Reorientation of a nonspherical capsule in creeping shear flow

Shear annealing of a self-interacting sheet

2D materials such as graphene, graphene oxide, transition metal dichalcogenides, and 2D polymers have unique properties which allow them to be used in many applications from electronics to energy to biotechnology. Producing and applying these materials often involves solution processing. Previous computational studies have observed 2D sheets in shear and extensional flows, but have focused on steady flows, even though the dynamics of these materials might exhibit hysteresis. In this work, we study 2D sheets with short-ranged attractive interactions under time-varying shear. We show that, even with relatively simple protocols, the properties of sheet suspensions can be tuned.

Dynamics of a self-interacting sheet in shear flow

Solution processing of 2D materials such as graphene is important for applications thereof, yet a complete fundamental understanding of how 2D materials behave dynamically in solution is lacking. Here, we extend previous work by Silmore et al., Soft Matter, 2021, 17(18), 4707-4718 by adding short-ranged Lennard-Jones interactions to 2D sheets in shear flow. We find that the addition of these interactions allows for a rich landscape of conformations which depend on the balance between shear strength, bending rigidity, and interaction strength as well as the initial configuration of the sheet. We explore this conformational space and classify sheets as flat, tumbling, 1D folded, or 2D folded based on their conformational properties. We use kinetic and energetic arguments to explain why sheets adopt certain conformations within the folded regime. Finally, we calculate the stresslet and find that, even in the absence of thermal fluctuations and multiple sheet interactions, shear-thinning followed by shear-thickening behavior can appear.

The shape effect of flagella is more important than bottom-heaviness on passive gravitactic orientation in Chlamydomonas reinhardtii

The way the unicellular, biflagellated, green alga Chlamydomonas orients upward has long been discussed in terms of both mechanics and physiology. In this study, we focus on the mechanics, i.e. the 'passive' mechanisms, of gravitaxis. To rotate the body upwards, cellular asymmetry is critical. Chlamydomonas can be depicted as a nearly spherical cell body with two anterior, symmetric flagella. The present study looks at the question of whether the existence of the flagella significantly affects torque generation in upward reorientation. The 'density asymmetry model' assumes that the cell is spherical and bottom-heavy and that the shape and weight of the flagella are negligible, while the 'shape asymmetry model' considers the shape of the flagella. Both our experimental and simulation results revealed a considerable contribution from shape asymmetry to the upward orientation of Chlamydomonas reinhardtii, which was several times larger than that of density asymmetry. From the experimental results, we also quantified the extent of bottom-heaviness, i.e. the distance between the centers of gravity and the figure when the cell body is assumed to be spherical. Our estimation was approximately 30 nm, only one-third of previous assumptions. These findings indicate the importance of the viscous drag of the flagella to the upward orientation, and thus negative gravitaxis, in Chlamydomonas.

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.

Passive swimming of a microcapsule in vertical fluid oscillation

The artificial microswimmer is a cutting-edge technology with applications in drug delivery and micro-total-analysis systems. The flow field around a microswimmer can be regarded as Stokes flow, in which reciprocal body deformation cannot induce migration. In this study, we propose a microcapsule swimmer that undergoes amoeboidlike shape deformations under fluid oscillation conditions. This is a study on the propulsion principle using a capsule with a solid membrane, and one of only a few studies using fluid oscillation. The microswimmer consists of an elastic capsule containing fluid and a rigid sphere. Opposing forces are generated when fluid oscillations are applied, because the densities of the internal fluid and sphere are different. The opposing forces induce nonreciprocal body deformation, which leads to migration of the microswimmer under Stokes flow conditions. Using numerical simulations, we found that the microswimmer propels itself in one of two modes, i.e., stroke swimming or drag swimming. We discuss the feasibility of the proposed microswimmer and show that the most efficient swimmer can migrate tens of micrometers per second. These findings pave the way for future artificial microswimmer designs.

Flow-Induced Transitions of Red Blood Cell Shapes under Shear

A recent study of red blood cells (RBCs) in shear flow [Lanotte et al., Proc. Natl. Acad. Sci. U.S.A. 113, 13289 (2016)PNASA60027-842410.1073/pnas.1608074113] has demonstrated that RBCs first tumble, then roll, transit to a rolling and tumbling stomatocyte, and finally attain polylobed shapes with increasing shear rate, when the viscosity contrast between cytosol and blood plasma is large enough. Using two different simulation techniques, we construct a state diagram of RBC shapes and dynamics in shear flow as a function of shear rate and viscosity contrast, which is also supported by microfluidic experiments. Furthermore, we illustrate the importance of RBC shear elasticity for its dynamics in flow and show that two different kinds of membrane buckling trigger the transition between subsequent RBC states.

Bifurcation Dynamics of a Particle-Encapsulating Droplet in Shear Flow

To understand the behavior of composite fluid particles such as nucleated cells and double emulsions in flow, we study a finite-size particle encapsulated in a deforming droplet under shear flow as a model system. In addition to its concentric particle-droplet configuration, we numerically explore other eccentric and time-periodic equilibrium solutions, which emerge spontaneously via supercritical pitchfork and Hopf bifurcations. We present the loci of these solutions around the codimension-two point. We adopt a dynamic system approach to model and characterize the coupled behavior of the two bifurcations. By exploring the flow fields and hydrodynamic forces in detail, we identify the role of hydrodynamic particle-droplet interaction which gives rise to these bifurcations.

Flow structures and red blood cell dynamics in arteriole of dilated or constricted cross section

Vessel with 'circular' or 'star-shaped' cross sections are studied, representing respectively dilated or constricted cases where endothelial cells smoothly line or bulge into the lumen. Computational haemodynamics simulations are carried out on idealised periodic arteriole-sized vessels, with red blood cell 'tube' hematocrit value=24%. A further simulation of a single red blood cell serves for comparison purposes. The bulk motion of the red blood cells reproduces well-known effects, including the presence of a cell-free layer and the apparent shear-thinning non-Newtonian rheology. The velocity flow field is analysed in a Lagrangian reference frame, relative to any given red blood cell, hence removing the bulk coaxial motion and highlighting instead the complex secondary flow patterns. An aggregate formation becomes apparent, continuously rearranging and dynamic, brought about by the inter-cellular fluid mechanics interactions and the deformability properties of the cells. The secondary flow field induces a vacillating radial migration of the red blood cells. At different radial locations, the red blood cells express different residence times, orientation and shape. The shear stresses exerted by the flow on the vessel wall are influenced by the motion of red blood cells, despite the presence of the cell-free layer. Spatial (and temporal) variations of wall shear stress patters are observed, especially for the 'circular' vessel. The 'star-shaped' vessel bears considerable stress at the protruding endothelial cell crests, where the stress vectors are coaxially aligned. The bulging endothelial cells hence regularise the transmission of stresses on the vessel wall.

Dynamics of a single red blood cell in simple shear flow

This work describes simulations of a red blood cell (RBC) in simple shear flow, focusing on the dependence of the cell dynamics on the spontaneous curvature of the membrane. The results show that an oblate spheroidal spontaneous curvature maintains the dimple of the RBC during tank-treading dynamics as well as exhibits off-shear-plane tumbling consistent with the experimental observations of Dupire et al. [J. Dupire, M. Socol, and A. Viallat, Proc. Natl. Acad. Sci. USA 109, 20808 (2012)] and their hypothesis of an inhomogeneous spontaneous shape. As the flow strength (capillary number Ca) is increased at a particular viscosity ratio between inner and outer fluid, the dynamics undergo transitions in the following sequence: tumbling, kayaking or rolling, tilted tank-treading, oscillating-swinging, swinging, and tank-treading. The tilted tank-treading (or spinning frisbee) regime has been previously observed in experiments but not in simulations. Two distinct classes of regime are identified: a membrane reorientation regime, where the part of membrane that is at the dimple at rest moves to the rim and vice versa, is observed in motions at high Ca such as tilted tank-treading, oscillating-swinging, swinging, and tank-treading, and a nonreorientation regime, where the part of the membrane starting from the dimple stays at the dimple, is observed in motions at low Ca such as rolling, tumbling, kayaking, and flip-flopping.

Hemodynamics in the microcirculation and in microfluidics

Hemodynamics in microcirculation is important for hemorheology and several types of circulatory disease. Although hemodynamics research has a long history, the field continues to expand due to recent advancements in numerical and experimental techniques at the micro-and nano-scales. In this paper, we review recent computational and experimental studies of blood flow in microcirculation and microfluidics. We first focus on the computational studies of red blood cell (RBC) dynamics, from the single cellular level to mesoscopic multiple cellular flows, followed by a review of recent computational adhesion models for white blood cells, platelets, and malaria-infected RBCs, in which the cell adhesion to the vascular wall is essential for cellular function. Recent developments in optical microscopy have enabled the observation of flowing blood cells in microfluidics. Experimental particle image velocimetry and particle tracking velocimetry techniques are described in this article. Advancements in micro total analysis system technologies have facilitated flowing cell separation with microfluidic devices, which can be used for biomedical applications, such as a diagnostic tool for breast cancer or large intestinal tumors. In this paper, cell-separation techniques are reviewed for microfluidic devices, emphasizing recent advances and the potential of this fast-evolving research field in the near future.

Deformation and dynamics of red blood cells in flow through cylindrical microchannels

The motion of red blood cells (RBCs) in microcirculation plays an important role in blood flow resistance and in the cell partitioning within a microvascular network. Different shapes and dynamics of RBCs in microvessels have been previously observed experimentally including the parachute and slipper shapes. We employ mesoscale hydrodynamic simulations to predict the phase diagram of shapes and dynamics of RBCs in cylindrical microchannels, which serve as idealized microvessels, for a wide range of channel confinements and flow rates. A rich dynamical behavior is found, with snaking and tumbling discocytes, slippers performing a swinging motion, and stationary parachutes. We discuss the effects of different RBC states on the flow resistance, and the influence of RBC properties, characterized by the Föppl-von Kármán number, on the shape diagram. The simulations are performed using the same viscosity for both external and internal fluids surrounding a RBC; however, we discuss how the viscosity contrast would affect the shape diagram.

Numerical analysis of a red blood cell flowing through a thin micropore

Red blood cell (RBC) deformability plays a key role in microcirculation, especially in vessels that have diameters even smaller than the nominal cell size. In this study, we numerically investigate the dynamics of an RBC in a thin micropore. The RBC is modeled as a capsule with a thin hyperelastic membrane. In a numerical simulation, we employ a boundary element method for fluid mechanics and a finite element method for membrane mechanics. The resulting RBC deformation towards the flow direction is suppressed considerably by increased cytoplasm viscosity, whereas the gap between the cell membrane and solid wall becomes smaller with higher cytoplasm viscosity. We also measure the transit time of the RBC and find that nondimensional transit time increases nonlinearly with respect to the viscosity ratio, whereas it is invariant to the capillary number. In conclusion, cytoplasmic viscosity plays a key role in the dynamics of an RBC in a thin pore. The results of this study will be useful for designing a microfluidic device to measure cytoplasmic viscosity.

Three-dimensional dynamics of oblate and prolate capsules in shear flow

We study computationally the dynamics of oblate and prolate spheroidal capsules in simple shear flow with small inertia for a range of dimensionless shear rates. The capsule is modelled as a liquid droplet enclosed by a hyperelastic membrane, and its equatorial plane is initially tilted out of the plane of shear. We find, at low shear rates, the well-accepted tumbling motion is not always stable for both oblate and prolate capsules. For an oblate capsule, the dominant stable modes for increasing dimensionless shear rate are as follows: rolling with the equatorial plane staying in the plane of shear, precessing following Jeffery's orbit [Proc. R. Soc. London A 102, 161 (1922)], and tumbling. Interestingly, the order of modes is reversed for a prolate capsule: tumbling, precessing, and rolling with increasing dimensionless shear rate. At transitional regimes, we find the stable motion of a capsule can depend on its initial titled angle, even at the same shear rate. At high dimensionless shear rates, a spheroidal capsule undergoes a complicated oscillating-swinging motion: Its major axis oscillates about the plane of shear in addition to the swinging about a mean angle with flow direction found previously, and the amplitudes of both oscillations decrease when increasing the dimensionless shear rate towards a steady tank treading motion asymptotically. We summarize the results in phase diagrams and discuss the reorientation of both oblate and prolate capsules in a wide range of dimensionless shear rates.

Electrohydrodynamic rotations of a viscous droplet

We report a fluid system which exhibits chaotic dynamics under creeping flow conditions. A droplet in a uniform dc electric field deforms into an ellipsoid that can undergo irregular rotational motions. The nonlinear drop electrohydrodynamics is explained by a theoretical model which includes anisotropy in the polarization relaxation due to drop asphericity and charge convection due to rotational drop flow.

Human red blood cell behavior under homogeneous extensional flow in a hyperbolic-shaped microchannel

It is well known that certain pathological conditions result in a decrease of red blood cells (RBCs) deformability and subsequently can significantly alter the blood flow in microcirculation, which may block capillaries and cause ischemia in the tissues. Microfluidic systems able to obtain reliable quantitative measurements of RBC deformability hold the key to understand and diagnose RBC related diseases. In this work, a microfluidic system composed of a microchannel with a hyperbolic-shaped contraction followed by a sudden expansion is presented. We provide a detailed quantitative description of the degree of deformation of human RBCs under a controlled homogeneous extensional flow field. We measured the deformation index (DI) as well as the velocity of the RBCs travelling along the centerline of the channel for four different flow rates and analyze the impact of the particle Reynolds number. The results show that human RBC deformation tends to reach a plateau value in the region of constant extensional rate, the value of which depends on the extension rate. Additionally, we observe that the presence of a sudden expansion downstream of the hyperbolic contraction modifies the spatial distribution of cells and substantially increases the cell free layer (CFL) downstream of the expansion plane similarly to what is seen in other expansion flows. Beyond a certain value of flow rate, there is only a weak effect of inlet flow rates on the enhancement of the downstream CFL. These in vitro experiments show the potential of using microfluidic systems with hyperbolic-shaped microchannels both for the separation of the RBCs from plasma and to assess changes in RBC deformability in physiological and pathological situations for clinical purposes. However, the selection of the geometry and the identification of the most suitable region to evaluate the changes on the RBC deformability under extensional flows are crucial if microfluidics is to be used as an in vitro clinical methodology to detect circulatory diseases.

Tension of red blood cell membrane in simple shear flow

When a red blood cell (RBC) is subjected to an external flow, it is deformed by the hydrodynamic forces acting on its membrane. The resulting elastic tensions in the membrane play a key role in mechanotransduction and govern its rupture in the case of hemolysis. In this study, we analyze the motion and deformation of an RBC in a simple shear flow and the resulting elastic tensions on the membrane. The large deformation of the red blood cell is modelled by coupling a finite element method to solve the membrane mechanics and a boundary element method to solve the flows of the internal and external liquids. Depending on the capillary number Ca, ratio of the viscous to elastic forces, we observe three kinds of RBC motion: tumbling at low Ca, swinging at larger Ca, and breathing at the transitions. In the swinging regime, the region of the high principal tensions periodically oscillates, whereas that of the high isotropic tensions is almost unchanged. Due to the strain-hardening property of the membrane, the deformation is limited but the membrane tension increases monotonically with the capillary number. We have quantitatively compared our numerical results with former experimental results. It indicates that a membrane isotropic tension O(10{-6} N/m) is high enough for molecular release from RBCs and that the typical maximum membrane principal tension for haemolysis would be O(10{-4} N/m). These findings are useful to clarify not only the membrane rupture but also the mechanotransduction of RBCs.