Electrokinetic and hydrodynamic properties of charged-particles systems

Dynamic processes in dispersions of charged spherical particles are of importance both in fundamental science, and in technical and bio-medical applications. There exists a large variety of charged-particles systems, ranging from nanometer-sized electrolyte ions to micron-sized charge-stabilized colloids. We review recent advances in theoretical methods for the calculation of linear transport coefficients in concentrated particulate systems, with the focus on hydrodynamic interactions and electrokinetic effects. Considered transport properties are the dispersion viscosity, self- and collective diffusion coefficients, sedimentation coefficients, and electrophoretic mobilities and conductivities of ionic particle species in an external electric field. Advances by our group are also discussed, including a novel mode-coupling-theory method for conduction-diffusion and viscoelastic properties of strong electrolyte solutions. Furthermore, results are presented for dispersions of solvent-permeable particles, and particles with non-zero hydrodynamic surface slip. The concentration-dependent swelling of ionic microgels is discussed, as well as a far-reaching dynamic scaling behavior relating colloidal long- to short-time dynamics.     

Hydrodynamic and brownian fluctuations in sedimenting suspensions

We use a mesoscopic computer simulation method to study the interplay between hydrodynamic and Brownian fluctuations during steady-state sedimentation of hard sphere particles for Peclet numbers (Pe) ranging from 0.1-15. Even when the hydrodynamic interactions are an order of magnitude weaker than Brownian forces, they still induce backflow effects that dominate the reduction of the average sedimentation velocity with increasing particle packing fraction. Velocity fluctuations, on the other hand, begin to show nonequilibrium hydrodynamic character for Pe>1.     

Numerical simulation of the sedimentation of a sphere in a sheared granular fluid: a granular Stokes experiment

We study, computationally, the sedimentation of a sphere of higher mass in a steady, gravity-driven granular flow of otherwise identical spheres, on a rough inclined plane. Taking a hydrodynamic approach at the scale of the particle, we find the drag force to be given by a modified Stokes law and the buoyancy force by the Archimedes principle, with excluded volume effects taken into account. We also find significant differences between the hydrodynamic case and the granular case, which are highlighted.     

On the orientational characteristics and transport coefficients of an oblate spheroidal hematite particle in a simple shear flow

We have developed the basic equation of the orientational distribution function of oblate spheroidal hematite particles with rotational Brownian motion in a simple shear flow under an applied magnetic field. An oblate spheroidal hematite particle has an important characteristic in that it is magnetized in a direction normal to the particle axis. Since a dilute dispersion is addressed in the present study, we have taken into account only the friction force (torque) whilst neglecting the hydrodynamic interactions among the particles. This basic equation has been solved numerically in order that we may investigate the dependence of the orientational distribution on the magnetic field strength, shear rate and rotational Brownian motion and the relationship between the orientational distribution and the transport coefficients such as viscosity and diffusion coefficient. We found that if the effect of the magnetic field is more dominant, the particle inclines in such a way that the oblate surface aligns in the magnetic field direction. If the Peclet number increases and the effect of the shear flow becomes more dominant, the particle inclines such that the oblate surface tilts in the shear flow direction. The viscosity due to the magnetic torque is shown to increase as the magnetic field increases, since the magnetic torque due to the applied magnetic field becomes the more dominant effect. Moreover, the viscosity increase is shown to be more significant for a larger aspect ratio or for a more oblate hematite particle. We have applied the analysis to the problem of particle sedimentation under gravity in the presence of a magnetic field applied in the sedimentation direction. The particles are found to sediment with the oblate surface aligning more significantly in the sedimentation direction as the applied magnetic field strength increases.     

Short-time dynamics in quasi-two-dimensional colloidal suspensions

The short-time dynamic properties of colloidal particles in quasi-two-dimensional geometries are studied by digital video microscopy. We demonstrate experimentally that the effective-two-dimensional physical quantities such as the dynamic structure factor, the hydrodynamic function, and the hydrodynamic diffusion coefficients are related in exactly the same manner as their three-dimensional counterparts.     

Hemiasterlin analogues incorporating an aromatic,and heterocyclic type C-terminus: design,synthesis and biological evaluation

A representative series of structural analogs of the antimitotic tripeptides hemiasterlins have been designed and synthesized, as potential inhibitors of tubulin polymerization. Relying also on a computational approach, we aimed to explore unknown extensive changes at the C-fragment, by incorporating the conformationally required double bond into five- and six-membered rings. Key steps of the synthetic strategy are a dynamic resolution affording the A-fragment in 97 % ee and the preparation of six new cyclic C fragments, all potentially able to interact with tubulin by means of H bonds. Unexpectedly, biological evaluation of these analogs did not provide evidences neither for cytotoxic effect nor for inhibition of tubulin polymerization.     

Nonequilibrium Sources of Hydrodynamic Fluctuations Mutual Influence of Hydrodynamic Motion and Nonequilibrium Fluctuations on the Kinetic Coefficients

From generalized expressions for the entropy production the kinetic coefficients in the hydrodynamic equations are determined taking into account the mutual influence of the hydrodynamic motion and the fluctuations. Nonlinear effective and turbulent kinetic coefficients are obtained. The usefulness of the introduced coefficients is demonstrated for boundary layer and tube flows.     

On the influence of the hydrodynamic interactions on the aggregation rate of magnetic spheres in a dilute suspension

Magnetostatic attraction may lead to formation of aggregates in stable colloidal magnetic suspensions and magneto-rheological suspensions. The aggregation problem of magnetic composites under differential sedimentation is a key problem in the control of the instability of non-Brownian suspensions. Against these attractive forces are the electrostatic repulsion and the hydrodynamic interactions acting as stabilizing effects to the suspension. This work concerns an investigation of the pairwise interaction of magnetic particles in a dilute sedimenting suspension. We focus attention on suspensions where the Péclet number is large (negligible Brownian motion) and where the Reynolds number (negligible inertia) is small. The suspension is composed of magnetic micro-spheres of different radius and density immersed in a Newtonian fluid moving under the action of gravity. The theoretical calculations are based on direct computations of the hydrodynamic and the magnetic interactions among the rigid spheres in the regime of low particle Reynolds number. From the limiting trajectory in which aggregation occurs, we calculate the collision efficiency, representing the dimensionless rate at which aggregates are formed. The numerical results show clear evidence that the hydrodynamic interactions are of fundamental relevance in the process of magnetic particle aggregation. We compare the stabilizing effects between electrostatic repulsion and hydrodynamic interactions.     

Swimming in external fields

Microswimmers move autonomously but are subject to external fields, which influence their swimming path and their collective dynamics. With three concrete examples we illustrate swimming in external fields and explain the methodology to treat it. First, an active Brownian particle shows a conventional sedimentation profile in a gravitational field but with increased sedimentation length and some polar order along the vertical. Bottom-heavy swimmers are able to invert the sedimentation profile.Second, active Brownian particles interacting by hydrodynamic flow fields in a three-dimensional harmonic trap can spontaneously break the isotropic symmetry. They develop polar order, which one can describe by mean-field theory reminiscent to Weiss theory of ferromagnetism, and thereby pump fluid.Third, a single microswimmer shows interesting non-linear dynamics in Poiseuille flow including swinging and tumbling trajectories. For pushers, hydrodynamic interactions with bounding surfaces stabilize either straight swimming against the flow or tumbling close to the channel wall, while pushers always move on a swinging trajectory with a specific amplitude as limit cycle.     

Diffusion of colloidal particles in swimming suspensions

Previously, we have proposed to analyse the hydrodynamic interactions in a suspension of swimmers with respect to an effective hydrodynamic diffusion coefficient, which only considers the fluctuating motion caused by the stirring of the fluid. In this work, we study the diffusion of colloidal particles immersed in a bath of swimmers. To accurately resolve the many-body hydrodynamic interactions responsible for this diffusion, we use a direct numerical simulation scheme based on the smooth profile method. We consider a squirmer model for the self-propelled swimmers, as it accurately reproduces the flow field generated by real microorganisms, such as bacteria or spermatozoa. We show that the diffusion coefficients of the colloids are comparable with the effective diffusion coefficients of the swimmers, provided that the concentration of swimmers is high enough. At low concentrations, the difference in the way colloids and swimmers react to the flow leads to a reduction in the diffusion coefficient of the colloids. This is clearly seen in the appearance of a negative-correlation region for the velocity-correlation function of the colloids, which does not exist for the swimmers.     

Numerical method for hydrodynamic modulation equations describing Bloch oscillations in semiconductor superlattices

We present a finite difference method to solve a new type of nonlocal hydrodynamic equations that arise in the theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices. The hydrodynamic equations describe the evolution of the electron density, electric field and the complex amplitude of the Bloch oscillations for the electron current density and the mean energy density. These equations contain averages over the Bloch phase which are integrals of the unknown electric field and are derived by singular perturbation methods. Among the solutions of the hydrodynamic equations, at a 70 K lattice temperature, there are spatially inhomogeneous Bloch oscillations coexisting with moving electric field domains and Gunn-type oscillations of the current. At higher temperature (300 K) only Bloch oscillations remain. These novel solutions are found for restitution coefficients in a narrow interval below their critical values and disappear for larger values. We use an efficient numerical method based on an implicit second-order finite difference scheme for both the electric field equation (of drift-diffusion type) and the parabolic equation for the complex amplitude. Double integrals appearing in the nonlocal hydrodynamic equations are calculated by means of expansions in modified Bessel functions. We use numerical simulations to ascertain the convergence of the method. If the complex amplitude equation is solved using a first order scheme for restitution coefficients near their critical values, a spurious convection arises that annihilates the complex amplitude in the part of the superlattice that is closer to the cathode. This numerical artifact disappears if the space step is appropriately reduced or we use the second-order numerical scheme.     

Weakly nonlinear model for oscillatory instability in Saturn's dense rings

Viscous overstability (oscillatory instability) may play an important role in the formation of small scale structure in dense planetary rings such as Saturn's B ring. We investigate the growth and saturation of such modes in local particle simulations. Starting from a hydrodynamic model, we develop a set of ordinary differential equations to model the evolution of the amplitudes of the linearly overstable modes in the nonlinear regime. The NASA/ESA space probe Cassini can make direct observations of these modes in Saturn's rings, including their sizes and temporal development.     

Linear response theory of sedimentation and diffusion in a suspension of spherical particles

We discuss the problem of sedimentation and diffusion in a suspension of interacting spherical particles. We consider external forces acting on the particles and study the linear response of density and current on the basis of the generalized Smoluchowski equation. The theory leads to a natural distinction between a hydrodynamic and a diffusion current. Each of these is defined as an observable in terms of the generalized mobility matrix. We derive general relations for the response functions.     

Generalized hydrodynamics of systems of Brownian particles

A generalized hydrodynamic theory is developed for systems of interacting Brownian particles on the basis of a Fokker-Planck equation. General results are derived for correlation functions, frequency- and wave-vector dependent transport coefficients. Explicit expressions for moments, cumulants and the hydrodynamic limits of the transport coefficients are given. For the special cases of overdamped systems with and without hydrodynamic interaction the general results are simplified. As an example for the application of this approach the system of charged spherical polystyrene spheres in aqueous solution is treated in detail. The generalized transport functions are evaluated in mode-mode coupling approximation and detailed numerical results are presented for various collective and single-particle properties. Finally, the relationship to a corresponding Smoluchowski approach is discussed.     

Elliptic and triangular flow in event-by-event D=3+1 viscous hydrodynamics

We present results for the elliptic and triangular flow coefficients v(2) and v(3) in Au+Au collisions at √s=200 AGeV using event-by-event D=3+1 viscous hydrodynamic simulations. We study the effect of initial state fluctuations and finite viscosities on the flow coefficients v(2) and v(3) as functions of transverse momentum and pseudorapidity. Fluctuations are essential to reproduce the measured centrality dependence of elliptic flow. We argue that simultaneous measurements of v(2) and v(3) can determine η/s more precisely.     

Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids

The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.     

Collective effects in settling of spheroids under steady-state sedimentation

We study the settling dynamics of non-Brownian prolate spheroids under steady-state sedimentation. We consider the case of moderate particle Reynolds numbers properly taking into account the hydrodynamic effects. For small volume fractions, we find an orientational transition of the spheroids, characterized by enhanced density fluctuations. Around the transition, the average settling velocity has a maximum which may even exceed the terminal velocity of a single spheroid, in accordance with experiments.     

二分量胶体悬浮系统的短时间动力学

研究了二分量带电粒子悬浮系统的短时间平动和转动自扩散系数.由于存在静电相互作用和流体力学作用,扩散系数与两种粒子的尺寸比,它们的体积分数,以及所带的有效电荷都有关.计入了流体力学相互作用对扩散张量的二体贡献和首项三体贡献.计算结果表明,流体力学作用对于带电粒子系统的影响要小于它对硬球粒子系统的影响.扩散系数随两种粒子的尺寸比和它们的体积分数变化的关系可以用有效硬球模型来解释,而其定性结果与实验相符合.     

Disclination motion in liquid crystalline films

We theoretically study a single disclination motion in a thin free-standing liquid crystalline film. Backflow effects and the own dynamics of the orientational degree of freedom (bond or director angle) are taken into account. We find the orientation field and the hydrodynamic velocity distribution around the moving disclination, which allows us to relate the disclination velocity to the angle gradient far from the disclination. Different cases are examined depending on the ratio of the rotational and shear viscosity coefficients.