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.     

Diffusion and spatial correlations in suspensions of swimming particles

Populations of swimming micro-organisms produce fluid motions that lead to dramatically enhanced diffusion of tracer particles. Using simulations of suspensions of swimming particles in a periodic domain, we capture this effect and show that it depends qualitatively on the mode of swimming: swimmers "pushed" from behind by their flagella show greater enhancement than swimmers that are "pulled" from the front. The difference is manifested by an increase, that only occurs for pushers, of the diffusivity of passive tracers and the velocity correlation length with the size of the periodic domain. A physical argument supported by a mean field theory sheds light on the origin of these effects.     

Transport and collective dynamics in suspensions of confined swimming particles

Direct simulations of large populations of confined hydrodynamically interacting swimming particles at low Reynolds number are performed. Hydrodynamic coupling between the swimmers leads to large-scale coherent vortex motions in the flow and regimes of anomalous diffusion that are consistent with experimental observations. At low concentrations, swimmers propelled from behind (like spermatazoa) strongly migrate toward solid surfaces in agreement with simple theoretical considerations; at higher concentrations this localization is disrupted by the large-scale coherent motions.     

Hydrodynamic Synchronisation of Model Microswimmers

We define a model microswimmer with a variable cycle time, thus allowing the possibility of phase locking driven by hydrodynamic interactions between swimmers. We find that, for extensile or contractile swimmers, phase locking does occur, with the relative phase of the two swimmers being, in general, close to 0 or π, depending on their relative position and orientation. We show that, as expected on grounds of symmetry, self T-dual swimmers, which are time-reversal covariant, do not phase-lock. We also discuss the phase behaviour of a line of tethered swimmers, or pumps. These show oscillations in their relative phases reminiscent of the metachronal waves of cilia.     

Motion and mixing for multiple ferromagnetic microswimmers

This paper concerns the interaction of several ferromagnetic microswimmers, their motion and the resulting fluid mixing. Each swimmer consists of two ferromagnetic beads joined by an elastic link, and is driven by an external, time-dependent magnetic field. The external field provides a torque on a swimmer and, together with the varying attraction between the magnetic beads, generates a time-irreversible motion leading to persistent swimming in a low Reynolds number environment. The aim of the present paper is to consider the interactions between several swimmers. A regime is considered in which identical swimmers move in the same overall direction, and their motion is synchronised because of driving by the external field. It is found that two swimmers tend to encircle one another while three undergo more complicated motion that may involve the braiding of swimmer trajectories. By means of approximations it is established that the interaction between pairs of swimmers gives circulatory motion which falls off with an inverse square law and is linked to their overall speed of motion through the fluid. As groups of two or more swimmers move through the fluid they process fluid, leaving behind a trail of fluid that has undergone mixing: this is investigated by following streak lines numerically.     

Enhanced diffusion due to active swimmers at a solid surface

We consider two systems of active swimmers moving close to a solid surface, one being a living population of wild-type E.?coli and the other being an assembly of self-propelled Au-Pt rods. In both situations, we have identified two different types of motion at the surface and evaluated the fraction of the population that displayed ballistic trajectories (active swimmers) with respect to those showing randomlike behavior. We studied the effect of this complex swimming activity on the diffusivity of passive tracers also present at the surface. We found that the tracer diffusivity is enhanced with respect to standard Brownian motion and increases linearly with the activity of the fluid, defined as the product of the fraction of active swimmers and their mean velocity. This result can be understood in terms of series of elementary encounters between the active swimmers and the tracers.     

Hydrodynamic interaction between two swimmers at low Reynolds number

We investigate the hydrodynamic interactions between micro-organisms swimming at low Reynolds number. By considering simple model swimmers, and combining analytic and numerical approaches, we investigate the time-averaged flow field around a swimmer. At short distances the swimmer behaves like a pump. At large distances the velocity field depends on whether the swimming stroke is invariant under a combined time-reversal and parity transformation. We then consider two swimmers and find that the interaction between them consists of two parts: a passive term, independent of the motion of the second swimmer, and an active term resulting from the simultaneous swimming action of both swimmers. The swimmer-swimmer interaction is a complicated function of their relative displacement, orientation, and phase, leading to motion that can be attractive, repulsive, or oscillatory.     

Simulations of single and multiple swimmers with non-divergence free deforming geometries

We present a vortex particle method coupled with a penalization technique to simulate single and multiple swimmers in an incompressible, viscous flow in two and three dimensions. The proposed algorithm can handle arbitrarily deforming bodies and their corresponding non-divergence free deformation velocity fields. The method is validated on a number of benchmark problems with stationary and moving boundaries. Results include flows of tumbling objects and single and multiple self-propelled swimmers.     

核壳结构对弛豫铁电体介电行为的影响

介电弥散和介电隔离率的温度非线性关系是弛豫铁电体的主要特征. 通过对掺杂成分以线性梯度递减的核壳结构进行热力学函数分析, 认为核壳结构能够在低温区保持较高的介电常数, 但不能导致介电隔离率与温度的非线性关系. 通过对不同浓度掺杂的铁电体扩散相变的比较, 认为掺杂浓度会影响晶粒掺杂成分的不均匀性, 在较宽的分布条件下会导致介电隔离率与温度的非线性关系. 因而在介电常数的峰值温度区域, 顺电相与铁电相的晶粒共存. 温度变化会影响两相比例及铁电畴的变化, 从而导致弛豫铁电体的介电弥散性. 核壳结构会增大介电弥散性. 铁电陶瓷的掺杂物种类、掺杂物浓度和烧结温度均会影响核壳结构的成分不均匀性和介电弥散性.     

Stirring by swimming bodies

We consider the stirring of an inviscid fluid caused by the locomotion of bodies through it. The swimmers are approximated by non-interacting cylinders or spheres moving steadily along straight lines. We find the displacement of fluid particles caused by the nearby passage of a swimmer as a function of an impact parameter. We use this to compute the effective diffusion coefficient from the random walk of a fluid particle under the influence of a distribution of swimming bodies. We compare with the results of simulations. For typical sizes, densities and swimming velocities of schools of krill, the effective diffusivity in this model is five times the thermal diffusivity. However, we estimate that viscosity increases this value by two orders of magnitude.     

Optimal swimming at low Reynolds numbers

Efficient swimming at low Reynolds numbers is a major concern of microbots. To compare the efficiencies of different swimmers we introduce the notion of "a swimming drag coefficient" which allows for the ranking of swimmers. We find the optimal swimmer within a certain class of two-dimensional swimmers using conformal mapping techniques.     

Quantifying the sorting efficiency of self-propelled run-and-tumble swimmers by geometrical ratchets

Suitable asymmetric microstructures can be used to control the direction of motion in microorganism populations. This rectification process makes it possible to accumulate swimmers in a region of space or to sort different swimmers. Here we study numerically how the separation process depends on the specific motility strategies of the microorganisms involved. Crucial properties such as the separation efficiency and the separation time for two bacterial strains are precisely defined and evaluated. In particular, the sorting of two bacterial populations inoculated in a box consisting of a series of chambers separated by columns of asymmetric obstacles is investigated. We show how the sorting efficiency is enhanced by these obstacles and conclude that this kind of sorting can be efficiently used even when the involved populations differ only in one aspect of their swimming strategy.     

Onsager Reciprocity in Premelting Solids

The diffusive motion of foreign particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids allows us to derive an expression for the Dufour coefficient and independently verify the Onsager reciprocal relation coupling diffusion to the flow of heat.     

局域浓度调控扩散系数的次氯酸-碘离子-丙二酸系统图灵斑图形成中的反常扩散

通过数值模拟及振幅方程解析解方法,从实空间和倒空间分析了受局域浓度扩散系数调控下次氯酸-碘离子-丙二酸反应扩散系统图灵斑图形成的扩散机理.在零扩散系数调节下,斑图形成为典型的菲克扩散;而在负向正向扩散系数调节下,斑图的形成依赖欠扩散和超扩散.图灵系统的浓度稳态振幅对随机初始条件敏感性随局域浓度扩散调控系数k的增大而增加.     

Swimmers in thin films: from swarming to hydrodynamic instabilities

We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally exert active stresses on the fluid. We find that hydrodynamic interactions mediated by the film can give rise to spontaneous continuous symmetry breaking (swarming), to states with either polar or nematic homogeneous order. For dipolar swimmers, the stroke averaged dynamics are enough to determine the leading contributions to the collective behavior. In contrast, for quadrupolar swimmers, details of the internal dynamics are important in determining the bulk behavior. In the broken symmetry phases, fluctuations of hydrodynamic variables destabilize order. Interestingly, this instability is not generic and depends on the length scale.     

Hot microswimmers

Hot microswimmers are self-propelled Brownian particles that exploit local heating for their directed self-thermophoretic motion. We provide a pedagogical overview of the key physical mechanisms underlying this promising new technology. It covers the hydrodynamics of swimming, thermophoresis and -osmosis, hot Brownian motion, force-free steering, and dedicated experimental and simulation tools to analyze hot Brownian swimmers.     

Effect of noise on the standard mapping

The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term proportional to the reciprocal of the variance of the noise term. At large values of the stochasticity parameter, the accelerator modes exhibit a universal behavior. As a result the dependence of the diffusion coefficient on the stochasticity parameter also shows some universal behavior.     

Dynamical properties of colloidal systems: 1. Derivation of stochastic transport equations

To describe dynamical properties of a system of interacting Brownian particles stochastic transport equations are derived for the positions of the particles and their concentration fluctuations. This is achieved by an expansion of the Langevin equation for the momenta in terms of the reciprocal of the friction coefficient. As a by-product this procedure gives a new derivation of the generalized Smoluchowski equation. Using a local equilibrium approximation for the configurational distribution function a mode-mode coupling equation is derived for the local concentration, which still depends on the random forces of the solvent. For the interaction free case the relation to the ordinary diffusion approach is established.     

The holographic investigation of diffusion of azo-dye in liquid crystals host

The diffusion of azo-dye (DR-1) in a planar liquid crystals host (5CB) at various temperatures has been investigated by laser-induced holographic grating relaxation technique. The decay of the diffraction intensity provides information about the diffusion of photoexcited azo-dye molecules. The relaxation time constants can be derived from the time dependence of the diffraction intensity fitted by a single exponential function. Thus, the diffusion coefficients parallel and perpendicular to the director of liquid crystals at various temperatures can be obtained from the plots of the reciprocal of the relaxation time versus the square of the grating vector. From the analysis of the holographic grating relaxation, the diffusion is faster along the molecular director than for the perpendicular case, and the diffusion increases with rising temperature either parallel or perpendicular to the nematic director of liquid crystals. PACS 42.40.Eq; 42.40.Lx     

Melting evolution and diffusion behavior of vanadium nanoparticles

Molecular dynamics calculations have been performed to study the melting evolution, atomic diffusion and vibrational behavior of bcc metal vanadium nanoparticles with the number of atoms ranging from 537 to 28475 (diameters around 2–9 nm). The interactions between atoms are described using an analytic embedded-atom method. The obtained results reveal that the melting temperatures of nanoparticles are inversely proportional to the reciprocal of the nanoparticle size, and are in good agreement with the predictions of the thermodynamic liquid-drop model. The melting process can be described as occurring in two stages, firstly the stepwise premelting of the surface layer with a thickness of 2–3 times the perfect lattice constant, and then the abrupt overall melting of the whole cluster. The heats of fusion of nanoparticles are also inversely proportional to the reciprocal of the nanoparticle size. The diffusion is mainly localized to the surface layer at low temperatures and increases with the reduction of nanoparticle size, with the temperature being held constant. The radial mean square vibration amplitude (RMSVA) is developed to study the anharmonic effect on surface shells.