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

Marginated aberrant red blood cells induce pathologic vascular stress fluctuations in a computational model of hematologic disorders

Red blood cell (RBC) disorders such as sickle cell disease affect billions worldwide. While much attention focuses on altered properties of aberrant RBCs and corresponding hemodynamic changes, RBC disorders are also associated with vascular dysfunction, whose origin remains unclear and which provoke severe consequences including stroke. Little research has explored whether biophysical alterations of RBCs affect vascular function. We use a detailed computational model of blood that enables characterization of cell distributions and vascular stresses in blood disorders and compare simulation results with experimental observations. Aberrant RBCs, with their smaller size and higher stiffness, concentrate near vessel walls (marginate) because of contrasts in physical properties relative to normal cells. In a curved channel exemplifying the geometric complexity of the microcirculation, these cells distribute heterogeneously, indicating the importance of geometry. Marginated cells generate large transient stress fluctuations on vessel walls, indicating a mechanism for the observed vascular inflammation.

Settling mode of a bottom-heavy squirmer in a narrow vessel

The lattice Boltzmann-immersed boundary (IB-LB) method is used to numerically simulate the sedimentation motion of a single two-dimensional, bottom-heavy squirmer in a narrow vessel. The effects of the swimming Reynolds number Re_s = 0.1-3, eccentricity distance l = 0.15d-0.75d, and density ratio of squirmer to fluid γ = 1.1-2.0 on the settlement motion characteristics are investigated and analyzed. The results showed that four settling modes exist: vertical motion, unilateral oscillation, oscillation, and tilt. The bottom-heavy neutral squirmer and puller settle in the vessel during vertical motion when Re_s is 0.1-1.5. By increasing Re_s and swimming strength |β|, the bottom-heavy squirmer becomes more self-driven, shifting its settling mode from vertical motion to unilateral oscillation or oscillation. Increasing l or |β| does not affect the bottom-heavy neutral squirmer and puller's vertical settling mode but shifts the bottom-heavy pusher's settling mode from unilateral oscillation to oscillation or oscillation to unilateral oscillation. Similarly, altering γ or |β| has no impact on the eccentric neutral squirmer and puller's settling mode; however, pushers will switch from oscillation mode to attraction mode or from oscillation mode to tilt mode. Additionally, it was found that after the squirmer collided with the bottom wall, the bottom-heavy squirmer settled at the bottom of the vessel in a different state of motion.

Flexible fibers in shear flow approach attracting periodic solutions

The three-dimensional dynamics of a single non-Brownian flexible fiber in shear flow is evaluated numerically, in the absence of inertia. A wide range of ratios A of bending to hydrodynamic forces and hundreds of initial configurations are considered. We demonstrate that flexible fibers in shear flow exhibit much more complicated evolution patterns than in the case of extensional flow, where transitions to higher-order modes of characteristic shapes are observed when A exceeds consecutive threshold values. In shear flow, we identify the existence of an attracting steady configuration and different attracting periodic motions that are approached by long-lasting rolling, tumbling, and meandering dynamical modes, respectively. We demonstrate that the final stages of the rolling and tumbling modes are effective Jeffery orbits, with the constant parameter C replaced by an exponential function that either decays or increases in time, respectively, corresponding to a systematic drift of the trajectories. In the limit of C→0, the fiber aligns with the vorticity direction and in the limit of C→∞, the fiber periodically tumbles within the shear plane. For moderate values of A, a three-dimensional meandering periodic motion exists, which corresponds to intermediate values of C. Transient, close to periodic oscillations are also detected in the early stages of the modes.

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.

Dynamic characteristics of a deformable capsule in a simple shear flow

The dynamic characteristics of a two-dimensional deformable capsule in a simple shear flow are studied with an immersed boundary-lattice Boltzmann method. Simulations are conducted by varying the Reynolds number (Re) from 0.0125 to 2000 and the dimensionless shear rate (G) from 0.001 to 0.5. The G-Re plane can be divided into four regions according to the deformation dependence on the parameters considered: viscous dominant, inertia dominant, transitional, and anomalous regions. There are four typical dynamic behaviors over the G-Re plane: steady deformation, prerupture state, quasisteady deformation, and continuous elongation. Analysis indicates that the pressure distribution and its variations due to the interplay of the fluid inertia force, the viscous shear stress, and the membrane elastic force determines the complex behaviors of the capsule. The effects of the bending rigidity and the internal-to-external viscosity ratio on the dynamics of the capsule are further studied. It is found that the capsule experiences smaller deformation when the higher bending rigidity is included, and the low bending rigidity does not have a remarkable influence on the capsule deformation. The capsule normally experiences smaller deformation due to the increase of the internal-to-external viscosity ratio.

Precise measurement of orientations of transparent ellipsoidal particles through digital holographic microscopy

A method to measure the orientations of transparent ellipsoidal particles using digital holographic microscopy (DHM) is proposed in this study. This approach includes volumetric recording and numerical reconstruction at different depths. Distinctive light scatterings from an ellipsoid with different angles of orientation are analyzed. A focus function is applied to obtain a reconstructed image that contains a bright line parallel to the major axis of the projected particle, which provides in-plane orientation information. An intensity profile is collected along the major axis of the projected particle in the direction of the optical axis, and this profile is then utilized to measure the out-of-plane orientation of the ellipsoid. After being verified for an ellipsoid with known orientations, the proposed method is applied to ellipsoids suspended in a pipe flow with random orientations. This DHM method can extract the essential information of ellipsoids and therefore has great potential applications in particle dynamics.

Sedimentation of an oblate ellipsoid in narrow tubes

Sedimentation behaviors of an oblate ellipsoidal particle inside narrow [R/a∈(1.2,2.0)] infinitely long circular tubes are studied by the lattice Boltzmann method, where R and a are the radius of the tube and the length of the semimajor axis of the ellipsoid, respectively. The Archimedes numbers (Ar) up to 70 are considered. Four periodic and two steady sedimentation modes are identified. It is the first time that the anomalous mode has been found in a circular tube for an ellipsoidal particle. The phase diagram of the modes as a function of Ar and R/a is obtained. The anomalous mode is observed in the larger R/a and lower-Ar regime. Through comparisons between the anomalous and oscillatory modes, it is found that R/a plays a critical role for the anomalous mode. Some constrained cases with two steady modes are simulated. It is found that the particle settles faster in the unconstrained modes than in the corresponding constrained modes. This might inspire further study on why the particle adopts a specific mode under a certain circumstance.

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.

Microparticle shape effects on margination, near-wall dynamics and adhesion in a three-dimensional simulation of red blood cell suspension

We present a 3D computational modeling study of the transport of micro-scale drug carriers modeled as microparticles of different shapes (spherical, oblate, and prolate) in whole blood represented as a suspension of deformable red blood cells. The objective is to quantify the effect of microparticle shapes on their margination, near-wall dynamics and adhesion. We observe that the near-wall accumulation is highest for oblate particles of moderate aspect ratio, followed by spherical particles, and lowest for very elongated prolate particles. The result is explained using micro-scale dynamics of individual particles, and their interaction with red blood cells. We observe that the orientation of microparticles in 3D space and the frequency of their collisions with red blood cells are the key factors affecting their margination. We show that due to repeated collisions with red blood cells in the presence of a bounding wall, the axes of revolution of oblate particles align near the plane of the shear flow, but those of prolate particles shift towards the vorticity axis with a wider distribution. Such specific orientations lead to more frequent collisions and a greater lateral drift for oblate particles than microspheres, but less frequent collisions and a reduced lateral drift for elongated prolate particles, resulting in the observed differences in their near-wall accumulation. Once marginated, the particle shape has an entirely different effect on the likelihood of making particle-wall contacts. We find that marginated prolate particles, due to their alignment along the vorticity axis and large angular fluctuations, are more likely to make contacts with the wall than spherical and oblate particles. We further simulate the adhesion between flowing microparticles and the wall in the presence of red blood cells, and observe that once wall contacts are established, the likelihood of firm adhesion is greater for disk-like particles, followed by elongated prolates, and microspheres. Consequently, this study suggests that the local hemorheological conditions near the targeted sites must be taken into consideration while selecting the optimum shape of micro-scale vascular drug carriers.

Fluid vesicles in flow

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.