Swinging and Tumbling of Fluid Vesicles in Shear Flow

The dynamics of fluid vesicles in simple shear flow is studied using mesoscale simulations of dynamically-triangulated surfaces, as well as a theoretical approach based on two variables, a shape parameter and the inclination angle, which has no adjustable parameters. We show that between the well-known tank-treading and tumbling states, a new ``swinging'' state can appear. We predict the dynamic phase diagram as a function of the shear rate, the viscosities of the membrane and the internal fluid, and the reduced vesicle volume. Our results agree well with recent experiments.Comment: 4 pages, 4 figure

Red blood cells and other non-spherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition

We consider the motion of red blood cells and other non-spherical microcapsules dilutely suspended in a simple shear flow. Our analysis indicates that depending on the viscosity, membrane elasticity, geometry and shear rate, the particle exhibits either tumbling, tank-treading of the membrane about the viscous interior with periodic oscillations of the orientation angle, or intermittent behavior in which the two modes occur alternately. For red blood cells, we compute the complete phase diagram and identify a novel tank-treading-to-tumbling transition at low shear rates. Observations of such motions coupled with our theoretical framework may provide a sensitive means of assessing capsule properties.Comment: 11 pages, 4 figure

Swinging of red blood cells under shear flow

We reveal that under moderate shear stress (of the order of 0.1 Pa) red blood cells present an oscillation of their inclination (swinging) superimposed to the long-observed steady tanktreading (TT) motion. A model based on a fluid ellipsoid surrounded by a visco-elastic membrane initially unstrained (shape memory) predicts all observed features of the motion: an increase of both swinging amplitude and period (1/2 the TT period) upon decreasing the shear stress, a shear stress-triggered transition towards a narrow shear stress-range intermittent regime of successive swinging and tumbling, and a pure tumbling motion at lower shear stress-values.Comment: 4 pages 5 figures submitted to Physical Review Letter

The role of tank-treading motions in the transverse migration of a spheroidal vesicle in a shear flow

The behavior of a spheroidal vesicle, in a plane shear flow bounded from one side by a wall, is analysed when the distance from the wall is much larger than the spheroid radius. It is found that tank treading motions produce a transverse drift away from the wall, proportional to the spheroid eccentricity and the inverse square of the distance from the wall. This drift is independent of inertia, and is completely determined by the characteristics of the vesicle membrane. The relative strength of the contribution to drift from tank-treading motions and from the presence of inertial corrections, is discussed.Comment: 16 pages, 1 figure, Latex. To appear on J. Phys. A (Math. Gen.

Dynamics of Fluid Vesicles in Oscillatory Shear Flow

The dynamics of fluid vesicles in oscillatory shear flow was studied using differential equations of two variables: the Taylor deformation parameter and inclination angle $\theta$. In a steady shear flow with a low viscosity $\eta_{\rm {in}}$ of internal fluid, the vesicles exhibit steady tank-treading motion with a constant inclination angle $\theta_0$. In the oscillatory flow with a low shear frequency, $\theta$ oscillates between $\pm \theta_0$ or around $\theta_0$ for zero or finite mean shear rate $\dot\gamma_{\rm m}$, respectively. As shear frequency $f_{\gamma}$ increases, the vesicle oscillation becomes delayed with respect to the shear oscillation, and the oscillation amplitude decreases. At high $f_{\gamma}$ with $\dot\gamma_{\rm m}=0$, another limit-cycle oscillation between $\theta_0-\pi$ and $-\theta_0$ is found to appear. In the steady flow, $\theta$ periodically rotates (tumbling) at high $\eta_{\rm {in}}$, and $\theta$ and the vesicle shape oscillate (swinging) at middle $\eta_{\rm {in}}$ and high shear rate. In the oscillatory flow, the coexistence of two or more limit-cycle oscillations can occur for low $f_{\gamma}$ in these phases. For the vesicle with a fixed shape, the angle $\theta$ rotates back to the original position after an oscillation period. However, it is found that a preferred angle can be induced by small thermal fluctuations.Comment: 11 pages, 13 figure

Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids

A Sub-Cellular Viscoelastic Model for Cell Population Mechanics

Understanding the biomechanical properties and the effect of biomechanical force on epithelial cells is key to understanding how epithelial cells form uniquely shaped structures in two or three-dimensional space. Nevertheless, with the limitations and challenges posed by biological experiments at this scale, it becomes advantageous to use mathematical and ‘in silico’ (computational) models as an alternate solution. This paper introduces a single-cell-based model representing the cross section of a typical tissue. Each cell in this model is an individual unit containing several sub-cellular elements, such as the elastic plasma membrane, enclosed viscoelastic elements that play the role of cytoskeleton, and the viscoelastic elements of the cell nucleus. The cell membrane is divided into segments where each segment (or point) incorporates the cell's interaction and communication with other cells and its environment. The model is capable of simulating how cells cooperate and contribute to the overall structure and function of a particular tissue; it mimics many aspects of cellular behavior such as cell growth, division, apoptosis and polarization. The model allows for investigation of the biomechanical properties of cells, cell-cell interactions, effect of environment on cellular clusters, and how individual cells work together and contribute to the structure and function of a particular tissue. To evaluate the current approach in modeling different topologies of growing tissues in distinct biochemical conditions of the surrounding media, we model several key cellular phenomena, namely monolayer cell culture, effects of adhesion intensity, growth of epithelial cell through interaction with extra-cellular matrix (ECM), effects of a gap in the ECM, tensegrity and tissue morphogenesis and formation of hollow epithelial acini. The proposed computational model enables one to isolate the effects of biomechanical properties of individual cells and the communication between cells and their microenvironment while simultaneously allowing for the formation of clusters or sheets of cells that act together as one complex tissue