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.     

Spreading dynamics and dynamic contact angle of non-Newtonian fluids

The spreading dynamics of power-law fluids, both shear-thinning and shear-thickening fluids, that completely or partially wet solid substrate was investigated theoretically and experimentally. An evolution equation for liquid-film thickness was derived using a lubrication approximation, from which the dynamic contact angle versus the contact line moving velocity relationship was evaluated. In the capillary spreading regime, film thickness h is proportional to xi3/(n+2) (xi is the distance from the contact line), whereas in the gravitational regime, h is proportional to xi1/(n+2), relating to the rheological power exponent n. The derived model fit the experimental data well for a shear-thinning fluid (0.2% w/w xanthan solution) or a shear-thickening fluid (7.5% w/w 10 nm silica in polypropylene glycol) on a completely wetted substrate. The derived model was extended using Hoffmann's proposal for partially wetting fluids. Good agreement was also attained between model predictions and the shear-thinning fluid (1% w/w cmc solution) and shear-thickening fluid (10% w/w 15 nm silica) on partially wetted surfaces.     

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.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.     

Analysis of particle-wall interactions during particle free fall

In this study, the vertical motion of a particle in a quiescent fluid falling toward a horizontal plane wall is analyzed, based on simplified models. Using the distance between the particle and wall as a parameter, the effects of various forces acting on the particle and the particle motion are examined. Without the colloidal and Brownian forces being included, the velocity of small particles is found to be approximately equal to the inverse of the drag force correction function used in this study as the particle approaches the near-wall region. Colloidal force is added to the particle equation of motion as the particle moves a distance comparable to its size. It is found that the particle might become suspended above or deposited onto the wall, depending on the Hamaker constant, the surface potentials of the particle and wall, and the thickness of the electrical double layer (EDL). For strong EDL repulsive force and weaker van der Waals (VDW) attractive force, the particle will become suspended above the wall at a distance at which the particle velocity is zero. This location is referred to as the equilibrium distance. The equilibrium distance is found to increase with increased in EDL thickness when a repulsive force barrier appears in the colloidal force interaction. For the weak EDL repulsive force and strong VDW attractive force case, the particle can become deposited onto the wall without the Brownian motion effect. The Brownian jump length was found to be very small. Many Brownian jumps would be required in a direction toward the wall for a suspended particle to become deposited.     

Implementation of Lees-Edwards periodic boundary conditions for direct numerical simulations of particle dispersions under shear flow

A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the incompatibility of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shear-thinning regimes.     

Alignment of particles in sheared viscoelastic fluids

We investigate the shear-induced structure formation of colloidal particles dissolved in non-Newtonian fluids by means of computer simulations. The two investigated visco-elastic fluids are a semi-dilute polymer solution and a worm-like micellar solution. Both shear-thinning fluids contain long flexible chains whose entanglements appear and disappear continually as a result of Brownian motion and the applied shear flow. To reach sufficiently large time and length scales in three-dimensional simulations with up to 96 spherical colloids, we employ the responsive particle dynamics simulation method of modeling each chain as a single soft Brownian particle with slowly evolving inter-particle degrees of freedom accounting for the entanglements. Parameters in the model are chosen such that the simulated rheological properties of the fluids, i.e., the storage and loss moduli and the shear viscosities, are in reasonable agreement with experimental values. Spherical colloids dispersed in both quiescent fluids mix homogeneously. Under shear flow, however, the colloids in the micellar solution align to form strings in the flow direction, whereas the colloids in the polymer solution remain randomly distributed. These observations agree with recent experimental studies of colloids in the bulk of these two liquids.     

Diffusiophoresis of a moderately charged spherical colloidal particle

An analytic expression is obtained for the diffusiophoretic mobility of a charged spherical colloidal particle in a symmetrical electrolyte solution. The obtained expression, which is expressed in terms of exponential integrals, is correct to the third order of the particle zeta potential so that it is applicable for colloidal particles with low and moderate zeta potentials at arbitrary values of the electrical double-layer thickness. This is an improvement of the mobility formula derived by Keh and Wei, which is correct to the second order of the particle zeta potential. This correction, which is related to the electrophoresis component of diffusiophoresis, becomes more significant as the difference between the ionic drag coefficients of electrolyte cations and anions becomes larger and vanishes in the limit of thin or thick double layer. A simpler approximate mobility expression is further obtained that does not involve exponential integrals.     

Inertial Hydrodynamic Effects in Electrophoresis of Particles in an Alternating Electric Field

The influence of the effects associated with the inertia of particles and the surrounding fluid on the electrophoresis in an alternating electric field has been theoretically investigated. From solving the hydrodynamic equations the electrophoretic velocity of a spherical particle was found to depend on the frequency of the external electric field and on the particle-to-fluid-density ratio. It is shown that, due to inertial effects, the liquid flow around particles with a thin electrical double layer (EDL) is no longer potential. A mechanism of the formation of steady-state flow in the vicinity of oscillating particles with a thin EDL is proposed. Using numerical methods, a picture of the fluid streamlines in such a flow is obtained. The spatial distribution of the fluid velocity in the vicinity of a particle is also found. It was established that with an increasing frequency of the electric field the steady-state flow velocity passes through a maximum. The flow direction depends on the ratio between the densities of a particle and the surrounding fluid. The reversal of direction takes place when this ratio is about 0.7. The case of a thick EDL has also been considered, and a comparative analysis of the flow distributions around the particles with a thin and those with a thick EDL has been carried out.     

Electrophoresis in a non-Newtonian fluid: sphere in a spherical cavity

The electrophoretic behavior of a sphere in a non-Newtonian fluid is investigated theoretically by analyzing the phenomenon that occurs in a spherical cavity under the condition of a weak applied electrical field. Non-Newtonian behavior in the liquid phase may be due to, for example, the addition of polymer to a colloidal dispersion to improve its stability. It may also arise from the increase in the volume fraction of the dispersed phase such as the slurry used in chemical mechanical polishing. A Carreau model is adopted to characterize the shear-thinning behavior of the liquid phase. We show that the difference between the mobility of the particle based on the present model and that based on the corresponding Newtonian fluid increases with the decrease in the thickness of a double layer. The shear-thinning nature of the liquid phase has the effect of increasing the mobility.     

Effect of a charged boundary on electrophoresis in a Carreau fluid: a sphere at an arbitrary position in a spherical cavity

The influence of a charged boundary on the electrophoretic behavior of an entity in a non-Newtonian fluid is studied by considering a sphere at an arbitrary position in a spherical cavity filled with a Carreau fluid under the conditions of low surface potential and weak applied electric field. The dependence of the mobility of a sphere on its position in a cavity, the size of a cavity, the thickness of a double layer, and the nature of a fluid is investigated. In addition to the fact that the effect of shear-thinning is advantageous to the movement of a sphere, several other interesting results are also observed. For instance, if an uncharged sphere is in a positively charged cavity, where the electroosmotic flow and the induced charge on the sphere surface play a role, the effect of shear-thinning is important only if the thickness of the double layer is either sufficiently thin or sufficiently thick. However, this might not be the case if a positively charged sphere is in an uncharged cavity.     

The Primary Electroviscous Effect: Thin Double Layers (akappa>1) and a Stern Layer

The primary electroviscous effect due to the charge clouds surrounding spherical charged particles suspended in an electrolyte was studied by Hinch and Sherwood (J. Fluid Mech. 132, 337 (1983)) in the limit of double layers thin compared to the particle radius a. Here we introduce the effect of a dynamic Stern layer into that analysis, in order to explain the numerical results of Rubio-Hernández et al. (J. Colloid Interface Sci. 206, 334 (1998)) in terms of the ratio of the tangential ionic fluxes within the charge cloud to those within the Stern layer. The predictions of the asymptotic analysis are compared with those of numerical computations. The thickness of the charge cloud is characterized by the Debye length kappa(-1). If akappa>10 the predictions of the asymptotic analysis exhibit the same qualitative behavior as the numerical results, but akappa>1000 is required to achieve quantitative agreement to within 2.5%. Copyright 2000 Academic Press.     

Viscoelastic Drag of Particles Settling in Wormlike Micellar Solutions of Varying Surfactant Concentration

Wormlike micellar octadecyl trimethyl ammonium chloride (OTAC) solution is a self-assembled fracturing fluid used to carry proppants into fractures in oil recovery. Slow settling velocity of proppant is desirably resulted from the viscoelastic drag with low viscosity of fracturing fluids for fracturing work. Steel spheres, as a substitute for proppants, fall into three semi-dilute OTAC solutions. The steady rheology demonstrates that OTAC solutions are divided into shear-thickening and shear-thinning regimes by the critical shear rate. The applied steel spheres always lie in the shear-thickening regime of the 2.8 wt% OTAC solution with aggregated micelles as their characteristic shear rates are less than the critical shear rate of the solution. Strong shear-thickening viscous drag results in lower settling velocity of steel spheres. Most of the applied steel spheres, on the other hand, lie in the shear-thinning regime of the 4 wt% OTAC solution with orientated micelles. Although the latter solution has small dissipation coefficient, high Weissenberg number, and consequently high elastic effect, the shear-thinning viscosity results in higher settling velocity of steel spheres.     

Preparation of ultrathin membranes by layer-by-layer (LBL) deposition of oppositely charged inorganic colloids

Nanofilms were prepared by alternating deposition of Mg–Al (2:1) NO ₃ ⁻ layered double hydroxide (LDH), hectorite and silica particles present study. The charge density of the oppositely charged materials strongly affect film properties like thickness and ordering. The specific charge of the colloidal particles was measured with the particle charge detector. The sequential build up of the thin films was followed by spectrophotometry and X-ray diffraction (XRD). The surface morphology of the formed multilayers was characterized and film thickness determination was performed by atomic force microscopy. The influence of the charge density of hectorite and silica particles on the LDH/hectorite, LDH/silica film thickness was studied. The results reveal that the LDH concentration has a significant effect on the film thickness while the hectorite and silica concentration were not important. Films prepared from the different types of negatively charged inorganic particles in the same concentration range (0.25–1.0%) have similar thickness because of the much higher surface charge relative to the LDH lamellae.     

Induced-charge electrophoresis of uncharged dielectric spherical Janus particles

We derive the equations governing the dipolophoretic motion of an electrically inhomogeneous Janus particle composed of two hemispheres with differing permittivities. The general formulation is valid for any electric forcing, including alternating current (AC) and makes no assumptions regarding the size of the electric double layer (EDL). The solution is thus valid even for nanoparticles where the particle radius can be of the same order as the EDL thickness. Semi-analytic and numerical solutions for the linear phoretic velocity and angular rotation of a single Janus particle suspended in an infinite medium are given in the limit of uniform direct current (DC) electric forcing. It is determined that particle mobility is a function of the permittivity in each hemisphere and the contrast between them as well as the EDL length. For a particle in which both hemispheres are characterized by a finite permittivity, we discover that maximum mobility and rotation is not obtained in the Helmholtz-Smoluchowski thin EDL limit but is rather a function of the permittivity and EDL properties.     

Particle Interactions in Diffusiophoresis and Electrophoresis of Colloidal Spheres with Thin but Polarized Double Layers

The diffusiophoretic and electrophoretic motions of two colloidal spheres in the solution of a symmetrically charged electrolyte are analyzed using a method of reflections. The particles are oriented arbitrarily with respect to the electrolyte gradient or the electric field, and they are allowed to differ in radius and in zeta potential. The thickness of the electric double layers surrounding the particles is assumed to be small relative to the radius of each particle and to the gap width between the particles, but the effect of polarization of the mobile ions in the diffuse layer is taken into account. A slip velocity of fluid and normal fluxes of solute ions at the outer edge of the thin double layer are used as the boundary conditions for the fluid phase outside the double layers. The method of reflections is based on an analysis of the electrochemical potential and fluid velocity disturbances produced by a single dielectric sphere placed in an arbitrarily varying electrolyte gradient or electric field. The solution for two-sphere interactions is obtained in expansion form correct to O(r(12)(-7)), where r(12) is the distance between the particle centers. Our analytical results are found to be in good agreement with the available numerical solutions obtained using a boundary collocation method. On the basis of a model of statistical mechanics, the results of two-sphere interactions are used to analytically determine the first-order effect of the volume fraction of particles of each type on the mean diffusiophoretic and eletrophoretic velocities in a bounded suspension. For a suspension of identical spheres, the mean diffusiophoretic velocity can be decreased or increased as the volume fraction of the particles is increased, while the mean electrophoretic velocity is reduced with the increase in the particle concentration. Generally speaking, the particle interaction effects can be quite significant in typical situations. Copyright 2000 Academic Press.     

Electrokinetic transport of a spherical gel-layer model particle: inclusion of charge regulation and application to polystyrene sulfonate

An electrokinetic gel-layer model of a spherical, highly charged colloid particle developed previously [S. Allison, J. Colloid Interface Sci. 277 (2004) 248], is extended in several ways. The charge of the particle is assumed to arise from deprotonation of acidic groups that are present, in uniform concentration, over a portion (or all) of the gel layer. Free energy considerations coupled with Poisson-Boltzmann theory are used to estimate how the local electrostatic environment of a charged gel layer alters the local pK(a) of the acidic groups. This modulation of the charge of the colloidal particle, or "charge regulation," can be significant even for colloidal particles with strongly acidic groups at moderate pH if the ambient salt concentration is low. The methodology is applied to the viscosity and electrophoretic mobility data of a particular polystyrene sulfonate latex over a broad range of monovalent salt (NaCl) concentration [M.J. Garcia-Salinas, F.J. de las Nieves, Langmuir 16 (2000) 715]. The experimental data can be accounted for by a gel layer model that decreases in thickness, but does not vanish, as the salt concentration is increased. Viscosity data provides valuable information about the degree of solvation of the colloidal particle and the thickness of the gel layer. The mobility data is best explained by a model in which only the outermost portion of the gel layer is charged. Charge regulation is significant at a monovalent salt concentration of 3 x 10(-3) mol/l and increases as the salt concentration decreases.     

Enhanced pearl-chain formation by electrokinetic interaction with the bottom surface of vessel

Counterions in an electric double layer (EDL) around a colloidal particle accumulate on one side of the EDL and are deficient on the other side under an electric field, resulting in an imbalance of ionic concentration in the EDL, that is to say, the ionic polarization of EDL. It is well known that the ionic polarization of EDL induces electric dipole moments whereby the alignments of colloidal particles (e.g., pearl chains) are formed under alternating electric fields. In this study, we focus on the effect of the frequency of applied electric fields (100 Hz-1 kHz) on the alignment of silica particles settling at the bottom of a silica glass vessel. In digital imaging analyses for pearl chains of silica particles, it is confirmed that surface distances between two neighboring particles decrease but the number of particles in a pearl chain increases as the frequency of the applied electric field is lowered from 1 kHz to 100 Hz. More interestingly, electrical conductance measurements suggest that the induced ionic polarization of EDL around silica particles at the bottom of the silica vessel is enhanced as the frequency is lowered from 1 kHz to 100 Hz, whereas the ionic polarization around isolated silica particles in uniform dispersions is alleviated by the relaxation of ionic concentration in the EDL as a result of the diffusion of counterions. This curious phenomenon can be explained by considering that the ionic polarization of EDL of silica particles at the bottom of a vessel is affected by the electro-osmosis of the silica surface at the bottom of the vessel.