Analysis of electroosmotic flow of power-law fluids in a slit microchannel

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.     

Mixing of non-Newtonian fluids in wavy serpentine microchannel using electrokinetically driven flow

A numerical investigation is performed into the mixing performance of electrokinetically driven non-Newtonian fluids in a wavy serpentine microchannel. The flow behavior of the non-Newtonian fluids is described using a power-law model. The simulations examine the effects of the flow behavior index, the wave amplitude, the wavy-wall section length, and the applied electric field strength on the mixing performance. The results show that the volumetric flow rate of shear-thinning fluids is higher than that of shear-thickening fluids, and therefore results in a poorer mixing performance. It is shown that for both types of fluid, the mixing performance can be enhanced by increasing the wave amplitude, extending the length of the wavy-wall section, and reducing the strength of the electric field. Thus, although the mixing efficiency of shear-thinning fluids is lower than that of shear-thickening fluids, the mixing performance can be improved through an appropriate specification of the flow and geometry parameters. For example, given a shear-thinning fluid with a flow behavior index of 0.8, a mixing efficiency of 87% can be obtained by specifying the wave amplitude as 0.7, the wavy-wall section length as five times the characteristic length, the nondimensional Debye-Huckel parameter as 100, and the applied electric field strength as 43.5 V/cm.     

Numerical analysis of thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions

Thermophoresis of colloidal particles in aqueous media is more frequently applied in biomedical analysis with processed fluids as biofluids. In this work, a numerical analysis of the thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions is presented. In a particle-fixed reference frame, the flow field of non-Newtonian fluids has been governed by the Cauchy momentum equation and the continuity equation, with the dynamic viscosity following the power-law fluid model. The numerical simulations reveal that the shear-thinning effect of pseudoplastic fluids is advantageous to the thermophoresis, and the shear-thickening effect of dilatant fluids slows down the thermophoresis. Both the shear-thinning and shear-thickening effects of non-Newtonian fluids on a thermodiffusion coefficient are pronounced for the case when the thickness of electric double layer (EDL) surrounding a particle is moderate or thin. Finally, the reciprocal of the dynamic velocity at the particle surface is calculated to approximately estimate the thermophoretic behavior of a charged particle with moderate or thin EDL thickness.     

The state of the art in the rheology of polymers: Achievements and challenges

The state of the art in the rheology of polymer fluids (polymer solutions and melts) and filled composites is reviewed. This review includes two parts: analysis of the basic principles for the construction of rheological constitutive equations in terms of the continuum mechanics and finding correlations between the rheological characteristics and molecular structure of polymers on the basis of molecular models. Possible approaches to the formulation of constitutive equations are discussed. Special attention is focused on the correct selection of the form of the elastic potential for rubbery deformations induced under the flow of polymer fluids. The use of a power-law potential leads to the best results. To gain unequivocal results and minimize the number of free constants, viscoelastic characteristics of polymer fluids should be described in terms of a continuous relaxation spectrum as a power-law function limited by the maximum relaxation time. To solve the boundary problems by the selected constitutive equation, analysis of the dynamic stability is required, because the combination of viscosity and elasticity controls the limits of flow upon shear and tensile. Deformation can also lead to changes in the phase state of a polymer system. Furthermore, correct formulation of the boundary conditions is necessary because, in many cases, polymer fluids and, in particular, filled materials tend to efficient slip along walls. The existing molecular models adequately describe the characteristics of monodisperse polymers; however, on passing to polydisperse polymers, the additional use of semiempirical approaches is required. The modern level of experimental studies allows test measurements over a wide range of deformation rates, frequencies, and temperatures. However, in this field, the mainstream tendency in experimental studies is concerned with hybrid methods, which combine direct rheological measurements with optical observations of local structure and its evolution in the material. In this case, various physical principles of measurements are applied. In recent years, much interest has been focused on studying polymer compositions containing nanosized fillers, which are able to produce their structures in melt.     

New analysis of yield stress on giant electrorheological fluids

A new universal yield stress scaling equation is proposed to accurately model experimental data for giant electrorheological (GER) fluids. This new equation expressed in modified Bessel function predicts both regions of polarization effect predominant in the low electric field strength applied and polar molecule-dominating GER behavior, as well as collapses the experimental data of yield stress in a single line for a broad range of electric field strengths.     

Single particle force distributions in simple fluids

The distribution function, W(F), of the magnitude of the net force, F, on particles in simple fluids is considered, which follows on from our previous publication [A. C. Bran?ka, D. M. Heyes, and G. Rickayzen, J. Chem. Phys. 135, 164507 (2011)] concerning the pair force, f, distribution function, P(f), which is expressible in terms of the radial distribution function. We begin by discussing the force on an impurity particle in an otherwise pure fluid but later specialize to the pure fluid, which is studied in more detail. An approximate formula, expected to be valid asymptotically, for W(F) referred to as, W(1)(F) is derived by taking into account only binary spatial correlations in the fluid. It is found that W(1)(F) = P(f). Molecular dynamics simulations of W for the inverse power (IP) and Lennard-Jones potential fluids show that, as expected, W(F) and P(f) agree well in the large force limit for a wide range of densities and potential forms. The force at which the maximum in W(F) occurs for the IP fluids follows a different algebraic dependence with density in low and high density domains of the equilibrium fluid. Other characteristic features in the force distribution functions also exhibit the same trends. An exact formula is derived relating W(F) to P(x)(F(x)), the distribution function of the x-cartesian components of the net force, F(x), on a particle. W(F) and P(x)(F(x)) have the same analytical forms (apart from constants) in the low and high force limits.     

Structural and dynamical properties of a core-softened fluid in a supercritical region

We present a theoretical study of the structural, thermodynamic, and transport properties of a supercritical fluid comprising particles interacting via isotropic attractive core-softened potential. The shear viscosity and self-diffusion coefficient are computed on the basis of the mode-coupling theory, with required structural input obtained from the thermodynamically self-consistent integral equation theory. We also consider dilute solutes in a core-softened fluid and use the anisotropic integral equation theory to obtain the solute-solute potential of mean force, which yields the second virial coefficient. We analyze its dependence on the solvent density and solute-solvent interaction strength.     

AaDd型氢键流体的统计理论（Ⅳ）：胶体粒子间的耗尽势

基于耗尽势的密度泛函理论研究了AaDd型氢键流体中胶体粒子间的耗尽势.针对胶体稀溶液,通过计算在不同条件下两个胶体粒子间的耗尽势和耗尽力,进一步分析了氢键流体中相关因素对二者的影响.结果表明,胶体粒子与流体分子的尺寸比率、氢键流体的体相密度、氢键键能、质子给体和受体数目以及胶体粒子与流体之间的弱相互作用等因素均可对胶体粒子间耗尽势产生显著影响.     

Lattice Poisson-Boltzmann simulations of electro-osmotic flows in microchannels

This paper presents the numerical results of electro-osmotic flows in micro- and nanofluidics using a lattice Poisson-Boltzmann method (LPBM) which combines a potential evolution method on discrete lattices to solve the nonlinear Poisson equation (lattice Poisson method) with a density evolution method on discrete lattices to solve the Boltzmann-BGK equation (lattice Boltzmann method). In an electrically driven osmotic flow field, the flow velocity increases with both the external electrical field strength and the surface zeta potential for flows in a homogeneous channel. However, for a given electrical field strength and zeta potential, electrically driven flows have an optimal ionic concentration and an optimum width that maximize the flow velocity. For pressure-driven flows, the electro-viscosity effect increases with the surface zeta potential, but has an ionic concentration that yields the largest electro-viscosity effect. The zeta potential arrangement has little effect on the electro-viscosity for heterogeneous channels. For flows driven by both an electrical force and a pressure gradient, various zeta potential arrangements were considered for maximize the mixing enhancement with a less energy dissipation.     

Statistical theory for a hydrogen bonding fluid system of A a D d type (IV): Depletion potential between colloid particles

The depletion potential between two colloid particles immersed in a hydrogen bonding fluid has been investigated by density functional theory. The study is motivated by the wide applications of hydrogen bonding fluids in the field of colloid science, and the effects of relevant factors on the depletion potential and depletion force between colloid particles have been studied. These factors include the size ratio of the colloid particle to the fluid molecule, the bulk density of the fluid, the functionality (the number of proton acceptors a and proton donors d) and hydrogen bonding strength as well as the colloid-fluid interaction energy. By comparing the depletion potential calculated under various conditions, it is shown that the effects of these factors on the depletion potential are very significant, and in particular in regulating the depletion force and its range.     

Electrokinetic diffusioosmotic flow of Ostwald-de Waele fluids near a charged flat plate in the thin double layer limit

Electrokinetic diffusioosmotic flow of Ostwald-de Waele, or power-law, fluids near a large charged flat plate is theoretically investigated for very thin double layers. Solutions to the flow velocity both up-close and far from the flat plate as well as the effective viscosity are presented for general values of the flow behavior index. Results show that given a wall zeta potential, ζ, diffusivity difference parameter, β, and constant imposed solute concentration gradient, both the near and far field diffusioosmotic flow velocities obtained for the respective dilatant and pseudoplastic liquids considerably deviate from those obtained for Newtonian liquids as found in previous literature. This likely suggests that the electrokinetic diffusioosmosis and its complementary effect of diffusiophoresis depend sensitively not only on the ζ-β parametric pair, but also on the possible non-Newtonian characteristics of the electrolytic liquid phase of the system. The theory presented herein can also be readily modified to model or describe electrodiffusioosmosis in power-law fluids, which is likely found in flow situations where the fluid non-Newtonian response, imposed solute concentration gradient, and an additional externally applied electric current density (or electric field) are of equal importance.     

石墨烯/聚合物纳米复合电流变材料

电流变智能流体在外电场刺激下能快速可逆地改变自身流变性能,具有重要技术应用价值.传统的基于微米颗粒的电流变流体易于沉降并且电致屈服强度不高限制了技术应用,最近基于纳米颗粒的非传统电流变材料研究受到重视,特别是具有各向异性形貌的纳米颗粒悬浮液被发现具有明显增强的电/磁流变效应.本文介绍了最近基于石墨烯的二维纳米复合电流变材料的研究进展,主要包括石墨烯/半导聚合物、石墨烯/极性聚合物、石墨烯/碳等几种典型的电流变材料的制备、结构和电流变行为.研究表明利用石墨烯独特的二维纳米结构、优异的电学和热学性质可能为制备新颖的高性能纳米电流变材料提供途径。     

Unsteady electroosmosis in a microchannel with Poisson-Boltzmann charge distribution

The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson-Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ<1), we recover the linearized PB equation - the Debye-Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors <1% for λ up to 2. The accurate solution to the PB equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time-harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time-harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ.     

Pressure dependence of the vapor-liquid-liquid phase behavior in ternary mixtures consisting of n-alkanes, n-perfluoroalkanes, and carbon dioxide

Expansion of an organic solvent by an inert gas can be used to tune the solvent's liquid density, solubility strength, and transport properties. In particular, gas expansion can be used to induce miscibility at low temperatures for solvent combinations that are biphasic at standard pressure. Configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out to investigate the vapor-liquid-liquid equilibria and microscopic structures for two ternary systems: n-decane/n-perfluorohexane/CO2 and n-hexane/n-perfluorodecane/CO2. These simulations employed the united-atom version of the transferable potential for phase equilibria (TraPPE-UA) force field. Initial simulations for binary mixtures of n-alkanes and n-perfluoroalkanes showed that special mixing parameters are required for the unlike interactions of CHx and CFy pseudoatoms to yield satisfactory results. The calculated upper critical solution pressures for the ternary mixtures at a temperature of 298 K are in excellent agreement with the available experimental data and predictions using the SAFT-VR (statistical associating fluid theory of variable range) equation of state. The simulations yield asymmetric compositions for the coexisting liquid phases and different degrees of microheterogeneity as measured by local mole fraction enhancements.     

The role of short-ranged energetic correlations in the mobility field dependence of disordered organic materials

We studied the mobility of charge carriers in a model for disordered organic solids where the energies of the localized states are Gaussianly distributed with short-ranged correlations. We obtained an expression for the mobility as a function of electric field, temperature, energetic variance, and correlation radius. The temperature dependence obtained with short-ranged energetic correlations is different from that obtained with power-law decaying energetic correlations and suggests a possible way to distinguish the two types of correlations from the measured mobility. This work also presents a practical way of computing the mobility, applicable to any transport model based on a linear master equation, directly from the matrix of the hopping rates.     

Thermally responsive phospholipid preparations for fluid steering and separation in microfluidics

Aqueous phospholipid preparations comprised of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) are prevalent materials for biological characterization and become gel-like near physiological temperature, but have a low viscosity below 24°C. The rheology of 20% phospholipid preparations of [DMPC]/[DHPC] = 2.5 reveals that, under conditions utilized for fluid steering, the materials are shear-thinning power-law fluids with a power-law index ranging from 0.30 through 0.90. Phospholipid preparations are utilized to steer fluids in microfluidic chips and support hydrodynamic delivery of sample across a double T injection region in a chip. The fact that the phospholipids are fully integrated as a valving material as well as a separation medium is demonstrated through the separation of linear oligosaccharides labeled with 1-aminopyrene-3,6,8-trisulfonic acid.     

Liquid transport in rectangular microchannels by electroosmotic pumping

The characteristics of electroosmotic flow in rectangular microchannels were investigated in this paper. A 2D Poisson–Boltzmann equation and the 2D momentum equation were used to model the electric double layer field and the flow field. The numerical solutions show significant influences of the channel cross-section geometry (i.e. the aspect ratio) on the velocity field and the volumetric flow rate. Also, the numerical simulation of the electroosmotic flow reveals how the velocity field and the volumetric flow rate depend on the ionic concentration, zeta potential, channel size and the applied electrical field strength.     

Magnetic field effects on natural convection flow of a non-Newtonian fluid in an L-shaped enclosure

The effect of magnetic field on natural convection heat transfer in an L-shaped enclosure filled with a non-Newtonian fluid is investigated numerically. The governing equations are solved by finite-volume method using the SIMPLE algorithm. The power-law rheological model is used to characterize the non-Newtonian fluid behavior. It is revealed that heat transfer rate decreases for shear-thinning fluids (of power-law index, n?<?1) and increases for shear-thickening fluids (n?>?1) in comparison with the Newtonian ones. Thermal behavior of shear-thinning and shear-thickening fluids is similar to that of Newtonian fluids for the angle of enclosure α?<?60° and α?>?60°, respectively.     

Correlation analysis of the power law parameters for viscosity of some engineering fluids

Knowledge and estimation of transport properties of fluids which are sensitive to temperature variation like viscosity are necessary in mass flow and heat transfer computation. In the present work, based on the use of econometric and statistical techniques for regression analysis and correlation tests, we propose an original equation modelling the relationship between the two parameters of viscosity power law equation. Empirical validation using data set of some pure fluids provided from the literature gives excellent statistical results which allow us to redefine the power law equation using only a single parameter. This result is important in fluids engineering since the validation of the proposed equation simplifies the estimation of viscous behaviour and the ensuing calculations by reducing the number of viscosity equation parameters and facilitating manipulations for fluids with low and moderate viscosity in engineering data which permits to estimate one unavailable parameter when the second one is available.