Suspensions In Shear Flow Research Articles

Thermodynamics description of startup flow of soft particles glasses.

Particle dynamics simulations are used to study the startup flow of jammed soft particle suspensions in shear flow from a thermodynamic perspective. This thermodynamic framework is established using the concept of the two-body excess entropy extracted from the transient pair distribution function and elastic energy of the suspension as a function of strain at different shear rates and suspension volume fractions. Although the evolution of the elastic energy in these soft particle glasses closely mimics the stress-strain behavior at different shear rates and volume fractions, there are several differences corresponding to their overshoots in terms of the broadness and location of the peaks. The transient excess entropy shows an anisotropic behavior due to the anisotropic distribution of contacts at high shear rates. The excess entropy at high shear rates increases as a function of the strain and attains a steady state. On the other hand, it is nearly constant and isotropic in the quasi-static regime, where the stress response is close to the dynamic yield stress. Using the transient elastic energy and excess entropy, a transient temperature is defined to establish a relationship between thermodynamics and the static yield stress data. This transient temperature increases with the strain and then diverges at strains close to the static yield point at high shear rates.

Numerical simulations of small amplitude oscillatory shear flow of suspensions of rigid particles in non-Newtonian liquids at finite inertia

We perform immersed-boundary-method numerical simulations of small amplitude oscillatory shear flow of suspensions of monodisperse noncolloidal rigid spherical particles in non-Newtonian liquids from the dilute to the concentrated regime. We study the influence of suspending liquid inertia and rheology and particle concentration on the computationally measured storage and loss moduli of the suspensions. In particular, the rheology of the suspending liquid is modeled through the inelastic shear-thinning Carreau–Yasuda constitutive equation and the viscoelastic Giesekus and Oldroyd-B constitutive equations. The role of inertia is quantified by the Stokes number, St, whereas the relevance of the non-Newtonian effects of the suspension matrix is measured through the Carreau number, Cu, for the Carreau–Yasuda liquid and the Deborah number, De, for the viscoelastic liquids. In suspensions with a Carreau–Yasuda matrix, both the storage and the loss modulus increase with St and decrease with Cu, yet the order of magnitude of Cu has to be greater than unity for these effects to be visible. In suspensions with a viscoelastic matrix, both the moduli increase with St and have a nonmonotonic trend with De, showing a maximum with no quantitative differences between the results pertaining suspensions with Giesekus and Oldroyd-B constitutive equations.

Investigation on effective thermal conductivity of microalgae suspensions in a shear flow

To enhance the production efficiency of microalgae products, heat transfer equipment deserves to be specifically designed to regulate the temperature field during the processing of microalgae. The effective thermal conductivity of microalgae suspension in shear flow fields varied with shear rate, which is one of an important property affecting the temperature fields of microalgae suspensions in reactors. Here we investigate the effective thermal conductivity of microalgae suspension in shear flow, which shows a significant difference with the static thermal conductivity. At low shear rates (<236 s−1), the effective thermal conductivity of microalgae suspensions is lower than the static thermal conductivity. In addition, the effective thermal conductivity of microalgae suspension increases with the increasing shear rate (236–471 s−1), while the static thermal conductivity keeps constant at different shear rates. The phenomena are probably because of the micro-motion of suspended microalgae cells in the shear flow field. Considering the effects of the volume fraction and thermal conductivity of microalgae cells, the shear rate, and particle Peclet number, an empirical formula correlation is proposed to predict the effective thermal conductivity of microalgae suspensions in shear flow.

Rheological behavior for laponite and bentonite suspensions in shear flow

The viscometric behavior of laponite and bentonite suspensions at different concentrations in shear flow is studied. It is discovered that in the equilibrium state, a master curve of viscosity can be constructed when the applied shear stress is normalized by the respective suspension’s yield stress. The interparticle interaction controlling the yield behavior at the gel state also dominates the behavior of particles at the equilibrium flowing state. A constitutive framework is developed to describe the master curve of viscosity as a function of the shear stress normalized by the yield stress. Based on the proposed model, the effect of concentration on the viscosity of clay suspensions can be estimated via their yield stress.

Numerical simulations of oscillatory shear flow of particle suspensions at finite inertia

We perform immersed-boundary-method numerical simulations of oscillatory shear flow of suspensions of mono-disperse non-colloidal rigid spherical particles in a Newtonian liquid from the dilute to ...

Polymeric suspensions in shear flow: Relaxation and normal stress differences

Viscometric properties of non-colloidal polymeric suspensions are investigated, showing a longer relaxation time with increasing volume fraction of the particulate phase, due to the influence of particles that form a pairwise close-contact microstructure. This results in a shift of the onset of the shear thinning to a lower shear rate, with a corresponding shift in the first normal stress difference. The effective relaxation time derived from the first normal stress difference and the shear stress is investigated as a function of the particle volume fraction. The relative relaxation time (normalized by the relaxation time of pure polymeric fluid) is independent of the polymeric suspending mediums used in our experiment (various silicone oils of different molecular weights).

Lubrication analysis of interacting rigid cylindrical particles in confined shear flow

Lubrication analysis is used to determine analytical expressions for the elements of the resistance matrix describing the interaction of two rigid cylindrical particles in two-dimensional shear flow in a symmetrically confined channel geometry. The developed model is valid for non-Brownian particles in a low-Reynolds-number flow between two sliding plates with thin gaps between the two particles and also between the particles and the walls. Using this analytical model, a comprehensive overview of the dynamics of interacting cylindrical particles in shear flow is presented. With only hydrodynamic interactions, rigid particles undergo a reversible interaction with no cross-streamline migration, irrespective of the confinement value. However, the interaction time of the particle pair substantially increases with confinement, and at the same time, the minimum distance between the particle surfaces during the interaction substantially decreases with confinement. By combining our purely hydrodynamic model with a simple on/off non-hydrodynamic attractive particle interaction force, the effects of confinement on particle aggregation are qualitatively mapped out in an aggregation diagram. The latter shows that the range of initial relative particle positions for which aggregation occurs is increased substantially due to geometrical confinement. The interacting particle pair exhibits tangential and normal lubrication forces on the sliding plates, which will contribute to the rheology of confined suspensions in shear flow. Due to the combined effects of the confining walls and the particle interaction, the particle velocities and resulting forces both tangential and perpendicular to the walls exhibit a non-monotonic evolution as a function of the orientation angle of the particle pair. However, by incorporating appropriate scalings of the forces, velocities, and doublet orientation angle with the minimum free fraction of the gap height and the plate speed, master curves for the forces versus orientation angle can be constructed.

The effect of shear flow on the rotational diffusion of a single axisymmetric particle

Understanding the orientation dynamics of anisotropic colloidal particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in shear flow, the orientation dynamics of non-spherical Brownian particles are poorly understood. Here we analytically calculate the time-dependent orientation distributions for non-spherical axisymmetric particles confined to rotate in the flow–gradient plane, in the limit of small but non-zero Brownian diffusivity. For continuous shear, despite the complicated dynamics arising from the particle rotations, we find a coordinate change that maps the orientation dynamics to a diffusion equation with a remarkably simple ratio of the enhanced rotary diffusivity to the zero shear diffusion:$D_{eff}^{r}/D_{0}^{r}=(3/8)(p-1/p)^{2}+1$, where$p$is the particle aspect ratio. For oscillatory shear, the enhanced diffusion becomes orientation dependent and drastically alters the long-time orientation distributions. We describe a general method for solving the time-dependent oscillatory shear distributions and finding the effective diffusion constant. As an illustration, we use this method to solve for the diffusion and distributions in the case of triangle-wave oscillatory shear and find that they depend strongly on the strain amplitude and particle aspect ratio. These results provide new insight into the time-dependent rheology of suspensions of anisotropic particles. For continuous shear, we find two distinct diffusive time scales in the rheology that scale separately with aspect ratio$p$, as$1/D_{0}^{r}p^{4}$and as$1/D_{0}^{r}p^{2}$for$p\gg 1$. For oscillatory shear flows, the intrinsic viscosity oscillates with the strain amplitude. Finally, we show the relevance of our results to real suspensions in which particles can rotate freely. Collectively, the interplay between shear-induced rotations and diffusion has rich structure and strong effects: for a particle with aspect ratio 10, the oscillatory shear intrinsic viscosity varies by a factor of${\approx}2$and the rotational diffusion by a factor of${\approx}40$.

Modeling and Analysis of Electrorheological Suspensions in Shear Flow

A model capable of describing the flow behavior of electrorheological (ER) suspensions under different electric field strengths and over the full range of shear rates is proposed. Structural reformation in the low shear rate region is investigated where parts of a material are in an undeformed state, while aligned structures reform under the shear force. The model's predictions were compared with the experimental data of some ER fluids as well as the CCJ (Cho-Choi-Jhon) model. This simple model's predictions of suspension flow behavior with subsequent aligned structure reformation agreed well with the experimental data, both quantitatively and qualitatively. The proposed model plausibly predicted the static yield stress, whereas the CCJ model and the Bingham model predicted only the dynamic yield stress. The master curve describing the apparent viscosity was obtained by appropriate scaling both axes, which showed that a combination of dimensional analysis and flow curve analysis using the proposed model yielded a quantitatively and qualitatively precise description of ER fluid rheological behavior based on relatively few experimental measurements.

Effect of repulsive interactions on structure and rheology of sheared colloidal dispersions

A previously developed Smoluchowski theory for concentrated hard-sphere suspensions in shear flow is extended to study structure and rheology of colloidal suspensions with soft repulsive interactions. Accelerated Stokesian Dynamics simulations are carried out to provide insight and to enable direct comparison with theoretical predictions. The effect of extended range repulsive interactions is studied by considering repulsive interactions with different steepness, using identical potentials in simulation and theory, for varying shear rates characterized in dimensionless form as 0.1 ≤ Pe ≤ 100; here, Pe = 6πηa3/kbT is the ratio of hydrodynamic to Brownian forces and η is the fluid viscosity, is the shear rate, a is the particle radius and kbT is the thermal energy. Examples of predicted microstructures and the equivalent simulated results for hard-sphere suspensions at ϕ = 0.40 are also presented for comparison. The predicted pair distribution function is in good agreement with simulations before the onset of a shear-induced ordering transition in simulations of the soft colloids. The calculations of shear viscosity based on the predicted microstructure were also in general agreement with simulation results. The role of hydrodynamic interactions on flow-induced structures is discussed in the context of the proposed theory.

Dynamics of Vesicle Suspensions in Shear Flow Between Walls

The behaviour of a vesicle suspension in a simple shear flow between plates (Couette flow) was investigated experimentally in parabolic flight and sounding rocket experiments by Digital Holographic Microscopy. The lift force which pushes deformable vesicles away from walls was quantitatively investigated and is found to be rather well described by a theoretical model by Olla (J Phys II (France) 7:1533, 1997). At longer shearing times, vesicles reach a steady distribution about the center plane of the shear flow chamber, through a balance between the lift force and shear induced diffusion due to hydrodynamic interactions between vesicles. This steady distribution was investigated in the BIOMICS experiment in the MASER 11 sounding rocket. The results allow an estimation of self-diffusion coefficients in vesicle suspensions and reveal possible segregation phenomena in polydisperse suspensions.

STRUCTURE AND PROPERTIES OF CONCENTRATED FIBER SUSPENSIONS IN A SHEAR FLOW

The concentrated fiber suspensions in a simple shear flow are simulated numerically by taking into account the hydrodynamic interactions and fiber–fiber mechanical contacts. The orientation probability distribution of fibers, the specific viscosity and the first normal stress difference are obtained. The comparison of the specific viscosity to experimental data is made and the agreement is good. The results show that initially randomly-oriented fibers are re-oriented in the flow direction. The hydrodynamic interactions and fiber–fiber mechanical contacts result in an increase in the spread of the orientation distribution and asymmetric orientation distribution about the flow direction. Fiber's alignment with the flow direction becomes more obvious with an increasing shear rate. In a concentrated fiber suspension, the force induced by the fiber–fiber mechanical contact plays a more important role than that induced by hydrodynamic interactions. The specific viscosity of fiber suspension grows with concentration for various aspect ratios. For a fixed concentration, the larger the aspect ratio is, the higher the specific viscosity is. The specific viscosity calculated by taking into account both hydrodynamic interactions and fiber–fiber mechanical contacts is larger than that only taking into account the fiber–fiber mechanical contacts. The effect of aspect ratio on the first normal stress difference is more obvious at high concentration. Taking into account the hydrodynamic interactions or not will make a big difference in the first normal stress difference.

Transient behavior of electrorheological fluids in shear flow

The transient response of electrorheological suspensions in shear flow subjected to a suddenly imposed electric field is investigated experimentally. Barium titanate∕silicone oil and alumina∕mineral oil suspensions are employed. The evolution of both the rheological properties and the suspension structure are investigated. Results are compared with predictions from a two-fluid continuum model reported previously. Transient responses appear above a critical field strength, and the critical Mason number for the onset of a transient rheological response is equivalent to the critical Mason number for the onset of lamella formation, within experimental uncertainty. These results are consistent with predictions. The experimentally determined values of the critical Mason number agree with those predicted, with differences of the order of the experimental uncertainty. However, we find that the critical Mason number depends on shear rate, rather than being independent of shear rate as predicted.

Correlation between stresses and microstructure in concentrated suspensions of non-Brownian spheres subject to unsteady shear flows

Stresses within unsteady simple shear flows of suspensions of non-Brownian spheres constrained to move in the velocity-gradient plane are calculated using Stokesian dynamics simulations. The unsteady flows considered include shear reversal and oscillatory flows of varying strain amplitude. The evolution of the stresses in time are reported along with the corresponding microstructural development for all flow conditions. For shear reversal, the shear stress rapidly decreases to a minimum before gradually returning to the steady state value reached in the previous direction, whereas the normal stress briefly changes sign upon reversal of shear before returning to the steady state value. For oscillatory shear flow, the shear stress increases with total strain before attaining a steady state that depends upon the applied strain amplitude, indicating irreversible behavior even at small strain amplitudes. The shear stresses show a nonmonotonic dependence on the applied strain amplitude that agrees with experimental results [Bricker and Butler, J. Rheol. 50, 711–728 (2006)]. The steady state normal stresses also depend on the strain amplitude and may change signs at low strain amplitudes.

Rheology of a dilute suspension of rigid spheres in a second order fluid

The stress tensor for a dilute suspension of buoyancy free, inertialess, nonBrownian, rigid spheres immersed in a viscoelastic liquid is determined via a perturbative expansion. The perturbation parameter is the Deborah number De, giving the ratio between the characteristic time of the liquid and the characteristic time of the imposed flow. The theoretical predictions upto order De are validated through numerical simulations of continuity and momentum equations for the single sphere problem. The analytic expressions for the local fields of velocity, pressure, and stresses are successfully compared with the results obtained with finite element calculations. Bulk rheological quantities from theory and simulations also show an excellent agreement with each other. Good agreement is found with respect to experimental data from the literature, e.g., on bulk normal stresses for dilute suspensions in shear flow.

Lattice-Boltzmann Simulation of Particle Suspensions in Shear Flow

Inclusion of short-range particle–particle interactions for increased numerical stability in a lattice-Boltzmann code for particle-fluid suspensions, and handling of the particle phase for an effective implementation of the code for parallel computing, are discussed and formulated. In order to better understand the origin of the shear-thickening behavior observed in real suspensions, two simplified cases are considered with the code thus developed. A chain-like cluster of suspended particles is shown to increase the momentum transfer in a shear flow between channel walls, and thereby the effective viscosity of the suspension in comparison with random configurations of particles. A single suspended particle is also shown to increase the effective viscosity under shear flow of this simple suspension for particle Reynolds numbers above unity, due to inertial effects that change the flow configuration around the particle. These mechanisms are expected to carry over to large-scale particle-fluid suspensions.

Transport phenomena and structuring in shear flow of suspensions near solidwalls

In this paper we apply the lattice Boltzmann method and an extension to particlesuspensions as introduced by Ladd et al to study transport phenomena and structuringeffects of particles suspended in a fluid near sheared solid walls. We find that a particle freeregion arises near walls, which has a width depending on the shear rate and the particleconcentration. The wall causes the formation of parallel particle layers at lowconcentrations, where the number of particles per layer decreases with increasing distancefrom the wall.

Rheology and Ultrasound Scattering from Aggregated Red Cell Suspensions in Shear Flow

The shear flow dynamics of reversible red cell aggregates in dense suspensions were investigated by ultrasound scattering, to study the shear disruption processes of Rayleigh clusters and examine the effective mean field approximation used in microrheological models. In a first section, a rheo-acoustical model, in the Rayleigh scattering regime, is proposed to describe the shear stress dependence of the low frequency scattered power in relation to structural parameters. The fractal scattering regime characterizing the anisotropic scattering from flocs of size larger than the ultrasound wavelength is further discussed. In the second section, we report flow-dependent changes in the low-frequency scattering coefficient in a plane-plane flow geometry to analyze the shear disruption processes of hardened or deformable red cell aggregates in neutral dextran polymer solution. Rheo-acoustical experiments are examined on the basis of the rheo-acoustical model and the effective medium approximation. The ability of ultrasound scattering technique to determine the critical disaggregation shear stress and to give quantitative information on particle surface adhesive energy is analyzed. Lastly, the shear-thinning behavior of weakly aggregated hardened or deformable red cells is described.

Aggregation and Breakup of Colloidal Particle Aggregates in Shear Flow, Studied with Video Microscopy

We used video microscopy to study the behavior of aggregating suspensions in shear flow. Suspensions consisted of 920 nm diameter silica spheres, dispersed in a methanol/bromoform solvent, to which poly(ethylene glycol) (M = 35.000 g) was added to effect weak particle aggregation. With our solvent mixture, the refractive index of the particles could be closely matched, to allow microscopic observations up to 80 microm deep into the suspension. Also the mass density is nearly equal to that of the particles, thus allowing long observation times without problems due to aggregate sedimentation. Particles were visualized via fluorescent molecules incorporated into their cores. Using a fast confocal scanning laser microscope made it possible to characterize the (flowing) aggregates via their contour-area distributions as observed in the focal plane. The aggregation process was monitored from the initial state (just after adding the polymer), until a steady state was reached. The particle volume fraction was chosen at 0.001, to obtain a characteristic aggregation time of a few hundred seconds. On variation of polymer concentration, cP (2.2-12.0 g/L), and shear rate, gamma (3-6/s), it was observed that the volume-averaged size, Dv, in the steady state became larger with polymer concentration and smaller with shear rate. This demonstrates that the aggregate size is set by a competition between cohesive forces caused by the polymer and rupture forces caused by the flow. Also aggregate size distributions were be measured (semiquantitatively). Together with a description for the internal aggregate structure they allowed a modeling of the complete aggregation curve, from t = 0 up to the steady state. A satisfactory description could be obtained by describing the aggregates as fractal objects, with Df = 2.0, as measured from CSLM images after stopping the flow. In this modeling, the fitted characteristic breakup time was found to increase with cP.

Shear Flow of Suspensions under Wall Influence: Phenomenological Theory and Effects

AbstractThe influence of solid boundary walls in shear flow of suspensions leads to structure formation and particle transport. We have developed a phenomenological model to describe the wall effects such as the formation of a wall boundary layer, the occurence of pseudo wall slip as well as discontinuities of the particle concentration. Using the model particle concentration profiles, thickness of boundary layer and suitably defined wall slip velocities depending on the total particle concentration of the suspension can be determined.