, such as the finite element method for membrane discretization and IBM for flow-membrane interaction, the errors from the viscous stress calculation are negligible. Moreover, extensive simulations are conducted for the dynamic deformation of a spherical capsule in shear flow, using different numerical schemes and various combinations of the artificial spring constants and calculation frequency for the membrane viscous stress calculation. No difference is observed among the results from the three schemes; and these viscous stress schemes require very little extra computation time compared to other components in IBM simulations. The simulation results converge gradually with the increase in the artificial spring stiffness; however, a threshold value exists for the spring stiffness to maintain the numerical stability. The viscous stress calculation frequency has noapparent influence on the calculation results, but a large frequency number can cause the simulation to collapse. We therefore suggest to calculate the membrane viscous stress at each simulation time step, such that a better numerical stabilitycan be achieved. The three numerical schemes have nearly identical performances in all aspects, and they can all be utilized in future IBM simulations of viscoelastic membranes.

Multiplicity of stable orbits for deformable prolate capsules in shear flow.

This work investigates the orbital dynamics of a fluid-filled deformable prolate capsule in unbounded simple shear flow at zero Reynolds number using direct simulations. The motion of the capsule is simulated using a model that incorporates shear elasticity, area dilatation, and bending resistance. Here the deformability of the capsule is characterized by the nondimensional capillary number Ca, which represents the ratio of viscous stresses to elastic restoring stresses on the capsule. For a capsule with small bending stiffness, at a given Ca, the orientation converges over time towards a unique stable orbit independent of the initial orientation. With increasing Ca, four dynamical modes are found for the stable orbit, namely, rolling, wobbling, oscillating-swinging, and swinging. On the other hand, for a capsule with large bending stiffness, multiplicity in the orbit dynamics is observed. When the viscosity ratio λ ≲ 1, the long-axis of the capsule always tends towards a stable orbit in the flow-gradient plane, either tumbling or swinging, depending on Ca. When λ ≳ 1, the stable orbit of the capsule is a tumbling motion at low Ca, irrespective of the initial orientation. Upon increasing Ca, there is a symmetry-breaking bifurcation away from the tumbling orbit, and the capsule is observed to adopt multiple stable orbital modes including nonsymmetric precessing and rolling, depending on the initial orientation. As Ca further increases, the nonsymmetric stable orbit loses existence at a saddle-node bifurcation, and rolling becomes the only attractor at high Ca, whereas the rolling state coexists with the nonsymmetric state at intermediate values of Ca. A symmetry-breaking bifurcation away from the rolling orbit is also found upon decreasing Ca. The regime with multiple attractors becomes broader as the aspect ratio of the capsule increases, while narrowing as viscosity ratio increases. We also report the particle contribution to the stress, which also displays multiplicity.

State diagram for wall adhesion of red blood cells in shear flow: from crawling to flipping.

Red blood cells in shear flow show a variety of different shapes due to the complex interplay between hydrodynamics and membrane elasticity. Malaria-infected red blood cells become generally adhesive and less deformable. Adhesion to a substrate leads to a reduction in shape variability and to a flipping motion of the non-spherical shapes during the mid-stage of infection. Here, we present a complete state diagram for wall adhesion of red blood cells in shear flow obtained by simulations, using a particle-based mesoscale hydrodynamics approach, multiparticle collision dynamics. We find that cell flipping at a substrate is replaced by crawling beyond a critical shear rate, which increases with both membrane stiffness and viscosity contrast between the cytosol and suspending medium. This change in cell dynamics resembles the transition between tumbling and tank-treading for red blood cells in free shear flow. In the context of malaria infections, the flipping-crawling transition would strongly increase the adhesive interactions with the vascular endothelium, but might be suppressed by the combined effect of increased elasticity and viscosity contrast.

Kinematic and dynamic forcing strategies for predicting the transport of inertial capsules via a combined lattice Boltzmann – Immersed Boundary method

Modeling the transport of deformable capsules under different flow regimens is crucial in a variety of fields, including oil rheology, blood flow and the dispersion of pollutants. The aim of this study is twofold. Firstly, a combined Lattice Boltzmann – Immersed Boundary (LBM – IB) approach is developed for predicting the transport of inertial deformable capsules. A Moving Least Squares (MLS) scheme has been implemented to correlate the pressure, velocity and force fields of the fluid domain with the capsule dynamics. This computational strategy has been named LBM – Dynamic IB. Secondly, this strategy is directly compared with a more conventional approach, named LBM – Kinematic IB, where capsules move with the same velocity of the surrounding fluid. Multiple test cases have been considered for assessing the accuracy and efficiency of the Dynamic over Kinematic IB scheme, including the stretching of circular capsules in shear flow, the transport in a plane Poiseuille flow of circular and biconcave capsules, with and without inertia. By monitoring the capsule geometry over time, the two schemes have been documented to be in excellent agreement, especially for low Capillary numbers (Ca ≤ 10−2), in the case of non-inertial capsules. Despite a moderate increase in computational burden, the presented LBM – Dynamic IB scheme is the sole capable of predicting the dynamics of both non-inertial and inertial deformable capsules. The proposed approach can be efficiently employed for studying the transport of blood cells, cancer cells and nano/micro capsules within a capillary flow.

Effects of membrane deformability and bond formation/dissociation rates on adhesion dynamics of a spherical capsule in shear flow.

Cellular adhesion plays a critical role in biological systems and biomedical applications. Cell deformation and biophysical properties of adhesion molecules are of significance for the adhesion behavior. In the present work, dynamic adhesion of a deformable capsule to a planar substrate, in a linear shear flow, is numerically simulated to investigate the combined influence of membrane deformability (quantified by the capillary number) and bond formation/dissociation rates on the adhesion behavior. The computational model is based on the immersed boundary-lattice Boltzmann method for the capsule-fluid interaction and a probabilistic adhesion model for the capsule-substrate interaction. Three distinct adhesion states, detachment, rolling adhesion and firm adhesion, are identified and presented in a state diagram as a function of capillary number and bond dissociation rate. The impact of bond formation rate on the state diagram is further investigated. Results show that the critical bond dissociation rate for the transition of rolling or firm adhesion to detachment is strongly related to the capsule deformability. At the rolling-adhesion state, smaller off rates are needed for larger capillary number to increase the rolling velocity and detach the capsule. In contrast, the critical off rate for firm-to-detach transition slightly increases with the capillary number. With smaller on rate, the effect of capsule deformability on the critical off rates is more pronounced and capsules with moderate deformability are prone to detach by the shear flow. Further increasing of on rate leads to large expansion of both rolling-adhesion and firm-adhesion regions. Even capsules with relatively large deformability can maintain stable rolling adhesion at certain off rate.

A Moving-Least-Square Immersed Boundary Method for Rigid and Deformable Boundaries in Viscous Flow

AbstractWe present a moving-least-square immersed boundary method for solving viscous incompressible flow involving deformable and rigid boundaries on a uniform Cartesian grid. For rigid boundaries, noslip conditions at the rigid interfaces are enforced using the immersed-boundary direct-forcing method. We propose a reconstruction approach that utilizes moving least squares (MLS) method to reconstruct the velocity at the forcing points in the vicinity of the rigid boundaries. For deformable boundaries, MLS method is employed to construct the interpolation and distribution operators for the immersed boundary points in the vicinity of the rigid boundaries instead of using discrete delta functions. The MLS approach allows us to avoid distributing the Lagrangian forces into the solid domains as well as to avoid using the velocity of points inside the solid domains to compute the velocity of the deformable boundaries. The present numerical technique has been validated by several examples including a Poiseuille flow in a tube, deformations of elastic capsules in shear flow and dynamics of red-blood cell in microfluidic devices.

Investigating the effects of membrane deformability on artificial capsule adhesion to the functionalized surface

Understanding, manipulating and controlling cellular adhesion processes can be critical in developing biomedical technologies. Adhesive mechanisms can be used to the target, pattern and separate cells such as leukocytes from whole blood for biomedical applications. The deformability response of the cell directly affects the rolling and adhesion behavior under viscous linear shear flow conditions. To that end, the primary objective of the present study was to investigate numerically the influence of capsule membrane's nonlinear material behavior (i.e. elastic-plastic to strain hardening) on the rolling and adhesion behavior of representative artificial capsules. Specifically, spherical capsules with radius of [Formula: see text] were represented using an elastic membrane governed by a Mooney-Rivlin strain energy functions. The surfaces of the capsules were coated with P-selectin glycoprotein-ligand-1 to initiate binding interaction with P-selectin-coated planar surface with density of [Formula: see text] under linear shear flow varying from 100 to [Formula: see text]. The numerical model is based on the Immersed Boundary Method for rolling of deformable capsule in shear flow coupled with Monte Carlo simulation for receptor/ligand interaction modeled using Bell model. The results reveal that the mechanical properties of the capsule play an important role in the rolling behavior and the binding kinetics between the capsule contact surface and the substrate. The rolling behavior of the strain hardening capsules is relatively smoother and slower compared to the elastic-plastic capsules. The strain hardening capsules exhibits higher contact area at any given shear rate compared to elastic-plastic capsules. The increase in contact area leads to decrease in rolling velocity. The capsule contact surface is not in complete contact with the substrate because of thin lubrication film that is trapped between the capsule and substrate. This creates a concave shape on the bottom surface of the capsule that is referred to as a dimple. In addition, the present study demonstrates that the average total bond force from the capsules lifetime increases by 37% for the strain hardening capsules compared to elastic-plastic capsules at shear rate of [Formula: see text]. Finally, the model demonstrates the effect of finite membrane deformation on the coupling between hydrodynamic and receptor/ligand interaction.

Numerical Simulation of the Motion of Inextensible Capsules in Shear Flow Under the Effect of the Natural State

AbstractIn this paper, a computational model for the natural state of an inextensible capsule has been successfully combined with a spring model of the capsule membrane to simulate the motion of the capsule in two-dimensional shear flow. Besides the viscosity ratio of the internal fluid and external fluid of the capsule, the natural state also plays a role for having the transition between two well known motions, tumbling and tank-treading (TT) with the long axis oscillates about a fixed inclination angle (a swinging mode), when varying the shear rate. Between tumbling and tank-treading, the intermittent behavior has been obtained for the capsule with a biconcave rest shape. The estimated critical value of the swelling ratio for having the intermittent transition behavior is less than 0.7, i.e., the capsules with rest shape closer to a full disk do not have the intermittent behavior in shear flow. The intermittent dynamics of the capsule in the transition region is a mixture of tumbling and TT with a swinging mode. Just like the motion of TT with a swing mode, which can be viewed as a tank-treading with an incomplete tumbling, the membrane tank-treads backward and forward within a small range during the tumbling motion.

Influence of bending resistance on the dynamics of a spherical capsule in shear flow

The objective of the paper is to study the effect of wall bending resistance on the motion of an initially spherical capsule freely suspended in shear flow. We consider a capsule with a given thickness made of a three-dimensional homogeneous elastic material. A numerical method is used to model the fluid-structure interactions coupling a boundary integral method for the fluids with a shell finite element method for the capsule envelope. For a given wall material, the capsule deformability strongly decreases when the wall bending resistance increases. But, if one expresses the same results as a function of the two-dimensional mechanical properties of the mid-surface, which is how the capsule wall is modeled in the thin-shell model, the capsule deformed shape is identical to the one predicted for a capsule devoid of bending resistance. The bending rigidity is found to have a negligible influence on the overall deformation of an initially spherical capsule, which therefore depends only on the elastic stretching of the mid-surface. Still, the bending resistance of the wall must be accounted for to model the buckling phenomenon, which is observed locally at low flow strength. We show that the wrinkle wavelength is only a function of the wall bending resistance and provide the correlation law. Such results can then be used to infer values of the bending modulus and wall thickness from experiments on spherical capsules in simple shear flow.

Response and Recovery Times of Elastic and Viscoelastic Capsules in Shear Flow

AbstractAmid the recent interest in the role of membrane viscosity in the deformation of a fluid-filled capsule, we consider the role of various capsule properties (shear elasticity, membrane bending stiffness and viscosity) in determining the response and recovery times of a spherical capsule in shear flow. These times are determined by fitting exponential functions to results for the Taylor deformation parameter Dxy. We focus on the relationship between the membrane and fluid viscosity ratios, as suggested by Diaz et al, and whether adjustments to the fluid viscosity ratio may be used to approximate the effects of membrane viscosity. Based on its ability to reproduce response and recovery times, our results suggest that such an approach holds promise.

Numerical study on dynamic sorting of a compliant capsule with a thin shell

Sorting compliant capsules is an interesting research topic. In this paper, a simple bifurcated micro-channel is used to sort the particles with different rigidities. The behavior of a compliant particle inside the channel is investigated numerically. The fluid flow and the particle’s deformation are solved by Lattice Boltzmann Method (LBM) and Lattice Spring Model (LSM), respectively. The fluid and solid solvers are coupled through interpolated bounce-back scheme. Two benchmark problems are used to validate our method. One is the motion of a compliant capsule in a channel and the other is the deformation of a capsule inside a simple shear flow. The results are quantitatively consistent with those in literature. By taking advantage of the rotating of capsules in shear flow, a simple distinguished bifurcated micro-channel is proposed to sort capsules with different rigidities. In this micro-channel, the initial offset and shear stress induce the rotating and lateral migration of the capsule and flux ratio is determined by the outlet pressures. The competition between the effect of initial offset and flux ratio contributes to the sorting mechanism. Compared to other micro-channels with different geometrical models, present one is more convenient and may be more efficient to screen the microcapsule we want.

The dynamics of inextensible capsules in shear flow under the effect of the natural state

The effect of the natural state on the motion of an inextensible capsule in two-dimensional shear flow has been studied numerically. The energy barrier based on such natural state plays a role for having the transition between two well-known motions, tumbling and tank-treading (TT) with the long axis oscillating about a fixed inclination angle (a swinging mode), when varying the shear rate. Between tumbling and TT with a swinging mode, the intermittent region has been obtained for the capsule with a biconcave rest shape. The estimated critical value of the swelling ratio for having the intermittent region is <0.7, i.e., the capsule with the rest shape closer to a full disk has no intermittent behavior. The capsule intermittent behavior is a mixture of tumbling and TT. Just like the TT with a swinging mode, which can be viewed as TT with an incomplete tumbling, the membrane tank-treads backward and forward within a small range while tumbling. As the capillary number is very close to and below the threshold for pure TT with a swinging mode, the capsule tumbles once after several TT periods in each cycle. The number of TT periods in one cycle decreases when decreasing the capillary number, until the capsule has one tumble and one TT period alternatively and such alternating motion exists over a range of the capillary number; and then the capsule performs more tumbling between two consecutive TT periods when reducing the capillary number further, and finally has tumbling only.

Hydrodynamic Interaction of Elastic Capsules in Bounded Shear Flow

AbstractThis paper presents a modified Loop’s subdivision algorithm for studying the deformation of a single capsule, the hydrodynamic interaction between two capsules and the hydrodynamic diffusion of a suspension of capsules in bounded shear flow. A subdivision thin-shell model is employed to compute the forces generated on the surface of the elastic capsule during deformation. The capsule surface is approximated using the modified Loop’s subdivision scheme which guarantees bounded curvature and C1 continuity everywhere on the limit surface. The present numerical technique has been validated by studying the deformation of a spherical capsule in shear flow. Computations are also performed for a biconcave capsule over a wide range of shear rates and viscosity ratios to investigate its dynamics. In addition, the hydrodynamic interaction between two elastic capsules in bounded shear flow is studied. Depending on the wall separation distance, the trajectory-bifurcation points that separate reversing and crossing motions for both spherical and biconcave capsules can be found. Compared to the spherical capsules, the biconcave capsules exhibit additional types of interaction such as rotation and head-on collision. The head-on collision results in a large trajectory shift which contribute to the hydrodynamic diffusion of a suspension. A suspension of a large number of biconcave capsules in shear flow is also simulated to show the ability of the modified scheme in running a large-scale simulation over a long period of time.

APPLICATION OF DISSIPATIVE PARTICLE DYNAMICS TO THE STUDY OF A RED BLOOD CELL IN SIMPLE SHEAR FLOW

The present work reports an attempt to apply the dissipative particle dynamics (DPD) method to study the dynamic behaviors of a red blood cell (RBC) in simple shear flow. The simulation system is discretized into four types of particles, namely wall particles, fluid particles, membrane particles and internal particles. The particle interaction is modeled by the DPD method, and the membrane particles are connected into a viscoelastic triangular network to represent the RBC membrane. As benchmarking tests, we simulate the deformation of a spherical capsule in shear flow and compare it with the past study, and also examine the effect of computational domain size. After that, we investigate the dynamics of a RBC in shear flow at different membrane shear and bending moduli. Our simulations reproduce the tank-treading, trembling and tumbling motions of the RBC at the shear modulus Es = 6, 60 and 600 μN/m, respectively. Moreover, we find that the RBC undergoes a trembling motion when its bending modulus is large enough, where the obvious stretching and smoothing of the RBC occur alternately in shape.