Failure and success of hydrodynamic interaction models

In suspensions with charged particles, electrostatic forces and hydrodynamic interactions are both important to describe the system. We study different models of hydrodynamic interaction for monopolarly charged particles in a non-polar liquid. In this case, there is no screening of the Coulomb repulsion, so the repulsion between all pairs must be taken into account. The particles are expected to drift away from each other, however at a lower rate when hydrodynamic interaction between the particles is taken into account. Existing, frequently used models of hydrodynamic interactions tend to overestimate the slowing down of the charged particles, even to the extent that the particles effectively attract each other. This is demonstrated for some selected particle setups. We find that these anomalies even occur in dilute systems, if they contain sufficiently many particles. We explain why these anomalies can be avoided by an approach, in which the superposition of interactions is done in the friction tensor instead of the mobility tensor.     

Experimental investigation of dipolar interaction in suspensions of magnetic nanoparticles

The structure and the magnetisation behaviour of two different systems of magnetic nanoparticles (MNP), namely Resovist^® with a wide core size distribution (diameter, σ=0.3) and SHP-20 with a rather narrow distribution (σ=0.1), were investigated by magnetorelaxometry (MRX) and magnetisation measurements in a wide concentration range. MRX on fluid and solid suspensions yielded the distribution of hydrodynamic diameters and effective magnetic anisotropy energies (E_A), where towards higher iron concentrations the spatial particle correlation, i.e. aggregation, and also the width of the E_A distribution were increased significantly. It was further found that these effects quantitatively depend on the suspension medium, where an increased salt concentration enhanced the aggregate size distribution and E_A dispersion. At mentioned higher MNP concentrations, the quasistatic magnetisation, normalised with respect to the iron content, decreased by up to 40%. In the case of SHP-20, where single core MNPs dominate, the maximum of this drop down of the magnetisation occurred at a field strength that corresponds to the strength of mean squared dipolar interaction.     

Kinetics of internal structures growth in magnetic suspensions

The kinetics of aggregation of non Brownian magnetizable particles in the presence of a magnetic field is studied both theoretically and by means of computer simulations. A theoretical approach is based on a system of Smoluchowski equations for the distribution function of the number of particles in linear chain-like aggregates. Results obtained in the two dimensional (2D) and three dimensional (3D) models are analyzed in relation with the size of the cell, containing the particles, and the particle volume fraction φ$\phi$. The theoretical model reproduces the change of the aggregation kinetics with the size of the cell and with the particle volume fraction as long as the lateral aggregation of chains is negligible.     

Electrically guided assembly of planar superlattices in binary colloidal suspensions

Binary colloidal suspensions are assembled into planar superlattices using ac electric fields. Either triangular or square-packed arrays form, depending on the frequency and relative particle concentrations. The frequency dependence is striking since superlattices develop at low and high frequencies but not at intermediate frequencies. We explain the low frequency behavior (<3 kHz) in terms of induced-dipole repulsion balanced by attraction resulting from electrohydrodynamic (EHD) flow. At high frequencies (20-200 kHz), EHD flow is negligible but aggregation occurs since dipole-dipole interactions become attractive.     

Effective screening of hydrodynamic interactions in charged colloidal suspensions

We investigate the hydrodynamic interaction in suspensions of charged colloidal silica spheres. The volume fraction as well as the range of the electrostatic repulsion between the spheres is varied. Using a combination of dynamic x-ray scattering, cross-correlated dynamic light scattering, and small angle x-ray scattering, the hydrodynamic function H(q) is determined experimentally. The effective hydrodynamic interactions are found to be screened, if the range of the direct interaction is relatively long and the static density correlations are strong. This observation of effective hydrodynamic screening is in marked contrast to hard-sphere-like systems.     

Lattice-Boltzmann Simulation of Particle Suspensions in Shear Flow

Inclusion of short-range particle–particle interactions for increased numerical stability in a lattice-Boltzmann code for particle-fluid suspensions, and handling of the particle phase for an effective implementation of the code for parallel computing, are discussed and formulated. In order to better understand the origin of the shear-thickening behavior observed in real suspensions, two simplified cases are considered with the code thus developed. A chain-like cluster of suspended particles is shown to increase the momentum transfer in a shear flow between channel walls, and thereby the effective viscosity of the suspension in comparison with random configurations of particles. A single suspended particle is also shown to increase the effective viscosity under shear flow of this simple suspension for particle Reynolds numbers above unity, due to inertial effects that change the flow configuration around the particle. These mechanisms are expected to carry over to large-scale particle-fluid suspensions.     

A Comparative Study of the Determination of Ferrofluid Particle Size by Means of Rotational Brownian Motion and Translational Brownian Motion

Two methods, the Toroidal Technique and the Forced Rayleigh Scattering (FRS) method, were used in the determination of the size of magnetic particles and their aggregates in magnetic fluids. The toroidal technique was used in the determination of the complex, frequency dependent magnetic susceptibility, x(w)=x'(w) - ix"(w) of magnetic fluids consisting of two colloidal suspensions of cobalt ferrite in hexadecene and a colloidal suspension of magnetite in isopar m with corresponding saturation magnetisation of 45.5 mT, 20 mT and 90 mT, respectively. Plots of the susceptibility components against frequency f over the range 10 Hz to 1 MHz, are shown to have approximate Debye-type profiles with the presence of relaxation components being indicated by the frequency, f _max, of the maximum of the loss-peak in the x"(w) profiles. The FRS method (the interference of two intense laser beams in the thin film of magnetic fluid) was used to create the periodical structure of needle like clusters of magnetic particles. This creation is caused by a thermodiffusion effect known as the Soret effect. The obtained structures are indicative of as a self diffraction effect of the used primary laser beams. The relaxation phenomena arising from the switching off of the laser interference field is discussed in terms of a spectrum of relaxation times. This spectrum is proportional to the hydrodynamic particle size distribution. Corresponding calculations of particle hydrodynamic radius obtained by both mentioned methods indicate the presence of aggregates of magnetic particles.     

Inclusion of magnetic dipole-dipole and hydrodynamic interactions in implant-assisted magnetic drug targeting

Mathematical modelling of the implant-assisted magnetic drug targeting system of Avilés, Ebner and Ritter is performed. In order to model the agglomeration of particles known to occur in this system, the magnetic dipole-dipole and hydrodynamic interactions are included. Such interactions were calculated previously by Mikkelsen et al. under low magnetic fields (~0.05 T) in microfluidic systems. Here, a higher magnetic field (0.7 T) is considered and the effect of interactions on two nanoparticles with a seed implant is calculated. The calculations were performed with the open-source software OpenFOAM. Different initial positions are considered and the system performance is assessed in terms of capture cross section. Inclusion of both interactions was seen to alter the capture cross section of the system by up to 7% in absolute terms.     

Aggregation and Deposition Characteristics of Fullerene Nanoparticles in Aqueous Systems

The propensity of n-C₆₀ to aggregate and deposit will play a key role in determining its longevity in aquatic systems, and therefore the potential exposure and risk presented by these colloids. We consider the origin of n-C₆₀ stability and compare the aggregation and deposition characteristics of n-C₆₀ under conditions of variable ionic strength using an indifferent electrolyte. Relatively weak electrolyte solutions (0.001 M) were observed to destabilize suspensions of n-C₆₀ resulting in the formation of settleable aggregates. This behavior supports the hypothesis that the stabilizing mechanism for n-C₆₀ clusters is electrostatic in origin. Similarly, the deposition of n-C₆₀ in porous media increased as ionic strength increased. These observations suggest that under some conditions present in natural aquatic systems, these materials may have limited mobility as they form large aggregates that may settle out of suspension or deposit on surfaces. These phenomena may, at least partially, offset any risk presented by n-C₆₀ toxicity due to a reduced potential for exposure.     

Settling and fluidization of non Brownian hard spheres in a viscous liquid

A mean field approach is used to estimate the energy dissipation during the homogeneous sedimentation or the particulate fluidization of non Brownian hard spheres in a concentrated suspension of infinite extent. Depending on inertial screening and the range of the hydrodynamic interactions, the effective buoyancy force is determined either from the average suspension density in a Stokes flow or from the fluid density in the turbulent flow regime. An energy balance then yields a settling or fluidization law depending on the particle Reynolds number in reasonable agreement with the Richardson and Zaki correlation and recent experimental results for particle settling or fluidization. We further estimate the energy dissipation in the turbulent boundary layers around the particles to precise the Reynolds number dependence of the hindered settling function in the intermediate flow regime. Received 22 February 1999 and Received in final form 14 June 1999     

A simple method to estimate the magnetic moment of magnetic micro-particles

Micro-particles in suspension in a fluid are an example of a very low Reynolds number problem. In this case, no inertial effects are observed. Magnetic micro-particles with magnetic moment m, suspended in a fluid orient to applied external magnetic fields B due to the interaction between the field and the magnetic moment. In this work, we present a simple method to estimate the total magnetic moment of magnetic micro-organisms. The method is based on the application of an external oscillating magnetic field in the sites where the micro-organisms are. In this case, it is possible to obtain theoretically the solution of the equation of motion (rotation of the organism and its trajectory). The solution is a transcendental equation relating the orientation angle and m and can be solved by numerical methods. Changing the frequency and/or the field intensity, it is possible to obtain a situation in which the crystal rotates uninterruptedly (a resonance regime). This condition is related to the applied field intensity, to the frequency, to the medium viscosity, to the crystal dimension, and to the micro-crystal magnetic moment m. The method can be used to estimate the total cellular magnetic moment of magnetic micro-particles.     

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.     

Electrostatic interaction of a spherical particle in the vicinity of a circular orifice

The electrostatic interaction of a charged spherical particle in the vicinity of an orifice plane has been investigated in this paper.The particle can creep along the axis of the orifice and is immersed in a bulk electrolyte.By solving the Poisson-Boltzmann problem,we have obtained the effective electrostatic interaction for several values of reduced orifice radius h,including the cases of h > 1,h = 1 and h < 1.Two kinds of boundary conditions of the orifice plane are considered.One is the constant potential model corresponding to a conducting plane,the other is the constant charge model.In the constant potential model,there is an electrostatic attraction between the particle and the orifice plane when they get close to each other,while there is a pure electrostatic repulsion in the constant charge model.The interactions in both boundary models are sensitive to the parameters of the reduced orifice radius,the reduced particle-orifice distance,surface charge densities of the particle and orifice plane,and the reduced Debye screen constant corresponding to the salt-ion concentration and ion valence.     

Simulation method of colloidal suspensions with hydrodynamic interactions: fluid particle dynamics

We develop a new simulation method of colloidal suspensions, which we call a "fluid particle dynamics" (FPD) method. This FPD method, which treats a colloid as a fluid particle, removes the difficulties stemming from a solid-fluid boundary condition in the treatment of hydrodynamic interactions between the particles. The importance of interparticle hydrodynamic interactions in the aggregation process of colloidal particles is demonstrated as an example. This method can be applied to a wide range of problems in colloidal science.     

Magnetophoresis and diffusion of colloidal particles in a thin layer of magnetic fluids

Experimental and theoretical studies were carried out to investigate the spatial distribution of colloidal particles in magnetic fluids formed under the influence of magnetophoresis and gradient diffusion in a strong magnetic field. Several theoretical models, describing the equilibrium concentration profiles for rigid chain-like and quasispherical aggregates, are discussed. The experiment was made for four samples of magnetic fluids, differing in the average diameter of magnetic particles and the width of the particle size distribution. The analysis of the experimental data shows that the aggregates essentially change the concentration profile, making it nonlinear even in small (2 mm) magnetic fluid samples. Good agreement between the experimental and theoretical curves is observed in the case when the aggregates contain on the average 40-50 particles. The average diameter of single particles, calculated from the concentration profile curves, coincides with the average diameter, found from the magnetogranulometric analysis.     

Quasi-2D Monte Carlo simulations of a colloidal dispersion composed of magnetic plate-like particles with magnetic moment normal to the particle axis

We have investigated aggregation phenomena of a colloidal dispersion composed of magnetic plate-like particles by means of Monte Carlo simulations. Such plate-like particles have been modelled as disk-like particles with magnetic moment normal to the particle axis at the particle centre, with the section shape of a spherocylinder. The main objective of the present study is to clarify the influences of the magnetic field strength and magnetic interactions between particles on particle aggregation phenomena. We have concentrated our attention on a quasi-2D system from an application point of view such as the development of surface quality changing technology using such magnetic plate-like particles. A magnetic field is applied along the direction perpendicular to the plane of the monolayer. Internal structures of particle aggregates are discussed quantitatively in terms of radial distribution and orientational pair correlation functions. For the case of strong magnetic interactions between particles, particles form long column-like clusters with their magnetic moments alternating in direction between the neighbouring particles. These tendencies appear under circumstances of a weak applied magnetic field. However, as the magnetic field strength increases, particles incline towards the magnetic field direction, so that particles do not form such clusters.     

优化磁共振纳米医学中磁性纳米粒子的热疗效率

磁共振热疗(magnetic resonance hyperthermia)是近年来新兴的一种纳米医学治疗方法,由磁共振的硬件架构产生特定交变磁场,有效地加热磁性纳米粒子,以直接或间接地杀死癌细胞,体现诊疗一体化。提高磁性纳米粒子的加热效率是当前磁共振热疗领域亟待解决的难题之一。磁性纳米粒子的加热效率不仅与粒子本身的大小、性质以及尺寸分布有关,还和聚集状态有关。该研究利用3D Metropolis蒙特卡罗模拟方法,模拟了不同温度下磁性纳米粒子的磁共振热动力学行为及其团聚与分离现象;并通过修正过的郎之万方程,建立了相变临界温度与外加磁场频率的函数关系。模拟结果显示,磁性纳米粒子悬浮液中多聚体的相对含量随着温度的升高而降低,达到临界温度后,多聚体完全分离成单体;而提高交变磁场频率可以显著降低临界温度,且存在临界频率,高于此临界频率后临界温度不再受外加磁场频率影响,达到稳定。因而在临界频率下预热磁性纳米粒子悬浮液,使得多聚体分离成单体,可优化磁性纳米粒子的热疗效率。     

Particles size effects of single domain CoFe2O4 on suspensions stability

Single domain magnetic CoFe₂O₄ nanoparticles with spinel structure were prepared by the coprecipitation method. Particles with size of 16, 20, 40 and 60 nm were synthesized by sintering the precursor at 500, 600, 800 and 900 °C, respectively. The magnetic hysteresis measurement of CoFe₂O₄ particles showed that particles were single domain particles with similar saturation magnetization (∼300 emu/cm³) at room temperature. The zeta potential study of suspensions (CoFe₂O₄-acetylacetone system) with various particle sizes showed the suspension systems had similar zeta potential values (∼40 mV). The effects of magnetic particle size on the suspension stability characterized by electrophoretic deposition yields and sediment volumes were studied. The suspension stability decreased with an increase in particle size and a flocculation threshold of particle radius a was found at 30 nm. A suspension stability theory approaching to the phenomenon was established. The theory based on the DLVO theory was developed by introducing an extra magnetic interaction force. Dormann model was adopted, in which the magnetic interactions of two spherical nanoparticles were investigated in terms of dipole-dipole interactions. Compared to DLVO, suspension's physical parameters not only zeta potential ζ and the Debye length 1/κ, but also particles' radius a brought about stable to flocculation transition in the theory.     

Kinetic arrest in polyion-induced inhomogeneously charged colloidal particle aggregation

Polymer chains adsorbed onto oppositely charged colloidal particles can significantly modify the particle-particle interactions. For sufficient amounts of added polymers, the original electrostatic repulsion can even turn into an effective attraction and relatively large aggregates can form. The attractive interaction contribution between two particles arises from the correlated adsorption of polyions at the oppositely charged particle surfaces, resulting in a non-homogeneous surface charge distribution. Here, we investigate the aggregation kinetics of polyion-induced colloidal complexes through Monte Carlo simulation, in which the effect of charge anisotropy is taken into account by a DLVO-like inter-particle potential, as recentely proposed by Velegol and Thwar (Langmuir 17, 7687 (2001)). The results reveal that the aggregation process slows down due to the progressive increase of the potential barrier height upon clustering. Within this framework, the experimentally observed cluster phases in polyelectrolyte-liposome solutions can be interpreted as a kinetic arrested state.