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.     

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.     

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.     

超疏水聚合物表面的水滴蒸发模拟

基于质量守恒和Fick第一定律，模拟了水滴在超疏水聚合物表面的蒸发全过程．研究从以往的接触角<90±扩展到>150±，液滴形貌扩展为椭球球帽模型进行疏水表面蒸发模拟．水滴在超疏水PC和FPU/PMMA表面蒸发的实验结果显示，计算的椭球球帽模型可以更好的反映出液滴接触角和高度的变化情况，并且不同聚合物表面接触角的相同变化趋势也揭示出微-纳二级结构表面结构不仅影响液滴接触角，也影响液滴蒸发模式．     

Coherent structures in monolayers of swimming particles

We report various types of coherent structures in suspensions of spherical particles swimming in a monolayer. We solve the fluid dynamics precisely from far-field hydrodynamic interactions to lubrication between two near-contact surfaces. The simulation results clearly illustrate that coherent structures, such as aggregation, mesoscale spatiotemporal motion, and band formation, can be generated by purely hydrodynamic interactions.     

An examination of the flow induced by the motion of many buoyant bubbles

The results of direct numerical simulations of the motion of many three-dimensional buoyant bubbles in periodic domains are examined. The bubble motion is computed by solving the full Navier-Stokes equations by a parallelized finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is about 25. Two cases are examined. In one, the bubbles are nearly spherical; in the other, the bubbles rise with an ellipsoidal shape. The ellipsoidal bubbles show a much larger fluctuation velocity and by visualizing the flow field it is possible to show that the difference is due to larger vorticity generation and stronger interactions of the deformable bubbles. The focus here is on the early stage of the flow, when both the spherical and the deformable bubbles are nearly uniformly distributed.     

随机取向群聚椭球粒子光散射特性研究

利用离散偶极子近似方法,考虑单元粒子之间的电磁相互作用,数值计算了随机取向的不同尺度参数、不同纵横比的群聚椭球粒子的缪勒矩阵元素,给出了各个缪勒矩阵元素的角分布曲线,探讨了随机取向的群聚椭球粒子的尺度参数、纵横比、基本粒子相对位置对其缪勒矩阵元素的影响。并将随机取向群聚椭球粒子的光散射特性与单个等效球形粒子的数值结果进行了比较。结果表明,随机取向群聚椭球粒子的光散射特性与等效球形粒子的光散射特性存在很大差别,基本粒子的形状越偏离球形,这种差别就越大; 随机取向群聚椭球粒子中椭球粒子的纵横比和相对位置对整个群聚粒子的缪勒矩阵元素存在不同程度的影响,并且此影响随着粒子尺度参数的增大而变得更加显著。     

随机取向群聚椭球粒子光散射特性研究

利用离散偶极子近似方法,考虑单元粒子之间的电磁相互作用,数值计算了随机取向的不同尺度参数、不同纵横比的群聚椭球粒子的缪勒矩阵元素,给出了各个缪勒矩阵元素的角分布曲线,探讨了随机取向的群聚椭球粒子的尺度参数、纵横比、基本粒子相对位置对其缪勒矩阵元素的影响。并将随机取向群聚椭球粒子的光散射特性与单个等效球形粒子的数值结果进行了比较。结果表明,随机取向群聚椭球粒子的光散射特性与等效球形粒子的光散射特性存在很大差别,基本粒子的形状越偏离球形,这种差别就越大; 随机取向群聚椭球粒子中椭球粒子的纵横比和相对位置对整个群聚粒子的缪勒矩阵元素存在不同程度的影响,并且此影响随着粒子尺度参数的增大而变得更加显著。     

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.     

Continuum modelling of spherical and spheroidal carbon onions

Carbon nanostructures are of considerable interest owing to their unique mechanical and electronic properties. Experimentally, a wide variety of different shapes are obtained, including both spherical and spheroidal carbon onions. A spheroid is an ellipsoid with two major axes equal and the term onion refers to a multi-layered composite structure. Assuming structures of either concentric spherical or ellipsoidal fullerenes comprising n layers, this paper examines the interaction energy between adjacent shells for both spherical and spheroidal carbon onions. The Lennard-Jones potential together with the continuum approximation is employed to determine the equilibrium spacing between two adjacent shells. We also determine analytical formulae for the potential energy which may be expressed either in terms of hypergeometric or Legendre functions. We find that the equilibrium spacing between shells decreases for shells further out from the inner core owing to the decreasing curvature of the outer shells of a concentric structure.     

Phoretic self-assembly of active colloidal molecules

We simulate the self-assembly of active colloidal molecules from binary mixtures of spherical particles using a Brownian dynamics algorithm. These particles interact via phoretic interactions, which are determined by two independently tunable parameters, surface activity and surface mobility. In systems composed of equal-size particles, we observe the formation of colloidal molecules with well-defined coordination numbers and spatial arrangement, which also display distinct dynamic functions, such as resting, translating, and rotating. By changing the size ratio to 2 : 1 between the two species,we further observe the formation of colloidal molecules with new structures arising from breaking the size symmetry. By tuning the mutual interactions between the smaller species via their surface mobility, we are able to control their spacing as well as the coordination number of the colloidal molecules. This study highlights the importance of tuning surface parameters and size asymmetry in controlling the structure and the active dynamics of colloidal molecules.     

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.     

Entanglement Dynamics of Two Coupled Spins in a Spin Star Environment

We theoretically study the entanglement dynamics of two coupled spins in a spin star environment, whose elements are coupled to local bosonic baths. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the interactions between the central system and the environment, as well as interactions between the bath spin and the reservoir. We also investigate the effect of non-Markovian dynamics in contrast with the Markovian case. It is found that the non-Markovian dynamics has a significant effect on the disentanglement between the two central spins.     

Coherent transmission and angular structure of light scattering by monolayer films of polymer dispersed liquid crystals with inhomogeneous boundary conditions

We consider monolayer polymer films with oriented droplets of a nematic liquid crystal (LC). Relations for the coherent transmission coefficients of a layer of oriented ellipsoidal droplets and for the intensity of light scattered by monolayers of spherical and spheroidal droplets have been obtained. The amplitude-phase screen model and the interference approximation of the theory of multiple wave scattering have been used. To describe light scattering by an individual ellipsoidal droplet with inhomogeneous surface binding, we have developed an anomalous diffraction approximation. For monolayers of spherical LC droplets, the coherent scattering coefficients and the angular scattering structure have been analyzed. The internal structure of nematic droplets have been calculated by the relaxation method based on the solution of the minimization problem of the free energy volume density. We have studied basic regular features of light scattering by a monolayer with homogeneous and inhomogeneous boundary conditions at the LC-polymer interface. We show that, for films that contain droplets with inhomogeneous boundary conditions of the tangentially normal type, the angular structure of the scattered light is asymmetric with respect to the polar scattering angle.     

The Ostwald ripening at nanoengineering of InAsSbP spherical and ellipsoidal quantum dots on InAs (100) surface

We present the results of growth of quasi-ternary InAsSbP spherical and ellipsoidal quantum dots (QDs) on InAs (100) surface by the method of liquid-phase epitaxy. Coarsening of QDs due to coalescence and Ostwald ripening was investigated by atomic-force and scanning electron microscopy. Ellipsoidal QDs prolated in [010] and oblated in [001] directions have been grown. Elongation ratios for the ellipsoidal QDs were measured in all three directions. It is shown that elongation of spherical QDs to ellipsoidal is started at QDs diameter of ～50 nm. Shape transformation of the QDs’ size distribution function from the Gram-Charlier-like to the Gaussian and then to the Lifshits-Slezov-like distribution was revealed at increasing the nucleation time.     

Surface effects in nanoparticles: application to maghemite -Fe O

We present a microscopic model for nanoparticles, of the maghemite (-Fe₂O₃) type, and perform classical Monte Carlo simulations of their magnetic properties. On account of M?ssbauer spectroscopy and high-field magnetisation results, we consider a particle as composed of a core and a surface shell of constant thickness. The magnetic state in the particle is described by the anisotropic classical Dirac-Heisenberg model including exchange and dipolar interactions and bulk and surface anisotropy. We consider the case of ellipsoidal (or spherical) particles with free boundaries at the surface. Using a surface shell of constant thickness ( nm) we vary the particle size and study the effect of surface magnetic disorder on the thermal and spatial behaviors of the net magnetisation of the particle. We study the shift in the surface “critical region” for different surface-to-core ratios of the exchange coupling constants. It is also shown that the profile of the local magnetisation exhibits strong temperature dependence, and that surface anisotropy is responsible for the non saturation of the magnetisation at low temperatures. Received 1 September 1999 and Received in final form 3 November 1999     

Experimental demonstration and stochastic modeling of autonomous formation of nanophotonic droplets

We have previously demonstrated a novel technique for autonomously forming a nanophotonic droplet, which is micro-scale spherical polymer structure that contains paired heterogeneous nanometric components. The sort-selectivity and alignment accuracy of the nanometric components in each nanophotonic droplet, and the related homogeneity of the optical function, are due to a characteristic pairing process based on a phonon-assisted photo-curing method. The proposed method requires irradiating a mixture of components with light to induce optical near-field interactions between each component, and subsequent processes based on these interactions. The pairing yield of components via the interactions is considered to mainly depend on the frequency of their encounters and the size-resonance effect between encountered components. In this paper, we model these two factors by individual stochastic procedures and construct a numerical model to describe the pairing process. Agreement between the results of numerical and experimental demonstrations shows the validity of our stochastic modeling.     

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.     

非球形效应对强声场中次Bjerknes力的影响

考虑了非球形气泡在声场中的形状振动,推导了非球形气泡和球形气泡之间的次Bjerknes力方程,数值模拟了声场中非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡之间的次Bjerknes力,并对非球形气泡和球形气泡之间的次Bjerknes力的影响因素进行了分析讨论.研究结果表明:当驱动声压振幅大于非球形气泡的Black阈值且又能使得非球形气泡稳定振动时,在第一个声驱动周期内,非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡的次Bjerknes力方向差异较大,在大小上是两个球形气泡次Bjerkens力的数倍,且有着更长的作用距离.非球形气泡和球形气泡之间的次Bjerknes力取决于非球形气泡的形状模态、两个气泡初始半径的比值、驱动声压振幅、气泡间距和两个气泡的相对位置.     

Hydrodynamic interaction between two rotating tori

The hydrodynamic interactions between two rotating tori is studied. Two kinds of problems are addressed. The interaction between two force free tori is examined, for co and counter rotating cases, which should be relevant in the case of swimming of two toroidal animals and form the basis for interaction of a swarm of such swimmers, apart from the dynamics of a collection of stiff polymer rings. The second problem is the case of two non-translating rotating tori, a possible configuration in toroidal mixers for microfluidic devices. In the former case, analytical expression for translational velocity shows good agreement with the theory in the far field case and show a strong reduction in the velocities in the lubrication limit for the co-rotating case. The velocities are found to monotonically reduce to zero in the case of counter-rotating tori. For the latter case, the expression for velocity field is derived the net force acting on the torus is analytically calculated. The comparison with numerical results is encouraging both in the case of co as well as counter-rotation. The expressions derived for velocities should be useful in estimating pseudo-potentials between such pairs.