Theory of electrostatics and electrokinetics of soft particles

Abstract

We investigate theoretically the electrostatics and electrokinetics of a soft particle, i.e. a hard particle covered with an ion-penetrable surface layer of polyelectrolytes. The electric properties of soft particles in an electrolyte solution, which differ from those of hard particles, are essentially determined by the Donnan potential in the surface layer. In particular, the Donnan potential plays an essential role in the electrostatics and electrokinetics of soft particles. Furthermore, the concept of zeta potential, which is important in the electrokinetics of hard particles, loses its physical meaning in the electrokinetics of soft particles. In this review, we discuss the potential distribution around a soft particle, the electrostatic interaction between two soft particles, and the motion of a soft particle in an electric field.     

AC electrothermal manipulation of conductive fluids and particles for lab-chip applications

AC electrokinetics has shown great potential for microfluidic functions such as pumping, mixing and concentrating particles. So far, electrokinetics are typically applied on fluids that are not too conductive (<0.02 S/m), which excludes most biofluidic applications. To solve this problem, this paper seeks to apply AC electrothermal (ACET) effect to manipulate conductive fluids and particles within. ACET generates temperature gradients in the fluids, and consequently induces space charges that move in electric fields and produce microflows. This paper reports two new ACET devices, a parallel plate particle trap and an asymmetric electrode micropump. Preliminary experiments were performed on fluids with conductivity at 0.224 S/m. Particle trapping and micropumping were demonstrated at low voltages, reaching ~100 mum/s for no more than 8 Vrms at 200 kHz. The fluid velocity was found to depend on the applied voltage as V⁴, and the maxima were observed to be ~20 mum above the electrodes     

A numerical investigation of the potential of rubber and mineral particles for toughening of semicrystalline polymers

The impact strength of many semicrystalline polymers can be improved by the dispersion of second-phase rubber particles. A criterion for the effect of this practice is based on the average interparticle matrix ligament thickness. The critical interparticle distance, below which a substantial toughness increase can be observed, is considered to be an intrinsic material property of the matrix. A toughening mechanism has recently been suggested which considers a layer of transcrystallized material around well-dispersed particles, having a reduced yield strength in certain preferentially oriented directions, thereby opening the possibility of using mineral fillers. In this work, the potential of toughening of semicrystalline polymeric material by local anisotropy in combination with soft rubber and hard mineral filler particles is investigated. The matrix material is modeled within the framework of anisotropic Hill plasticity with a rate dependent and hardening yield stress. Various particle/matrix interface conditions are used to study the role of debonding and cavitation. The presence of debonded moderately stiff or hard fillers is found to affect the shear yielding effect of local anisotropy that was found for voided material.     

Electrophoretic mobilities of dissolved polyelectrolyte charging agent and suspended non-colloidal titanium during electrophoretic deposition

Coarse (≤20 μm) titanium particles were deposited on low-carbon steel substrates by cathodic electrophoretic deposition (EPD) with ethanol as suspension medium and poly(diallyldimethylammonium chloride) (PDADMAC) as polymeric charging agent. Preliminary data on the electrophoretic mobilities and electrical conductivities on the suspensions of these soft particles as well as the solutions themselves as a function of PDADMAC level were used as the basis for the investigation of the EPD parameters in terms of the deposition yield as a function of five experimental parameters: (a) PDADMAC addition level, (b) solids loading, (c) deposition time, (d) applied voltage, and (e) electrode separation. These data were supported by particle sizing by laser diffraction and deposit surface morphology by scanning electron microscopy (SEM). The preceding data demonstrated that Ti particles of ∼1-12 μm size, electrosterically modified by the PDADMAC charging agent, acted effectively as colloidal particles during EPD. Owing to the non-colloidal nature of the particles and the stabilization of the Ti particles by electrosteric forces, the relevance of the zeta potential is questionable, so the more fundamental parameter of electrophoretic mobility was used. A key finding from the present work is the importance of assessing the electrophoretic mobilities of both the suspensions and solutions since the latter, which normally is overlooked, plays a critical role in the ability to interpret the results meaningfully. Further, algebraic uncoupling of these data plus determination of the deposit yield as a function of charging agent addition allow discrimination between the three main mechanistic stages of the electrokinetics of the process, which are: (1) surface saturation; (2) compression of the diffuse layer, growth of polymer-rich layer, and/or competition between the mobility of Ti and PDADMAC; and (3) little or no decrease in electrophoretic mobility of Ti, establishment of polymer-rich layer, and/or dominance of the mobility of the PDADMAC over that of Ti.     

Low‐Cost Zeta Potentiometry Using Solute Gradients

The zeta potential is an electric potential in the Debye screening layer of an electrolyte, which represents a key physicochemical surface property in various fields ranging from electrochemistry to pharmaceuticals. Thus, characterizing the zeta potential is essential for many applications, but available measurement techniques are limited. Electrophoretic light scattering is typically used to measure the zeta potential of particles in suspension, whereas zeta potential measurements of a solid wall in solution rely on either streaming potential or electroosmotic mobility measurement techniques, both of which are expensive and sophisticated. Here, a simple, robust method to simultaneously measure the zeta potential of particles in suspension and solid walls is presented. The method uses solute gradients to induce particle and fluid motions via diffusiophoresis and diffusioosmosis, respectively, which are both sensitive to the zeta potential of the particle and the wall. By visualizing the particle dynamics, both zeta potentials can be determined independently. Finally, a compact microscope is used to demonstrate low‐cost zeta potentiometry that allows measurement of both particle and wall zeta potentials, which suggests a cost‐effective tool for pharmaceuticals as well as for educational purposes.     

An exact analytical solution for freely vibrating piezoelectric coupled circular/annular thick plates using Reddy plate theory

Based on third-order shear deformation plate theory of Reddy, the authors aim to provide an exact analytical solution for free vibration analysis of thick circular/annular plates, both upper and lower surfaces of which are in contact with a piezoelectric layer. Natural frequencies are determined by the solution of the coupled electromechanical governing equations for a combination of free, soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the plate. The electrodes on each piezoelectric layer are assumed to be short-circuited. The Maxwell electrostatics equation is satisfied by adopting a half-sine distribution of the electric potential in the transverse direction of the piezoelectric layers. A comparison of the present exact natural frequencies for piezoelectric coupled circular/annular plates with different boundary conditions is made with previously published results obtained by the Mindlin plate theory and 3-D modified finite element method. The effects of plate parameters such as host thickness to radius ratios, inner to outer radius ratios and piezoelectric to host thickness ratios on the natural frequencies of laminated circular/annular plates are investigated for different combinations of boundary conditions. Results obtained by the present exact closed-form solutions can be served as benchmark data for investigators to validate their numerical and analytical methods in the future.     

Friction and wear reduction with tribological coatings

The basic requirements for a good tribological surface are (1) low sliding friction, (2) good resistance to scuffing, wear and abrasion, (3) long contact fatigue life and (4) adequate subsurface strength to provide dimensional stability. Coatings have inherent deficiencies. The major problem is failure at the interface between the coating and the substrate, which results in flaking, peeling or spalling of the coating under the repetitively applied contact stresses.Three types of coatings which employ different mechanisms to improve the tribological properties and to maintain coating integrity are described in this paper. Nitrocarburizing represents a class of coatings in which the elements are allowed to diffuse into the surface of the structural material to form an alloy with the substrate. Diffusion provides compositional gradients which result in hard wear-resistant surface and which at low shear strengths avoid the interfaces that frequently exist between coatings and substrates. Chemically vapor-deposited chromium and titanium carbides represent a class of coatings in which a chemically distinct layer is grown on top of the substrate and is bonded to the substrate by diffusion. In the third type of coating, hard particles are suspended in a soft matrix. The hard particles provide the wear and abrasion resistance and the soft matrix both bonds the particles together and provides the low friction. Although the bond strength of this coating to the substrate is lower than that provided by diffusion in the other coatings, the soft matrix will yield without flaking under the shear stresses which are developed at the interface.     

Excluded Volumes of Anisotropic Convex Particles in Heterogeneous Media: Theoretical and Numerical Studies

Understanding the excluded volume of anisotropic particle is of great importance in the evaluation of continuum percolation and random packing behaviors of soft/hard particle systems in heterogeneous disordered media. In this work, we obtain the excluded volumes of several anisotropic convex particles including prolate spheroids, oblate spheroids, spherocylinders, and Platonic particles, using theoretical and numerical approaches. According to the second virial coefficient, we first present a theoretical scheme for determining the excluded volumes of anisotropic particles. Also, the mean tangent diameters of anisotropic convex particles are formulated by the quantitative stereology. Subsequently, Monte Carlo simulations are demonstrated to numerically evaluate the excluded volumes. The theoretical results of the dimensionless excluded volume are thereafter compared with that of the numerical results to verify the validity of the theoretical scheme. We further investigate the dependence of the dimensionless excluded volume on the geometric characteristics of anisotropic particles based on the proposed theoretical and numerical schemes. Results show that the dimensionless excluded volume mainly relies on the shape and surface information of anisotropic particles. The developed theoretical and numerical schemes can provide theoretical insights into the percolation threshold and packing density of soft/hard anisotropic particle systems in heterogeneous materials, physics, and chemistry fields.     

The Movement of an Ion-exchange Microparticle in a Weak External Electric Field

The electrokinetic motion of spherical particle suspended in the electrolyte solution under influence of external electric field is studied. Due to impermeability of particle’s surface for one kind of ion species the particle exhibit behavior different to well investigated dielectric particles. Under an assumption of a weak external electric field, we derive the analytical estimation of the particle’s velocity by means of a method of matched asymptotic expansions. The analytical analysis is complemented by numerical solution, which gives the distribution of ion’s concentrations, electric potential profiles and flows streamlines. The analytical results are successfully compared with the results of numerical simulation.     

Study of single particle charge and Brownian motions with surface plasmon resonance

We demonstrated a method to accurately measure the zeta potentials and surface charges of individual particles by surface plasmon resonance microscopy (SPRM). The principle is based on the sensitive dependence of surface plasmons in a metal surface on the distance between a particle and the surface. By applying a periodic (ac) electric field to the metal surface, the charged particle oscillates, which is measured with SPRM, from which the zeta potential and the surface charge of the particle can be determined. The ac method reduces the electro-osmotic effect and noises induced by Brownian motions and allows for the rapid determination of the zeta potentials of individual particles.     

Theory of magnetographic printing

The magnetic force of attraction between a recording surface and magnetic particles (the "developer" or "toner") is analyzed. The recording medium is assumed to be magnetically hard, the toner particles to be magnetically soft. The distribution of recording magnetization is taken to be periodic in the interior of an image area and uniform in an image free area. The toner particles are assumed to be part magnetic, part nonmagnetic material. In most of the calculations it is assumed that the magnetic susceptibility of the toner particles is small compared to unity. In the interior of an image area the force density has primarily a component perpendicular to the recording plane. This component decreases exponentially with distance from the recording plane, if the distribution of magnetization is sinusoidal. Near the edge of an image area the force density also has a tangential component, but this is generally smaller than the normal component. For toner particles with similar internal structure the force per unit mass always decreases with increasing particle size. Considered as a function of recording wavelength (at constant particle size) it shows a maximum at a wavelength comparable to the particle diameter.The force acting on a small particle (simeq 10mum) in the immediate vicinity of the recording surface can be several hundred times the force of gravity. The implications of these results in regard to color printing are discussed.     

Immersed molecular electrokinetic finite element method

A unique simulation technique has been developed capable of modeling electric field induced detection of biomolecules such as viruses, at room temperatures where thermal fluctuations must be considered. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. The force induced on an arbitrary object due to an electric field is calculated based on the continuum electromechanics and the Maxwell stress tensor. The thermal fluctuations are included in the Navier–Stokes fluid equations via the stochastic stress tensor. Dielectrophoretic and fluctuating forces acting on the particle are coupled through the fluid–structure interaction force calculated within the surrounding environment. This method was used to perform concentration and retention efficacy analysis of nanoscale biosensors using gold particles of various sizes. The analysis was also applied to a human papillomavirus.     

Particulate-TiC-hardened steel surfaces by laser melt injection

Hardened surfaces were produced on 304 stainless steel by the recently developed process of injecting carbide particles into a shallow laser-melted surface layer. The injected TiC can alter the surface properties in two different ways. With processing conditions chosen to minimize the dissolution of the particles, the surface layer consists of the hard relatively coarse (a cross section of the order of 100 μm) injected particles in a soft matrix. With processing conditions chosen to promote the dissolution of the injected TiC, fine (a cross section of the order of 1 μm) dendritic carbides formed on cooling contribute to the hardening of the surface.     

Effects of soft hemispherical particle on local surface stress of hard matrix

Abstract

Finite element analysis was performed to investigate the stresses within and around a soft hemispherical particle located on the surface of a hard matrix under a remote external tensile load. The purpose was to understand the effects of neodymium rich particles on the fatigue properties of Ti-55 alloy. Three case studies were considered. First both particle and matrix were perfect, second a crack existed within the particle, and third a crack was located in the matrix adjacent to the particle. Numerical results show that soft particles cause stress concentration in regions of the matrix adjacent to the particle, but that such stress concentrations are much weaker than those associated with a cavity. A crack within the particle increases the stress concentration in the matrix only a little when the crack is far from the interface. However, a crack in the matrix significantly increases local stress in the particle.     

Experimental and numerical modeling of particle levitation and movement behavior on traveling-wave electric curtain for particle removal

Traveling-wave electric curtain (EC) has been developed for potential application in particle removal/shield on solar panels and other surfaces. Levitation and transport of a particle in a traveling-wave electric field were simulated. Results show that levitation directions/angles and levitation trajectories differ because of the difference in starting positions and starting times. The particles in the two positive acceleration regions are levitated in opposite directions, and the particles distributed on the dielectric surface are levitated and transported successively rather than simultaneously. Movement trajectories are complex and affected by various factors. In the current paper, movement trajectories are modeled to analyze which motion modes are advantageous or disadvantageous to particle removal. This process is beneficial to elucidate the mechanism of particle removal and provide a guidance for movement control by designing appropriate operating parameters.     

压电复合材料正交层板的精确理论

基于一个六自由度的位移场和电势场, 建立了压电复合材料层板的控制方程。在简支边界条件下, 得到了正交矩形压电复合材料层板的解析解。该理论是一个等效单层理论, 控制方程的变量仅六个, 且不随层数变化, 使解的数学过程简洁。在该理论中, 决定精度的位移分布函数和电势分布函数由三维应力和静电平衡方程的特解来确定, 使之满足压电层板界面连续条件与板面力及电条件。算例验证了本文中等效单层理论的高精度。     

Effects of Material Properties on Granular Flow in a Silo Using DEM Simulation

In order to test the effect of material properties on flowability of particulate materials, discharge procedures of spherical particles within a flat-bottomed model silo with three sets of material properties, i.e., soft and hard without adhesion and adhesive hard, were simulated using the Discrete Element Method. For each system, three particles on the center line were selected and their instant vertical velocity components were traced. In addition, both discharge and the rate were recorded throughout the procedure. The predicted results show that, for both the systems without adhesion, though the soft has a material modulus only 1/1000 of the hard, there are no significant differences in f low pattern and discharge rate. This suggests that a soft system can be used to predict the behavior of a hard one to save CPU time in a gravity-driven granular flow. On the other hand, comparison between both hard systems shows that adhesion can significantly reduce the flowability in granular flow. By analyzing the velocity plot for the traced particles, free fall was clearly detected above the decompression zone, indicating the motion of a particle in a granular flow can be resolved as free fall together with the movement due to particle collision. In addition, select dynamic behavior related to the kinetic fluctuations affecting flow was observed. discrete element method silo granule flow particulate material     

Effects of Material Properties on Granular Flow in a Silo Using DEM Simulation

In order to test the effect of material properties on flowability of particulate materials, discharge procedures of spherical particles within a flat-bottomed model silo with three sets of material properties, i.e., soft and hard without adhesion and adhesive hard, were simulated using the Discrete Element Method. For each system, three particles on the center line were selected and their instant vertical velocity components were traced. In addition, both discharge and the rate were recorded throughout the procedure. The predicted results show that, for both the systems without adhesion, though the soft has a material modulus only 1/1000 of the hard, there are no significant differences in f low pattern and discharge rate. This suggests that a soft system can be used to predict the behavior of a hard one to save CPU time in a gravity-driven granular flow. On the other hand, comparison between both hard systems shows that adhesion can significantly reduce the flowability in granular flow. By analyzing the velocity plot for the traced particles, free fall was clearly detected above the decompression zone, indicating the motion of a particle in a granular flow can be resolved as free fall together with the movement due to particle collision. In addition, select dynamic behavior related to the kinetic fluctuations affecting flow was observed.

discrete element method silo granule flow particulate material     

颗粒增强铝基复合材料阳极氧化与耐蚀性的研究

基体中加入与铝合金基体电位不同、高体积分数的碳化硅和石墨颗粒增强材料,可能导致材料的耐蚀性降低.采用盐雾腐蚀和硬质阳极氧化方法对4种喷射沉积制备的颗粒增强铝基复合材料和一种喷射沉积锭坯颗粒增强铝基复合材料的腐蚀行为及阳极氧化工艺进行了研究.结果表明,颗粒增强铝基复合材料具有较高的腐蚀率,腐蚀形态均为明显的点蚀;在适当阳极氧化工艺条件下,颗粒增强铝基复合材料表面可以制得优良耐蚀性的硬质阳极氧化膜.     

Microstructure and electrical conductivity in shape and size controlled molybdenum particle thick film

We study the effects of particle morphology on the microstructure and electrical conductivity of Mo particle thick films. In our study, the shape and size of molybdenum (Mo) particles are modified by mechanical ball-milling and atomic layer deposition (ALD). As the total number of collisions between Mo particles and ball-milling media increases, Mo particles are deformed, and the shape of Mo particles changed from irregular polyhedrons to thin flakes. In the ball-milling process, stress frequency is an important processing parameter governing the deformation and breakage of Mo particles. In addition, ALD-grown TiO₂ layer is found to significantly suppress the growth of Mo particles at high temperature. After 1000 °C annealing, the particle size of the TiO₂ layer-coated film is only half of that of bare Mo particle films. The shape of the particles changes electrical conductivity of the Mo thick films. Large contact area between flake shape particles can increase the carrier mobility of the film and the 5-nm thick TiO₂ layer can provide the inter-particle carrier transport path via a tunneling mechanism. Our results show that the combined use of the ball-milling and the ALD coating leads to Mo thick films with high electric conductivity and large surface area.