Laser diffraction determination of the crystalline structure of an electrorheological fluid

Vacancy formation in a 1D chain of dust particles in a DC discharge

The paper presents the first experimental observation of an atypical phenomena during self-organization of dust particles into a one-dimensional chain structure levitated vertically in the plasma of a DC glow discharge. Using a laser, the third (middle) dust particle was removed from the chain of five particles so that the positions of the remaining particles did not significantly change, and a vacancy occurred in the place of the removed particle. This state of the chain turned out to be very stable, which is confirmed by the observation of the subsequent exchange of places of the fourth and the fifth particles of the chain upon the action of the laser on the forth particle. After the exchange process, vertical positions of all particles (first, second, fourth and fifth) in the chain remained almost the same as before the exchange, and the vacancy at the position of the third particle was preserved. The experimental data and the video record of the observed phenomena as well as the estimates of the plasma parameters are presented. An assumption has been made about the mechanism of the discovered phenomena that at present discharge conditions both the vacancy formation and the dust particles positions exchange are possible due to a strong ion wakes which are formed behind the upstream dust particles of the chain.

Long-term evolution of the three-dimensional structure of string-fluid complex plasmas in the PK-4 experiment

Microparticle suspensions in a polarity-switched discharge plasma of the Plasmakristall-4 facility on board the International Space Station exhibit string-like order. As pointed out in [Phys. Rev. Research 2, 033314 (2020)2643-156410.1103/PhysRevResearch.2.033314], the string-order is subject to evolution on the timescale of minutes at constant gas pressure and constant parameters of polarity switching. We perform a detailed analysis of this evolution using the pair correlations and length spectrum of the string-like clusters (SLCs). Average exponential decay rate of the SLC length spectrum is used as a measure of string order. The analysis shows that the improvement of the string-like order is accompanied by the decrease of the thickness of the microparticle suspension, microparticle number density, and total amount of microparticles in the field of view. This suggests that the observed long-term evolution of the string-like order is caused by the redistribution of the microparticles, which significantly modifies the plasma conditions.

Self-assembled wiggling nano-structures and the principle of maximum entropy production

While behavior of equilibrium systems is well understood, evolution of nonequilibrium ones is much less clear. Yet, many researches have suggested that the principle of the maximum entropy production is of key importance in complex systems away from equilibrium. Here, we present a quantitative study of large ensembles of carbon nanotubes suspended in a non-conducting non-polar fluid subject to a strong electric field. Being driven out of equilibrium, the suspension spontaneously organizes into an electrically conducting state under a wide range of parameters. Such self-assembly allows the Joule heating and, therefore, the entropy production in the fluid, to be maximized. Curiously, we find that emerging self-assembled structures can start to wiggle. The wiggling takes place only until the entropy production in the suspension reaches its maximum, at which time the wiggling stops and the structure becomes quasi-stable. Thus, we provide strong evidence that maximum entropy production principle plays an essential role in the evolution of self-organizing systems far from equilibrium.

Electrical conductivity equations derived with the rate process theory and free volume concept

Inspired by the Marcus theory of electron transfer, electrical conductivity equations without reference to any specific materials are derived on the basis of Eyring’s rate process theory and the free volume concept.

Suppressing turbulence and enhancing liquid suspension flow in pipelines with electrorheology

Flows through pipes, such as crude oil through pipelines, are the most common and important method of transportation of fluids. To enhance the flow output along the pipeline requires reducing viscosity and suppressing turbulence simultaneously and effectively. Unfortunately, no method is currently available to accomplish both goals simultaneously. Here we show that electrorheology provides an efficient solution. When a strong electric field is applied along the flow direction in a small section of pipeline, the field polarizes and aggregates the particles suspended inside the base liquid into short chains along the flow direction. Such aggregation breaks the rotational symmetry and makes the fluid viscosity anisotropic. In the directions perpendicular to the flow, the viscosity is substantially increased, effectively suppressing the turbulence. Along the flow direction, the viscosity is significantly reduced; thus the flow along the pipeline is enhanced. Recent field tests with a crude oil pipeline fully confirm the theoretical results.

Effect of external electric fields on the phase behavior of colloidal silica rods

We examine the effect of external electric fields on the behavior of colloidal silica rods. We find that the electric fields can be used to induce para-nematic and para-smectic phases, and to reduce the number of defects in smectic phases. At high field strengths, a new crystal structure was observed that consisted of strings of rods ordered in a hexagonal pattern in which neighboring rods were shifted along their length. We also present a simple model to describe this system, which we used in computer simulations to calculate the phase diagram for rods of L/D = 6, with L the end-to-end length of the rods and D the diameter of the rods. Our theoretical predictions for the phase behavior agree well with the experimental observations.

Driving self-assembly and emergent dynamics in colloidal suspensions by time-dependent magnetic fields

In this review we discuss recent research on driving self-assembly of magnetic particle suspensions subjected to alternating magnetic fields. The variety of structures and effects that can be induced in such systems is remarkably broad due to the large number of variables involved. The alternating field can be uniaxial, biaxial or triaxial, the particles can be spherical or anisometric, and the suspension can be dispersed throughout a volume or confined to a soft interface. In the simplest case the field drives the static or quasistatic assembly of unusual particle structures, such as sheets, networks and open-cell foams. More complex, emergent collective behaviors evolve in systems that can follow the time-dependent field vector. In these cases energy is continuously injected into the system and striking flow patterns and structures can arise. In fluid volumes these include the formation of advection and vortex lattices. At air-liquid and liquid-liquid interfaces striking dynamic particle assemblies emerge due to the particle-mediated coupling of the applied field to surface excitations. These out-of-equilibrium interface assemblies exhibit a number of remarkable phenomena, including self-propulsion and surface mixing. In addition to discussing various methods of driven self-assembly in magnetic suspensions, some of the remarkable properties of these novel materials are described.

Structure of electrorheological fluids: a dielectric study of chain formation

A dielectric measurement method has been proposed to apply to the study of the microstructure of electrorheological (ER) fluids. To test our measurement method the dielectric permittivity increment caused by pair and chain formation was measured in dilute Brownian ER fluids composed of silicone oil and nanosized silica particles. The critical values of the electric field required to induce structure formation were experimentally determined from the electric field dependence of the measured permittivity increment. From the electric field induced time evolution of the relative permittivity of ER fluids, the characteristic times of the pair and chain formation were calculated. Our experimental results for the time constants are in good agreement with the corresponding theoretical data obtained from the Eyring theory.

Self-assembly of colloidal particles into strings in a homogeneous external electric or magnetic field

Colloidal particles with a dielectric constant (magnetic susceptibility) mismatch with the surrounding solvent acquire a dipole moment in a homogeneous external electric (magnetic) field. The resulting dipolar interactions can lead to aggregation of the particles into string-like clusters. Recently, several methods have been developed to make these structures permanent. However, especially when multiple particle sizes and/or more complex shapes than single spheres are used, the parameter space for these experiments is enormous. We therefore use Monte Carlo simulations to investigate the structure of the self-assembled string-like aggregates in binary mixtures of dipolar hard and charged spheres, as well as dipolar hard asymmetric dumbbells. Binary mixtures of spheres aggregate in different types of clusters depending on the size ratio of the spheres. For highly asymmetric systems, the small spheres form ring-like and flame-like clusters around strings of large spheres, while for size ratios closer to 1, alternating strings of both large and small spheres are observed. For asymmetric dumbbells, we investigate both the effect of size ratio and dipole moment ratio, leading to a large variety of cluster shapes, including chiral clusters.

Self organization of exotic oil-in-oil phases driven by tunable electrohydrodynamics

Self organization of large-scale structures in nature - either coherent structures like crystals, or incoherent dynamic structures like clouds - is governed by long-range interactions. In many problems, hydrodynamics and electrostatics are the source of such long-range interactions. The tuning of electrostatic interactions has helped to elucidate when coherent crystalline structures or incoherent amorphous structures form in colloidal systems. However, there is little understanding of self organization in situations where both electrostatic and hydrodynamic interactions are present. We present a minimal two-component oil-in-oil model system where we can control the strength and lengthscale of the electrohydrodynamic interactions by tuning the amplitude and frequency of the imposed electric field. As a function of the hydrodynamic lengthscale, we observe a rich phenomenology of exotic structure and dynamics, from incoherent cloud-like structures and chaotic droplet dynamics, to polyhedral droplet phases, to coherent droplet arrays.

Droplet based microfluidics

Droplet based microfluidics is a rapidly growing interdisciplinary field of research combining soft matter physics, biochemistry and microsystems engineering. Its applications range from fast analytical systems or the synthesis of advanced materials to protein crystallization and biological assays for living cells. Precise control of droplet volumes and reliable manipulation of individual droplets such as coalescence, mixing of their contents, and sorting in combination with fast analysis tools allow us to perform chemical reactions inside the droplets under defined conditions. In this paper, we will review available drop generation and manipulation techniques. The main focus of this review is not to be comprehensive and explain all techniques in great detail but to identify and shed light on similarities and underlying physical principles. Since geometry and wetting properties of the microfluidic channels are crucial factors for droplet generation, we also briefly describe typical device fabrication methods in droplet based microfluidics. Examples of applications and reaction schemes which rely on the discussed manipulation techniques are also presented, such as the fabrication of special materials and biophysical experiments.

Simulation of a two-dimensional model for colloids in a uniaxial electric field

We perform Monte Carlo simulations of a simplified two-dimensional model for colloidal hard spheres in an external uniaxial ac electric field. Experimentally, the external field induces dipole moments in the colloidal particles, which in turn form chains. We therefore approximate the system as composed of well-formed chains of dipolar hard spheres of a uniform length. The dipolar interaction between colloidal spheres gives rise to an effective interaction between the chains, which we treat as disks in a plane, that includes a short-range attraction and long-range repulsion. Hence, the system favors finite clustering over bulk phase separation, and indeed we observe at low temperature and density that the system does form a cluster phase. As the density increases, percolation is accompanied by a pressure anomaly. The percolated phase, despite being composed of connected, locally crystalline domains, does not bear the typical signatures of a hexatic phase. At very low densities, we find no indication of a "void phase" with a cellular structure seen recently in experiments.

Structure parameter of electrorheological fluids in shear flow

A structure parameter, Sn = η(c)γ/τ(E), is proposed to represent the increase of effective viscosity due to the introduction of particles into a viscous liquid and to analyze the shear behavior of electrorheological (ER) fluids. Sn can divide the shear curves of ER fluids, τ/E(2) versus Sn, into three regimes, with two critical values Sn(c) of about 10(-4) and 10(-2), respectively. The two critical Sn(c) are applicable to ER fluids with different particle volume fractions φ in a wide range of shear rate γ and electric field E. When Sn < 10(-4), the shear behavior of ER fluids is mainly dominated by E and by shear rate when Sn > 10(-2). The electric current of ER fluids under E varied with shear stress in the same or the opposite trend in different shear rate ranges. Sn(c) also separates the conductivity variation of ER fluids into three regimes, corresponding to different structure evolutions. The change of Sn with particle volume fraction and E has also been discussed. The shear thickening in ER fluids can be characterized by Sn(c)(L) and Sn(c)(H) with a critical value about 10(-6). As an analogy to friction, the correspondence between τ/E(2) and friction coefficient, Sn and bearing numbers, as well as the similarity between the shear curve of ER fluids and the Stribeck curve of friction, indicate a possible friction origin in ER effect.

Self-assembly of nanoparticles into heterogeneous structures with gradient material properties

We present a mechanism to form self-assembled functional gradient superlattice structures by subjecting binary nanoparticles in an electric field. The interaction among different dipoles leads to the controllable formation of diverse structures, including particle columns with gradient material properties from inside to outside and various hierarchical layered or three-dimensional particle chain networks. We elucidate how permittivity, volume fraction, particle size, and the frequency of the electric field can be utilized to control the morphology of the induced structures, which would enable designed nanofabrication.

First observation of electrorheological plasmas

We report the experimental discovery of "electrorheological (ER) complex plasmas," where the control of the interparticle interaction by an externally applied electric field is due to distortion of the Debye spheres that surround microparticles (dust) in a plasma. We show that interactions in ER plasmas under weak ac fields are mathematically equivalent to those in conventional ER fluids. Microgravity experiments, as well as molecular dynamics simulations, show a phase transition from an isotropic to an anisotropic (string) plasma state as the electric field is increased.

Electrorheological fluids: structures and mechanisms

Electrorheology denotes the control of a colloid's flow properties through an electric field. We delineate the basic characteristics of electrorheological (ER) fluids, and show that the use of an effective dielectric constant concept can yield quantitative predictions. In particular, the ground state structure, the structural transition that occurs under crossed electric and magnetic fields, the high-field yield stress and its variation with particle size are all in good agreement with the experiments. The recently discovered giant electrorheological effect, owing its origin to molecular dipoles, is described and contrasted with the conventional ER effect that arises from induced polarization effects.

Field-induced columnar structures in a quasi-two-dimensional system of dipolar particles

We study the formation of columnar structures of uniaxial dipoles in an external magnetic field both experimentally and theoretically. By applying an external magnetic field parallel to a thin layer of a magnetorheological fluid, we manipulate a single initial cluster of suspended colloidal particles. We find that the cluster breaks up into columns that have approximately uniform widths and intercolumnar spacings. Both the average column width and inter column spacing are observed to vary linearly with column length. The observed linear relationships between column width and spacing versus the column length are interpreted theoretically by computing the potential energy of an ensemble of closed-packed columns of spherical dipolar particles.

Phase behavior of dipolar hard and soft spheres

We study the phase behavior of hard and soft spheres with a fixed dipole moment using Monte Carlo simulations. The spheres interact via a pair potential that is a sum of a hard-core Yukawa (or screened-Coulomb) repulsion and a dipole-dipole interaction. The system can be used to model colloids in an external electric or magnetic field. Two cases are considered: (i) colloids without charge (or dipolar hard spheres) and (ii) colloids with charge (or dipolar soft spheres). The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres shows, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and is in agreement with the experimental phase diagram [Nature (London) 421, 513 (2003)]. In both cases, the fluid phase is inhomogeneous but we find no evidence of a gas-liquid phase separation. The validity of the dipole approximation is verified by a multipole moment expansion.

Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field

Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field.

Phase behavior of polarizable spherocylinders in external fields

Applied electric fields are known to induce significant changes in the properties of systems of polarizable molecules or particles. For rod-shaped molecules, the field-induced behavior can be rather surprising, as in the case of the negative electric birefringence of concentrated solutions of rodlike polyelectrolytes. We have investigated the interplay of shape anisotropy and field-induced anisotropy in molecular dynamics simulations of systems of polarizable soft spherocylinders in an electric field, in the limit of infinitely anisotropic polarizability, taking full account of mutual induction effects. We find a novel crystalline structure (K(2)) in the high-field limit, whose formation is driven by interactions between induced dipoles. For high pressures, the phase diagram exhibits a polar nematic phase between the hexagonal close-packed crystal phase and the K(2) phase. We also compare this system with an analogous system of spherocylinders with permanent electric dipoles and find that qualitatively similar behavior is obtained in the limit of strong coupling of the permanent dipoles to the external field.

Patterns formed by paramagnetic particles in a horizontal layer of a magnetorheological fluid subjected to a dc magnetic field

We investigate the patterns formed by paramagnetic particles, which are dispersed in a liquid solvent subjected to a dc magnetic field. We calculate the dynamics of paramagnetic particles by the Brownian dynamics method based on the Langevin equation. We, in particular, focus on the effect of the system height on the pattern formations. We also discuss the mechanism of the pattern formations and the dynamics of the structure creation processes.

Ground state of a polydisperse electrorheological solid: beyond the dipole approximation

The ground state of an electrorheological (ER) fluid has been studied based on our recently proposed dipole-induced dipole (DID) model. We obtained an analytical expression of the interaction between chains of particles which are of the same or different dielectric constants. The effects of dielectric constants on the structure formation in monodisperse and polydisperse electrorheological fluids are studied in a wide range of dielectric contrasts between the particles and the base fluid. Our results showed that the established body-centered tetragonal ground state in monodisperse ER fluids may become unstable due to a polydispersity in the particle dielectric constants. While our results agree with that of the fully multipole theory, the DID model is much simpler, which offers a basis for computer simulations in polydisperse ER fluids.

Electrorheological Toners for Electrophotography

The electrorheological (ER) behavior of pigment suspensions dispersed in a nonaqueous solvent was examined for their application as liquid toners for electrophotography. In electric fields, particles can align into chains along the field vector by dielectric polarization forces and the suspensions undergo a rapid transition from Newtonian fluids to Bingham bodies. However, the migration and deposition of particles can take place by the electrophoretic effect, because charge control agents are added to liquid toners for fast development. The combined effects of dielectric polarization forces, electrophoretic forces, and hydrodynamic forces make rheological behavior very complicated. To simulate the ER behavior of liquid toners in reprographic processes, viscosity measurements were carried out in electrodes with a honeycomb pattern. Nonuniform electric fields enhance the dipole-dipole interactions between particles and give rise to a striking ER effect. Based on measurements in honeycomb pattern electrodes, new ER toners were developed which can reproduce images with high quality.

In Situ Sol–Gel Preparation of Polysaccharide/Titanium Oxide Hybrid Colloids and Their Electrorheological Effect

A new type of organic/inorganic hybrid colloid, made of modified carboxylmethyl starch (CMS) and titanium oxide (TiO(2)), was synthesized by an in situ sol-gel technique. IR spectra analysis shows strong a interaction of functional groups between two components, whose dispersion is almost at the molecular level. Due to the highly active surfaces hybrid particles and their characteristic dielectric behavior in accordance with the previous theoretic calculation, the suspensions of hybrids in silicone oil display a remarkable ER effect. The static yield stress can be above 20 kPa (shear rate 5 S(-1)) under a direct current field of 4 kV/mm at room temperature, much higher than that of simple blends of starch and titanium dioxide. In the meanwhile, the temperature dependence and sedimentation stability were optimized. Based on existing experimental results, we propose that dielectric properties and surface (interface) activity are two necessary conditions fulfilling the requirement of high ER activity. The combination of both factors may effectively reduce the activation energy needed for ERF restructuring.

Electrorheological suspensions

The objective of this article is to give a review of electrorheological (ER) suspensions whose rheological properties can abruptly change under an external electric field. Attention is given to the physical backgrounds behind ER phenomena reported recently. The criteria on how to design a high performance ER fluid and mechanisms explaining how an ER suspension displays the ER effect are focused upon. We begin with a brief historic introduction, ER materials, followed by positive ER effect, negative ER effect and photo-ER effect discussions. The physical parameters that can substantially affect the ER effect are discussed thereafter, and physical processes occurring in ER suspensions under an electric field are reviewed. The mechanisms of the ER effect proposed before are summarized. A future outlook on the ER material development and ER fluid applications is given.

Electrorheological Response and Structure Growth of Colloidal Silica Suspensions

The electrorheological response and structure growth of colloidal silica suspension was studied with in situ measurements of the shear stress, electric conductivity, and dielectric permittivity of the suspension. The measurements were carried out under steady and sweep shears after the application of an electric field of alternative current (100 Hz) using silica particles with a diameter of 630 nm and a water content of 4.5 wt%. The measurements of the conductivity enabled the detection of structure growth formed by particle aggregation and clarified that the development of the particle aggregation enlarged the dielectric permittivity and the shear stress. Hysteretic behavior observed in the electrorheological response was explained by considering structure growth of the particle aggregation. The correlation equation for the shear stress and the dielectric permittivity obtained in our previous work (1) was found to be applicable to the present results. Copyright 2001 Academic Press.

Crystal structures and freezing of dipolar fluids

We investigate the crystal structure of classical systems of spherical particles with an embedded point dipole at T=0. The ferroelectric ground state energy is calculated using generalizations of the Ewald summation technique. Due to the reduced symmetry compared to the nonpolar case the crystals are never strictly cubic. For the Stockmayer (i.e., Lennard-Jones plus dipolar) interaction three phases are found upon increasing the dipole moment: hexagonal, body-centered orthorhombic, and body-centered tetragonal. An even richer phase diagram arises for dipolar soft spheres with a purely repulsive inverse power law potential approximately r(-n). A crossover between qualitatively different sequences of phases occurs near the exponent n=12. The results are applicable to electro- and magnetorheological fluids. In addition to the exact ground state analysis we study freezing of the Stockmayer fluid by density-functional theory.

Magnetic-field-induced structural transitions in a ferrofluid emulsion

A ferrofluid emulsion, subjected to a slowly increasing magnetic field, exhibits a complicated structural behavior: a gas of Brownian particles changes to columnar solid structures due to induced dipole interaction. Two transition (intermediate) structural regimes are observed: (i) randomly distributed chains and particles and (ii) distinct thin columns and randomly distributed chains and particles. Three structural transition magnetic fields are found, one marking each structural transition, from the initial to the final structural regime. A structural diagram of the structural transition magnetic fields, H(C), versus particle volume fractions, straight phi, is constructed experimentally. Theoretical models of scaling calculations, based upon the dominant magnetic interaction in each structural regime, give the three structural transition magnetic-field relations as H(C1) proportional to straight phi(-1/2), H(C2) proportional to straight phi(-1/4), and H(C3) proportional to (straight phi(gamma)/G2)exp(piG/straight phi((gamma/2))), where gamma=0.39 and G=0.29 for our sample. The final end shape of columns and the relative position between columns show that the end-end repulsion between chains is important in the structural formation.

Time scales for structural formation in an electrorheological suspension probed by optical and electrical responses

Responses of the diffuse transmitted light intensity and the current passing through an electrorheological suspension to the stepwise electric field were measured in the quiescent state, and the time scales for the structural formation of the polarized particles were reported. It was found experimentally that both of the responses consist of plural modes, the faster and slower modes even in the quiescent state. The optical response was also expressed as an exponential function with two modes, which take place in succession.

Ground state of a dipolar crystal

We provide some of the strongest evidence to date that the ground state structure of an infinite collection of point dipoles with hardcore sphere interactions is body-centered tetragonal. The structure with the next highest binding energy is not face-centered cubic; a particular honeycomb structure has lower energy.

Phase behavior of aligned dipolar hard spheres: integral equations and density functional results

Using reference hypernetted chain integral equations, we investigate the phase behavior of a system of dipolar hard spheres with perfect orientational order. At low densities, the correlation functions show a strong tendency to the formation of head-to-tail chains. The occurrence of a condensation of the chains, as suggested by a recent simulation, is critically discussed. At higher densities the structure of the liquid phase already reflects well defined positions of the chains relative to each other, similar to a body-centered-tetragonal structure. Minimizing a density functional of the grand canonical free energy which is based on the liquid correlation functions, we calculate the coexistence lines at freezing. Interestingly, the system freezes at much lower temperatures than the corresponding isotropic fluid.