Hydrodynamics of Rod-Like Colloids and Vesicles

We investigate the dynamics of rod-like colloids and vesicles by means of computer simulations. These two systems are examples of the rich dynamics in "soft-matter" systems, which is characterized by large relaxation times. Therefore, dynamical behavior in soft-matter systems is easily accessable experimentally, and soft materials are driven into non-equilibrium states, already by weak external fields. Both systems have in common that they serve as model systems for transport phenomena in cell biology. We focus on the influence of hydrodynamic interactions. This is realized by the use of a mesoscale hydrodynamics simulation technique called the "Multi Particle Collision Dynamics" (MPC) method, which takes the solvent into account explicitly. We calculate self-diffusion constants of rod-like colloids in the isotropic and nematic phases. Rod diffusion is strongly influenced by steric and hydrodynamic interactions between rods. Due to the anisotropy of the nematic phase also diffusion is anisotropic in such systems. We find that hydrodynamic effects lead to an increased diffusion. Moreover, our simulations show that the diffusion anisotropy of the nematic phase depends on the rod aspect ratio. Our simulation results are compared to experimental measurements of our cooperation partners (group J. K. G. Dhont, FZ-Jülich) who measured diffusion constants of rod-like fd-viruses suspensions. Our observations of the hydrodynamic enhancement and the anisotropy of rod self-diffusion are in good agreement with the experiments. A small amount of spherical tracer colloids is added to the rod suspensions described above, and tracer-sphere diffusion constants are determined. They also exhibit a strong diffusion anisotropy in the nematic phase. The effect of the rod network on tracer-sphere diffusion can be divided into a steric and hydrodynamic contribution. Our results are in good agreement with theoretical predictions which incorporate hydrodynamic effects. An important quantity for the calculation of the theoretical diffusion constants is the hydrodynamic screening length, which is difficult to measure in experiments, but can be directly calculated in simulations. Due to the high concentration of rods, the typically long-ranged hydrodynamic interactions, which depend inversely proportional on the distance between colloids, are screened such that they decay exponentially. We have developed a method which allows us to calculate hydrodynamic screening lengths from the equilibrium fluctuations of solvent shear waves. With this method, we are also able to determine anisotropic screening lengths in nematic systems. We show that hydrodynamic screening lengths are of the order of typical distances between neighboring rods. The calculated screening lengths are able to explain tracer-sphere diffusion constants quantitatively. Far more complex than rod suspensions are vesicles, as they have an internal dynamics. We study vesicles in shear flow in a two-dimensional model system which shows a variety of interesting dynamical phenomena. Depending on the viscosity ratio, i.e. the ratio between the inner and the outer viscosity of the vesicle, they can either ``tumble'', ``swing'' or show ``tank-treading''. In the tumbling regime, the vesicle orientation permanently rotates, in the swinging regime the vesicle exhibits temporally periodical changes in shape and orientation and in the tank-treading regime both shape and orientation are constant, whereas the membrane rotates around the enclosed volume. For the first time, a transition from tank-treading to swinging with increasing viscosity contrast could be shown in computer simulations. Our simulations are in good agreement with a phenomenological theoretical description. Close to walls, tumbling is strongly suppressed. Furthermore, the vesicle is repelled from the wall. The origin of this repulsion is the hydrodynamical lift force. We find that the lift force decays inversely proportional to the squared wall distance and that it decays with increasing viscosity contrast. The lift force is of relevance for the motion of blood cells in blood flow

Dynamical regimes and hydrodynamic lift of viscous vesicles under shear

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities $\eta_{\rm in}$ and $\eta_{\rm out}$ inside and outside, respectively, is studied using mesoscale simulation techniques. Besides the well-known tank-treading and tumbling motions, an oscillatory swinging motion is observed in the simulations for large shear rate. The existence of this swinging motion requires the excitation of higher-order undulation modes (beyond elliptical deformations) in two dimensions. Keller-Skalak theory is extended to deformable two-dimensional vesicles, such that a dynamical phase diagram can be predicted for the reduced shear rate and the viscosity contrast $\eta_{\rm in}/\eta_{\rm out}$. The simulation results are found to be in good agreement with the theoretical predictions, when thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic lift force, acting on vesicles under shear close to a wall, is determined from simulations for various viscosity contrasts. For comparison, the lift force is calculated numerically in the absence of thermal fluctuations using the boundary-integral method for equal inside and outside viscosities. Both methods show that the dependence of the lift force on the distance $y_{\rm {cm}}$ of the vesicle center of mass from the wall is well described by an effective power law $y_{\rm {cm}}^{-2}$ for intermediate distances $0.8 R_{\rm p} \lesssim y_{\rm {cm}} \lesssim 3 R_{\rm p}$ with vesicle radius $R_{\rm p}$. The boundary-integral calculation indicates that the lift force decays asymptotically as $1/[y_{\rm {cm}}\ln(y_{\rm {cm}})]$ far from the wall.Comment: 13 pages, 13 figure

Performance and limitations of using ELT and MCAO for 50 μas astrometry

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