流体动力学作用对粒子聚集影响的布朗动力学模拟

采用布朗动力学模拟方法, 研究了流体动力学作用对稀溶液中悬浮粒子聚集过程的影响. 模拟中忽略了一个粒子同时与多个粒子碰撞聚集的可能, 引入了前人有关两粒子间流体动力学作用影响的研究成果. 模拟结果证实了流体动力学的作用在比较大的幅度上减缓了粒子的聚集过程, 是导致粒子聚集速率的实验值低于Smoluchowski理论值的重要原因之一. 另外, 在分别加入和排除重力作用, 以及考虑和忽略粒子间流体动力学作用在内的各种条件下模拟了粒子的聚集过程, 得到了两种因素相互耦合作用时各因素对粒子聚集过程影响的结果, 并从动力学的角度对这些因素的影响机制进行了相应的讨论.     

Computer simulation on the collision-sticking dynamics of two colloidal particles in an optical trap

Collisions of a particle pair induced by optical tweezers have been employed to study colloidal stability. In order to deepen insights regarding the collision-sticking dynamics of a particle pair in the optical trap that were observed in experimental approaches at the particle level, the authors carry out a Brownian dynamics simulation. In the simulation, various contributing factors, including the Derjaguin-Landau-Verwey-Overbeek interaction of particles, hydrodynamic interactions, optical trapping forces on the two particles, and the Brownian motion, were all taken into account. The simulation reproduces the tendencies of the accumulated sticking probability during the trapping duration for the trapped particle pair described in our previous study and provides an explanation for why the two entangled particles in the trap experience two different statuses.     

The influence of bond rigidity and cluster diffusion on the self-diffusion of hard spheres with square well interaction

Hard spheres interacting through a square well potential were simulated by using two different methods: Brownian cluster dynamics (BCD) and event driven Brownian dynamics (EDBD). The structure of the equilibrium states obtained by both methods was compared and found to be almost identical. Self-diffusion coefficients (D) were determined as a function of the interaction strength. The same values were found by using BCD or EDBD. Contrary to EDBD, BCD allows one to study the effect of bond rigidity and hydrodynamic interaction within the clusters. When the bonds are flexible, the effect of attraction on D is relatively weak compared to systems with rigid bonds. D increases first with increasing attraction strength, and then decreases for stronger interaction. Introducing intracluster hydrodynamic interaction weakly increases D for a given interaction strength. Introducing bond rigidity causes a strong decrease in D which no longer shows a maximum as function of the attraction strength.     

Reversible coagulation of colloidal suspension in shallow potential wells: Direct numerical simulation

Brownian dynamics computer simulations of aggregation in 2D colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. The chosen mathematical model enables to predict the correct values of diffusion coefficient of freely moving particle, the mean value of kinetic energy for each particle in ensemble of interacting colloidal particles and residence times of colloidal particles inside the potential wells of different depths. The simulations allow monitoring formation and breakage of clusters in a suspension as well as time dependence of the mean cluster size. The article is published in the original.     

电解质水溶液传递性质的布朗动力学模拟研究

在传统布朗动力学的基础上, 考虑流体力学的影响, 并且引入Smart Monte Carlo方法的接受概率, 对电解质溶液进行布朗动力学模拟, 得到不同浓度和温度下KCl溶液中离子间的径向分布函数, 并且与超网链积分方程理论计算结果进行了比较, 同时, 模拟了KCl和NaCl溶液的摩尔电导率. 模拟过程基于电解质溶液的原始模型, 溶剂被看作连续介质, 溶质分子之间的相互作用采用软核加静电的势能函数模型, 长程静电力的处理采用Ewald加和方法. 结果显示, 流体力学的作用对于电解质溶液的结构性质没有明显的影响, 但是对于传递性质的影响显著; 考虑流体力学作用的布朗动力学模拟结果与实验数据吻合良好.     

Computer simulations of diffusion and dynamics of short-chain polyelectrolytes

Brownian dynamics simulations are conducted to investigate the diffusional and dynamic properties of polyelectrolytes in dilute salt-free solutions. The polyelectrolyte molecule is represented by a bead-spring chain in a primitive model. The long-range hydrodynamic and Coulomb interactions are both taken into consideration through the Ewald summations for the first time. The major finding of our simulations is that the dependence of the long-time chain diffusivity on the Coulomb interaction strength is very different from that of the Kirkwood short-time diffusivity, which simply shows a trend nearly opposite to the chain size. When ignoring the hydrodynamic interaction (HI), the coupling effect between the chain and its counterions gives rise to a noticeable increase in the long-time diffusivity at intermediate electrostatic interaction strengths. However, the incorporation of HI suppresses this effect to a degree that one can no longer discern it. Moreover, the rotational relaxation is found to show a dependence opposite to that of the gyration radius relaxation.     

Brownian dynamics investigation of magnetization and birefringence relaxations in ferrofluids

Brownian dynamics simulations are used to investigate the dynamics of orientational properties of real charge-stabilized ferrofluids, i.e. stable colloidal dispersions of magnetic nanoparticles. The relaxation times of the magnetization and of the birefringence, data accessible by experimental techniques, have been computed at several volume fractions. Besides, the effect of hydrodynamic interactions has been investigated. Equilibrium simulations without field are found to be inadequate to determine the aforementioned relaxation times for the systems under study, the dipolar interaction being too weak. Thus a nonequilibrium simulation procedure that mimics the experimental operating mode has been developed. After equilibrium simulations under a magnetic field, both birefringence and magnetization decays are recorded once the field is suppressed. Birefringence and magnetization decays are markedly impeded as the volume fraction increases, whereas they are barely enhanced when the intensity of the initial magnetic field is increased at a fixed volume fraction. Eventually, hydrodynamic interactions exhibit a slight but systematic lengthening of the relaxation times.     

Strong effect of hydrodynamic coupling on the electric dichroism of bent rods

The effect of hydrodynamic coupling on the spatial orientation of rigid bent rods in electric fields has been analyzed by Brownian dynamics simulations. Bead models for smoothly bent rods were constructed with dimensions of DNA double helices, and established simulation procedures were used to calculate their diffusion tensor, including the translational-rotational coupling tensor. The electric and optical parameters were assigned on the basis of known properties of double helices. Brownian dynamics simulations of the orientation of these models in electric fields showed that both transients and amplitudes of the calculated dichroism are very strongly dependent on translational-rotational coupling over a wide range of electric field strengths. For example, the stationary dichroism of a smoothly bent 179 bp DNA fragment calculated at low field strengths is positive in the presence and negative in the absence of hydrodynamic coupling. The transients are converted from a biphasic to a monophasic shape, when hydrodynamic coupling is turned off. The large changes resulting from hydrodynamic coupling were controlled by calculations based on analytical expressions derived for electrooptical response curves in the limit of low electric field strengths; the results obtained by this independent approach are in very satisfactory agreement with our Brownian dynamics simulations. The effect is strongly dependent on the electric dipole and on its direction. In the absence of any dipole the coupling effect was not observed. The coupling effect increases with the size of the bent rods. Because most macromolecular structures are known to have induced and/or permanent dipole moments, large effects of hydrodynamic coupling on both the amplitudes and the transients of the electric dichroism/birefringence must be expected in general for structures with nonsymmetric shape.     

Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles

We introduce a "virtual-move" Monte Carlo algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an important realization being self-assembling particles endowed with strong, short-ranged, and angularly specific ("patchy") attractions. Standard Monte Carlo techniques employ sequential updates of particles and can suffer from low acceptance rates when attractions are strong. In this event, collective motion can be strongly suppressed. Our algorithm avoids this problem by proposing simultaneous moves of collections (clusters) of particles according to gradients of interaction energies. One particle first executes a "virtual" trial move. We determine which of its neighbors move in a similar fashion by calculating individual bond energies before and after the proposed move. We iterate this procedure and update simultaneously the positions of all affected particles. Particles move according to an approximation of realistic dynamics without requiring the explicit computation of forces and without the step size restrictions required when integrating equations of motion. We employ a size- and shape-dependent damping of cluster movements, motivated by collective hydrodynamic effects neglected in simple implementations of Brownian dynamics. We discuss the virtual-move algorithm in the context of other Monte Carlo cluster-move schemes and demonstrate its utility by applying it to a model of biological self-assembly.     

Effect of molecular topology on the transport properties of dendrimers in dilute solution at Theta temperature: a Brownian dynamics study

Structure and transport properties of dendrimers in dilute solution are studied with the aid of Brownian dynamics simulations. To investigate the effect of molecular topology on the properties, linear chain, star, and dendrimer molecules of comparable molecular weights are studied. A bead-spring chain model with finitely extensible springs and fluctuating hydrodynamic interactions is used to represent polymer molecules under Theta conditions. Structural properties as well as the diffusivity and zero-shear-rate intrinsic viscosity of polymers with varied degrees of branching are analyzed. Results for the free-draining case are compared to and found in very good agreement with the Rouse model predictions. Translational diffusivity is evaluated and the difference between the short-time and long-time behavior due to dynamic correlations is observed. Incorporation of hydrodynamic interactions is found to be sufficient to reproduce the maximum in the intrinsic viscosity versus molecular weight observed experimentally for dendrimers. Results of the nonequilibrium Brownian dynamics simulations of dendrimers and linear chain polymers subjected to a planar shear flow in a wide range of strain rates are also reported. The flow-induced molecular deformation of molecules is found to decrease hydrodynamic interactions and lead to the appearance of shear thickening. Further, branching is found to suppress flow-induced molecular alignment and deformation.     

Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing Brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the Brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N(2)) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the "block" version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10 000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing large-scale Brownian dynamics simulations with hydrodynamic interactions.     

Excluded volume effects on the intrachain reaction kinetics

On the basis of the recently developed optimized Rouse-Zimm theory of chain polymers with excluded volume interactions, we calculate the long-time first-order rate constant k(1) for end-to-end cyclization of linear chain polymers. We first find that the optimized Rouse-Zimm theory provides the longest chain relaxation times tau(1) of excluded volume chains that are in excellent agreement with the available Brownian dynamics simulation results. In the free-draining limit, the cyclization rate is diffusion-controlled and k(1) is inversely proportional to tau(1), and the k(1) values calculated using the Wilemski-Fixman rate theory are in good agreement with Brownian dynamics simulation results. However, when hydrodynamic interactions are included, noticeable deviations are found. The main sources of errors are fluctuating hydrodynamic interaction and correlation hole effects as well as the non-Markovian reaction dynamic effect. The physical natures of these factors are discussed, and estimates for the magnitudes of required corrections are given. When the corrections are included, the present theory allows the prediction of accurate k(1) values for the cyclization of finite-length chains in good solvents as well as the correct scaling exponent in the long-chain limit.     

Hydrodynamic interactions induce movement against an external load in a ratchet dimer Brownian motor

We use the Brownian dynamics with hydrodynamic interactions simulation in order to describe the movement of a elastically coupled dimer Brownian motor in a ratchet potential. The only external forces considered in our system were the load, the random thermal noise and an unbiased thermal fluctuation. For a given set of parameters we observe direct movement against the load force if hydrodynamic interactions were considered.     

Screening of hydrodynamic interactions in Brownian rod suspensions

We present the details and results of a simulation study addressing the dynamics and rheology of rod suspensions over a wide regime of concentrations ranging from dilute to concentrated systems. Our study compares the results of two complementary simulation methods. The first method adapts a recently proposed explicit solvent simulation strategy and incorporates both hydrodynamical effects and steric interactions between the rod units. We compare the results of such a method with those obtained from a Brownian dynamics simulation approach which retains the steric interactions but neglects the effects of hydrodynamic interactions. Overall, our results in the context of the translational and rotational diffusivities are in agreement with the hydrodynamical predictions in the dilute regime and the corresponding results of the tube model and its extensions thereof in the semidilute regimes. The latter results suggest that effects of hydrodynamic interactions on the translational and rotational diffusivities are secondary relative to the steric interactions and at best lead only to a small correction to the results of the classical tube model. Our results in the context of linear viscoelasticity also broadly confirms the predictions of the tube model for the storage and loss moduli and allows us to extract for the first time the independent hydrodynamic and Brownian contributions to the zero shear viscosity. While the relative magnitudes of these contributions are consistent with the theoretical predictions, the quantitative magnitudes are quite different from the theoretical predictions. Overall, these results confirm the validity of the hydrodynamic "screening" hypothesis and ratify the neglect of hydrodynamical stresses in quantifying the linear rheology of Brownian rod suspensions.     

Pair diffusion, hydrodynamic interactions, and available volume in dense fluids

We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard sphere particles in a dense monodisperse fluid. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from molecular dynamics simulations. At distances exceeding ~3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with predictions from exact macroscopic hydrodynamic theory for large Brownian particles suspended in a solvent bath, as well as the Oseen approximation. However, the asymptotic 1/r distance dependence of D(r) associated with hydrodynamic effects emerges only after the pair distance dynamics has been followed for relatively long times, indicating non-negligible memory effects in the pair diffusion at short times. Deviations of the calculated D(r) from the hydrodynamic models at short distances r reflect the underlying many-body fluid structure, and are found to be correlated to differences in the local available volume. The procedure used here to determine the pair diffusion coefficients can also be used for single-particle diffusion in confinement with spherical symmetry.     

电解质溶液自扩散系数的布朗动力学模拟

采用布朗动力学方法对电解质溶液进行了模拟,在传统布朗动力学的基础上综合考虑了流体力学的影响,并且引入SmartMonteCarlo方法的接受概率,避免了离子不现实的移动和位型重叠,这样不仅可以将模拟过程中的时间步长大幅度提高,而且还可使溶质在相空间的演化过程更接近实际.模拟过程以电解质溶液的原始模型为基础,将溶剂看作连续介质,溶质分子之间的相互作用采用软核加静电的势能函数模型,长程静电力采用Ewald加和的处理方法.模拟得到KCl和NaCl溶液的径向分布函数g+-(r),g++(r)和g--(r),并与文献中HNC计算以及模拟的结果进行比较,使用推广的Green-Kubo公式模拟计算溶液中各种离子的自扩散性质,计算结果与实验数据吻合良好.     

Boëder PDF Brownian simulations for macromolecular rod-like particles near uneven solid surfaces

A molecular dynamics simulation is presented to calculate the Probability Distribution Functions (PDF) for the spatial positions and angular orientations of macromolecular rod-like particles in dilute solutions, under hydrodynamic flow, in the vicinity of uneven solid boundaries. The Brownian and hydrodynamic restitution model for ideally flat surfaces is generalized to simulate the diffusive collisions between the macromolecular particles and an uneven solid surface. Two types of uneven surfaces are particularly considered: the periodic grating and the random rough, with characteristic profiles of heights and lateral variations. Different from ideally flat surfaces, the simulation results demonstrate that uneven surfaces have characteristic depletion layers, and characteristic and variable PDF. This is the case under varying conditions of hydrodynamic flow, Brownian movement and diffusive collisions. These characteristics uniquely identify Boeder PDF signatures for the uneven surface topography.     

Brownian dynamics simulations with stiff finitely extensible nonlinear elastic-Fraenkel springs as approximations to rods in bead-rod models

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.     

Brownian dynamics simulations of a flexible polymer chain which includes continuous resistance and multibody hydrodynamic interactions

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the "freely draining" case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.