Self-consistent particle simulation of model-stabilized colloidal suspensions

Dynamics of model-stabilized colloidal suspensions were investigated by the self-consistent particle simulation method (SC), a new simulation algorithm that takes into account the interaction between the particles and suspending fluid. In this method, the fluid-particle interaction is introduced self-consistently by combining the finite element method (FEM) for fluid motion with Brownian dynamics (BD) for particle dynamics. To validate the reliability of the proposed algorithm, the shear dynamics of the stable particle suspensions were investigated. Relative viscosity and microstructure as a function of dimensionless shear rate at different volume fractions were in good agreement with previous observations. The robustness of the method was also verified through numerical convergence test. The effect of the fluid-particle interaction was well represented in simulations of two model problems, pressure-driven channel flow and rotating Couette flow. Plug-shaped velocity profile was observed in pressure-driven channel flow, which arised from shear thinning behavior of the stable suspension. In rotating Couette flow, shear banded nonlinear flow profile was observed. Although full hydrodynamic interaction (HI) was not rigorously taken into account, it successfully captured the macroscopic structure-induced flow field. It also takes advantage of the geometrical adaptability of FEM and computational efficiency of BD. We expect this newly developed simulation platform to be useful and efficient for probing the complex flow dynamics of particle systems as well as for practical applications in the complex flow of complex fluids.     

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

The particle migration effects and fluid–particle interactions occurring in the flow of highly concentrated fluid–particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear‐induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear‐induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse‐flux model. Semi‐implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration. Copyright © 2008 John Wiley & Sons, Ltd.     

Resolution sensitivity of momentum‐exchange and immersed boundary methods for solid–fluid interaction in the lattice Boltzmann method

In the lattice Boltzmann method (LBM), the mechanism of fluid–solid interaction can be effectively captured by appropriately enforcing the no‐slip conditions in shear direction, and bounce‐back of the non‐equilibrium distribution portion in the normal direction at fluid–solid interfaces. Among various solid–fluid interaction schemes being proposed for LBM in recent decades, two simple fluid–solid interaction methods—the momentum exchange algorithm (MEA) and the immersed boundary scheme (IBS)—were developed based on the above concept. In this paper, MEA and IBS are implemented in a D2Q9 LBGK system and applied to measure the wall correction factors of drag force upon a stationary circular particle midway in the Poiseuille channel flow at very low Reynolds number and drag coefficients at low to moderate Reynolds numbers. MEA and IBS are also employed to compare the fluid‐induced torque over the cylinder in the Taylor–Couette flow, and the steady velocity of a particle settling under the influence of gravity inside a tube. The above experiments show that IBS seems to be more accurate and less demanding on lattice resolution. Copyright © 2010 John Wiley & Sons, Ltd.     

On the gating of mechanosensitive channels by fluid shear stress

Mechanosensation is an important process in biological fluid–structure interaction. To understand the biophysics underlying mechanosensation, it is essential to quantify the correlation between membrane deformation,membrane tension, external fluid shear stress, and conformation of mechanosensitive(MS) channels. Smoothed dissipative particle dynamics(SDPD) simulations of vesicle/cell in three types of flow configurations are conducted to calculate the tension in lipid membrane due to fluid shear stress from the surrounding viscous flow. In combination with a simple continuum model for an MS channel, SDPD simulation results suggest that shearing adhered vesicles/cells is more effective to induce membrane tension sufficient to stretch MS channels open than a free shear flow or a constrictive channel flow. In addition, we incorporate the bilayer–cytoskeletal interaction in a two-component model to probe the effects of a cytoskeletal network on the gating of MS channels.     

Strain stiffening of non-colloidal hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region

Concentrated hard sphere suspensions often show an interesting nonlinear behavior, called strain stiffening, in which the viscosity or modulus starts to increase at critical strain amplitude. Sudden increase of rheological properties is similar to shear thickening; however, the particle dynamics in the strain stiffening under oscillatory shear flow does not necessarily coincide with the mechanism of shear thickening under step shear flow. In this study, we have systematically investigated the nonlinear rheology of non-colloidal (>1???m) hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region in order to better understand the strain stiffening behavior. The suspensions near liquid-and-crystal coexistence region are known to locally form the closed packing structure. The critical strain amplitude which is the onset of strain stiffening was different for the storage and loss modulus. But they converged to each other as the suspension forms a more crystalline structure. The critical strain amplitude was independent of medium viscosity, imposed angular frequency, and particle size, but was strongly dependent upon particle volume fraction. The onset of strain stiffening was explained in terms of shear-induced collision due to particle motion in the closed packing structure. Nonlinear stress wave-forms, which reflect the micro-structural change, were observed with the onset of strain stiffening. During the strain stiffening, enhanced elastic stress before and after flow reversal was observed which originates from changes in the suspension microstructure. Nonlinearity of the shear stress in terms of Fourier intensity was extremely increased up to 0.55. Beyond the strain stiffening, the suspension responded liquid-like and the nonlinearity decreased but the elastic shear stress was still indicating the microstructure rearrangement within a cycle.     

X-ray scattering measurements of particle orientation in a sheared polymer/clay dispersion

We report steady and transient measurements of particle orientation in a clay dispersion subjected to shear flow. An organically modified clay is dispersed in a Newtonian polymer matrix at a volume fraction of 0.02, using methods previously reported by Mobuchon et al. (Rheol Acta 46: 1045, 2007). In accord with prior studies, mechanical rheometry shows yield stress-like behavior in steady shear, while time dependent growth of modulus is observed following flow cessation. Measurements of flow-induced orientation in the flow-gradient plane of simple shear flow using small-angle and wide-angle X-ray scattering (SAXS and WAXS) are reported. Both SAXS and WAXS reveal increasing particle orientation as shear rate is increased. Partial relaxation of nanoparticle orientation upon flow cessation is well correlated with time-dependent changes in complex modulus. SAXS and WAXS data provide qualitatively similar results; however, some quantitative differences are attributed to differences in the length scales probed by these techniques.     

Development of a thixotropic fluid flow in a pipe

This paper deals with the interaction between the modifications of the internal structure of a thixotropic fluid and the flow development along a pipe. The experimental set-up consists of a pipe, where a flow of thixotropic fluid is provided from a large vessel. The axial velocity distribution was determined using particle image velocimetry technique and ultrasonic velocity profile monitor. At the entrance section, the fluid is assumed to be in a homogeneous structural state corresponding to a high shear rate. The experimental results show a progressive flatness of the velocity profiles due to the aggregation of the structural elements of the fluid. The flow evolution is governed essentially by the kinetics of aggregation and segregation since the associated time scales are longer than the relaxation time of the flow. Received: 23 November 2000/Accepted: 20 May 2001     

The motion of rodlike particles in the pressure-driven flow between two flat plates

The motion of freely suspended rodlike particles has been observed in the pressure-driven flow between the two flat plates of a Hele Shaw flow cell at low Reynolds numbers. Data are reported for rodlike particles with aspect ratios of 12.0 suspended in a Newtonian fluid for gap thickness to particle length ratios of 3, 6, and 20; and for rodlike particles with aspect ratios between 5 and 8 in a non-Newtonian fluid (79.25 wt.% water, 20.2 wt.% glycerine, and 0.55 wt.% polyacrylamide). For the Newtonian fluid, the time-dependent orientation of the particles near and far from walls was shown to be in quantitative agreement with Jeffery's theory for ellipsoids suspended in a simple shear flow if an effective aspect ratio is calculated from the experimental period of rotation. Particles aligned with the flow direction and less than a particle half-length from a wall interacted irreversibly with the wall. For the non-Newtonian fluid, the timedependent orientation far from a wall was shown to be in qualitative agreement with Leal's theory for a second-order fluid; however, particles that were aligned with the flow direction and were near walls did not rotate.     

Effects of vibrations on particle motion near a wall: Existence of attraction force

The effects of small vibrations on a particle oscillating near a solid wall in a fluid cell, relevant to material processing such as crystal growth in space, have been investigated experimentally and theoretically. Assuming the boundary layer around the particle to be thin compared to the particle radius at high vibration frequencies, an inviscid fluid model was developed to predict the motion of a spherical particle placed near a wall of a rectangular liquid-filled cell subjected to a sinusoidal vibration. Under these conditions, a non-uniform pressure distribution around the particle results in an average pressure that gives rise to an attraction force. Theoretical expressions for the attraction force are derived for the particle vibrating normal to and parallel with the nearest cell wall. The magnitude of this attractive force has been verified experimentally by measuring the motion of a steel particle suspended in the fluid cell by a thin wire. Experiments performed at high frequencies showed that the mean particle position, when the particle is brought near a cell wall, shifts towards the same wall, and is dependent on the cell amplitude and frequency, particle and fluid densities.     

Vortex shedding induced by a solitary wave propagating over a submerged vertical plate

Experimental study was conducted on the vortex shedding process induced by the interaction between a solitary wave and a submerged vertical plate. Particle image velocimetry (PIV) was used for quantitative velocity measurement while a particle tracing technique was used for qualitative flow visualization. Vortices are generated at the tip of each side of the plate. The largest vortices at each side of the plate eventually grow to the size of the water depth. Although the fluid motion under the solitary wave is only translatory, vortices are shed in both the upstream and downstream directions due to the interaction of the generated vortices as well as the vortices with the plate and the bottom. The process can be divided into four phases: the formation of a separated shear layer, the generation and shedding of vortices, the formation of a vertical jet, and the impingement of the jet onto the free surface. Similarity velocity profiles were found both in the separated shear layer and in the vertical jet.     

Migration of a solid particle in the vicinity of a plane fluid–fluid interface

The slow migration of a small and solid particle in the vicinity of a gas–liquid, fluid–fluid or solid–fluid plane boundary when subject to a gravity or an external flow field is addressed. By contrast with previous works, the advocated approach holds for arbitrarily shaped particles and arbitrary external Stokes flow fields complying with the conditions on the boundary. It appeals to a few theoretically established and numerically solved boundary-integral equations on the particle’s surface. This integral formulation of the problem allows us to provide asymptotic approximations for a distant boundary and also, implementing a boundary element technique, accurate numerical results for arbitrary locations of the boundary. The results obtained for spheroids, both settling or immersed in external pure shear and straining flows, reveal that the rigid-body motion experienced by a particle deeply depends upon its shape and also upon the boundary location and properties.     

Kinematics and normal stress differences of a viscoelastic fluid undergoing wiggle flow

An experimental program was carried out to determine the laminar regime kinematics and normal stress differences of a viscoelastic fluid in wiggle flow employing non-contact measurement techniques. The viscoelastic fluid was a 5% by weight solution of polyisobutylene dissolved in Primol 355, a high purity mineral oil.The kinematics were determined by Laser-Doppler Anemometry and compared with the data obtained for a Newtonian fluid, Primol 355, under identical flow conditions. It was found that the normalized axial velocity versus axial position curves along the centerline for both fluids superimposed at very low flow rates, an experimental verification that a viscoelastic fluid behaves like a Newtonian fluid under very low shear rates. However, at higher flow rates the behaviour of the viscoelastic fluid curves changed appreciably whereas the Newtonian fluid curves did not change at all. Thus, the effect of flow rate on viscoelastic fluid behaviour was also experimentally established.The normal stress differences were determined using a stress-birefringence apparatus. Data obtained along the centerline clearly exhibited a delayed growth of stress which should be attributed to the expected memory effects in viscoelastic fluid flow.     

A constitutive equation for a dilute solution of Hookean dumbbells with approximate hydrodynamic interaction

In a recent series of papers, Öttinger's consistently averaged hydrodynamic interaction has been shown to yield shear-rate dependent viscosity and normal stress coefficients in steady shear flow for dilute solutions of elastic dumbbells and chains. Even more recently, Fan has numerically solved the diffusion equation for the Hookean dumbbell with complete hydrodynamic interaction and he has compared his results with those of the Öttinger model.In this paper, a new approximation¹ for the Oseen—Burgers tensor is proposed where the configuration-dependent terms are replaced by appropriate averages rather than averaging the Oseen—Burgers tensor as a whole as in the Öttinger model. The proposed model leads to a differential constitutive equation which at low shear rates is similar to the Giesekus constitutive equation for a Hookean dumbbell with anistropic drag and anisotropic Brownian motion. The steady shear viscosity and normal stress coefficients for the proposed model are shear-rate dependent and are in close agreement with Fan's numerical calculations. Elongational viscosity for both positive and negative elongation rates are calculated.     

Suspensions of monodisperse spheres in polymer melts: particle size effects in extensional flow

Suspensions in polymeric, viscoelastic liquids have been studied in uniaxial extensional flow. The fibre wind-up technique has been used for this purpose. The effects of particle size and particle volume fraction have been investigated, using monodisperse, spherical particles. The results have been compared with shear flow data on the same materials. The values of the relative extensional viscosities at low stretching rates are in agreement with the relative shear viscosities and relative moduli. This indicates that hydrodynamic forces are stronger than the particle interaction forces. At larger strain rates strain hardening occurs; it is suppressed when particles are added. Small aggregating particles reduce the strain hardening more strongly than larger particles; strain hardening can even be totally eliminated. When further increasing the stretching rate, hydrodynamic effects dominate again and the effect of particle size effect on strain hardening disappears.     

On the motion of particles in turbulent duct flows

Existing knowledge on particle deposition rates on walls from turbulent pipe and channel flows is summarized and it is shown that discrepancies exist between experimental and theoretical findings. To contribute to the existing experimental information, laser Doppler measurements are reported of the flow field of a glass particle-air two-phase flow. The results reveal certain seemingly peculiar behaviors of the particles which obviously defy the predictions of the conventional analyses of turbulent two-phase suspension flows.In an accompanying approximate, yet pragmatic theoretical approach, an attempt is made to find a rational basis for the explanation of these experimentally observed particle behaviors. It is shown for the particles in the present study, there exists a limiting size above which their response to the agitation of the fluctuating motion of the surrounding fluid could be treated as if the flow were laminar. On this rational basis, these experimentally observed particle behaviors can then be qualitatively explained by the existing theory of particle excursion in a laminar shear flow field.Reported also is a suggestion to extend the present analysis to a dispersion of particles of multiple sizes.     

Mass and heat transfer during solid sphere dissolution in a non-uniform fluid flow

We studied a nonisothermal dissolution of a solvable solid spherical particle in an axisymmetric non-uniform fluid flow when the concentration level of the solute in the solvent is finite (finite dilution of solute approximation). It is shown that simultaneous heat and mass transfer during solid sphere dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with a parabolic velocity profile can be described by a system of generalized equations of convective diffusion and energy. Solutions of diffusion and energy equations are obtained in an exact analytical form. Using a general solution the asymptotic solutions for heat and mass transfer problem during spherical solid particle dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with parabolic velocity profile are derived. Theoretical results are in compliance with the available experimental data on falling urea particles dissolution in water and for solid sphere dissolution in a shear flow.     

Quiescent and shear-induced crystallization of polyprophylenes

In this paper, the effect of shear on the flow-induced crystallization (FIC) of several polypropylenes of various macrostructures was studied using rheometry combined with polarized microscopy. Generally, an increase in strain and strain rate or decrease of temperature is found to decrease the thermodynamic barrier for crystal formation and thus enhancing crystallization kinetics at temperatures between the melting and crystallization points. Secondly, popular models based on suspension theory which are used to relate the degree of crystallinity to normalized rheological functions (such as viscosity) are validated experimentally. For this purpose, the space filling of crystals in the polarized micrographs determined from image processing was plotted as a function of normalized viscosity under various shear rates. It is found that the constant(s) of various suspension models should be dependent on the flow parameters in order for the suspension models to describe the effect of shear on FIC, particularly at higher shear rates.     

Molecular theory for moderately concentrated polymer solutions in shear flow

A molecular theory for the rheological properties of moderately concentrated polymer solutions is developed on the basis of a model of interacting dumbbells. The interaction is treated in a mean field approximation, leading to an effective one-particle potential and a Gaussian stationary distribution function. Various rheological functions such as birefringence, shear viscosity and first normal-stress coefficient for simple shear flow and the Trouton viscosity for simple extensional flow are calculated. Good qualitative agreement with experimental observations is found, especially at intermediate flow rates. It is predicted, for example, that the birefringence increases approximately linearly with shear rate at intermediate shear rates and that the concentration dependence of the gradient varies asc ^1/2. The typical non-Newtonian behaviour is obtained for the shear viscosity. For small concentrations the onset of shear rate dependence decreases asc ^–1/2. At intermediate shear rates an apparent power law is obtained with an exponent between – 0.5 and – 1.0, decreasing with concentration.