Suspensions In Shear Flow Research Articles

Thermal conductivity of suspensions in shear flow fields

In the present article, the rheological behavior and the thermal conductivity of suspensions were investigated experimentally by examining the effects of shear rate, particle size, and volume concentration. The thermal conductivity measurements were conducted under rotating Couette flow conditions with a varying rotational speed of the outer cylinder. Homogeneous test suspensions were prepared with uniformly dispersed and neutrally buoyant micro-particles. Four different sizes of plastic particles (25–300 μm) were used as suspended particles. The volume concentrations of the particles and shear rates varied within the ranges of 0–10% and 0–900 1/s, respectively. For the test suspensions, the limiting viscosities at high shear rates were correlated with the Batchelor equation. The highly concentrated suspension in the present study showed the shear thinning viscosity. The thermal conductivities measured at stationary condition showed excellent agreements with values in saturated water table and were correlated satisfactorily with the Brailsford–Major equation. The thermal conductivity of the test suspensions in shear flow increased with shear rate and displayed asymptotic plateau values at high shear rates. The shear-rate-dependent conductivity was strongly affected by both particle size and volume concentration in shear flow field.

Simple Shear Flow of Suspensions of Elastic Capsules

The simple shear flow of homogeneous suspensions of two-dimensional capsules enclosed by elastic membranes is studied in the limit of vanishing Reynolds number, in the special case where the viscosity of the fluid enclosed by the capsules is equal to the viscosity of the ambient fluid. The deformation of capsules with circular, elliptical, and biconcave unstressed shapes, and the rheological and statistical properties of their infinitely dilute and moderately dense suspensions are investigated by dynamical simulation using the method of interfacial dynamics for Stokes flow. In a preliminary investigation, the behavior of solitary capsules suspended in an infinite fluid is studied as a function of the dimensionless membrane elasticity number expressing the capsule deformability or the strength of the shear flow. It is found that a critical elasticity number above which a capsule exhibits continued elongation does not exist, and an equilibrium configuration is reached no matter how large the shear rate, in agreement with previous results for three-dimensional flow. A correspondence is established between the elasticity numbers for two- and three-dimensional flow at which the capsules undergo the same degree of deformation. Simulations of pairwise capsule interceptions reveal behavior similar to that exhibited by liquid drops with uniform surface tension. Because of strong hydrodynamic interactions in two-dimensional Stokes flow, the concept of hydrodynamic diffusivity in the limit of infinite dilution is ill-defined in the absence of fluid inertia. Dynamical simulations of doubly periodic monodisperse suspensions with up to 50 capsules distributed in each periodic cell at areal fractions of 0.25 and 0.40 provide information on the effective rheological properties of the suspension and on the nature of the statistical properties of the particle motion. The character of the flow is found to be intermediate between that of liquid drops and rigid particles, and this is attributed to the membrane deformability and to the ability of the interfaces to perform tank-treading motion. The results are compared with rheological measurements of blood flow with good agreement.

Phase separation of rigid-rod suspensions in shear flow.

We analyze the behavior of a suspension of rigid-rod-like particles in shear flow using a modified version of the Doi model, and construct diagrams for phase coexistence under conditions of constant imposed stress and constant imposed strain rate, among paranematic, flow-aligning nematic, and log-rolling nematic states. We calculate the effective constitutive relations that would be measured through the regime of phase separation into shear bands. We calculate phase coexistence by examining the stability of interfacial steady states and find a wide range of possible "phase" behaviors.

Significance of the dispersed-phase viscosity on the simple shear flow of suspensions of two-dimensional liquid drops

The significance of drop-fluid viscosity on the effective rheological properties and on the dynamics of the microstructure of mono-disperse suspensions of two-dimensional liquid drops with constant interfacial tension is investigated by means of numerical simulations at vanishing Reynolds number, using the boundary integral method for Stokes flow. Three important features of the numerical method are the computation of the doubly-periodic Green's function and associated stress tensor by tabulation and interpolation, the iterative solution of a deflated integral equation for the interfacial velocity, and the repositioning of the drop interfaces at close proximity to avoid artificial coalescence. In the first part of the simulations, the interaction of two intercepting drops in simple shear flow is studied in an extended range of conditions, and the results are used to quantify the behaviour and develop insights into the physics of dilute systems. In the second part of the simulations, the motion of a random suspension of 25 drops repeated periodically in the two spatial directions is studied at the areal fraction Φ = 0.30, drop fluid to ambient fluid viscosity ratio λ = 1 or 10, and drop capillary number Ca = 0.10 or 0.30, a total of four combinations

A direct simulation of fibre suspensions

A numerical method to simulate fibre suspensions in shear flow is reported, which takes into account short range interaction via lubrication forces and long range interaction via slender body approximation, together with an appropriate Ewald summation technique. The numerical results are averaged to produce macroscopic properties of the suspension, including the Folgar–Tucker diffusion constant, the structure functions, and the reduced viscosity. In the semi-concentrated to concentrated regime, the fibres no longer follow Jeffery's orbits, they align mostly with the shear direction. Numerical data on the diffusivity constant, the structure functions, and the reduced viscosity agree reasonably well with available experimental data.

Simple shear flow of suspensions of liquid drops

The shearing motion of monodisperse suspensions of two-dimensional deformable liquid drops with uniform interfacial tension is studied by means of numerical simulations. In the theoretical model, the drops are distributed randomly within a square that is repeated periodically in two directions yielding a doubly periodic flow. Under the assumption that inertial effects are negligible and the viscosity of the drops is equal to that of the suspending fluid, the motion is investigated as a function of the area fraction of the suspended drops and of the capillary number. The evolution of the suspension from an initial configuration with randomly distributed circular drops is computed using an improved implementation of the method of interfacial dynamics which is based on the standard boundary integral formulation for Stokes flow. The numerical procedure incorporates the method of multipole expansions to account for far-drop interactions, and interpolation through tables for computing the doubly periodic Green's function ; the latter allows considerable savings in the cost of the computations. Dynamic simulations are carried out for suspensions with up to 49 drops within each periodic cell, for an extended period of time up to kt = 60, where k is the shear rate. Comparisons with previous numerical results for solid particles reveal that particle deformability and interfacial mobility play an important role in the character of the motion. The effects of particle area fraction and capillary number on the effective rheological properties of the suspension are discussed, and the statistics of the drop motion is analysed with reference to the drop-centre pair distribution function and probability density functions of drop aspect ratio and inclination. It is found that the effective rheological properties may be predicted with remarkable accuracy from a knowledge of the instantaneous mean drop deformation and orientation alone, even at high area fractions. Cluster formation is not as important as in suspension of solid particles. The apparent random motion of the individual drops, when viewed at a sequence of time intervals that are large compared to the inverse shear rate, is described in terms of an effective non-isotropic long-time diffusivity tensor, and the transverse component of this tensor is computed from the results of the simulations with some uncertainty.

Dynamic simulation of fiber suspensions in shear flow

A new method is presented to simulate the motion of concentrated fiber suspensions in shear flow at low Reynolds numbers without Brownian motion. The hydrodynamic interaction among fibers is considered in a particle simulation method (PSM), in which a fiber is modeled by arrays of spheres. The motion of each constituent sphere of a fiber, which are dispersed into a unit cell with periodic boundaries, is followed to predict the microstructure and the rheological properties. The hydrodynamic interaction is decomposed into two parts, intra- and interfiber ones. In the former, the many-body problem is solved by calculating the mobility matrix for each fiber to obtain the hydrodynamic force and torque exerted on each sphere. In the latter, only the near-field lubrication force is considered between spheres of one fiber and another. The validity of this approximate treatment was first examined for the sphere dispersed system. The simulated microstructure and the rheological properties were in very good agreement with results of both experiments and the Stokesian dynamics. The methodology was then applied to concentrated rigid and flexible fiber suspensions. The overshoot of suspension viscosity was observed at the early stage for rigid fiber suspensions, but not for flexible ones. This was because of the transient change of the microstructure from the flow-directional orientation to the planar orientation of rigid fibers. The normal stress was calculated for the flexible fiber suspension and clearly showed that the elasticity of fiber suspensions was due to the deformation of fibers. The proposed simulation method can predict the effect of such parameters as the aspect ratio, flexibility, and volume fraction of fibers on the microstructure and the rheological properties of fiber suspensions.

On the mechanism of aggregation in the shear flow of suspensions

A theoretical analysis of aggregation and disaggregation processes in the laminar shear flow of a suspension is presented. Aggregate formation is attributed to orthokinetic coagulation, which is considered in terms of the hierarchical model (i.e., only the collisions of equal-sized aggregates are taken into account, whereas all other types of collisions are shown to be ineffective). Different limiting mechanisms of aggregate growth are considered. They include breakup of an aggregate due to the Brownian motion of particles or due to viscous stresses and its contraction, i.e., the increase in its fractal dimension. Three types of experiments are quantitatively interpreted in terms of the considered model of aggregation: the reduction of aggregate number concentration in flow due to orthokinetic coagulation, the measurement of the maximum aggregate size vs shear rate, and rheological tests.

Microrheological models of aggregated suspensions in shear flow

Theoretical analyses are presented of three previously proposed models of the aggregation—disaggregation process, with numerically calculated predictions of the corresponding viscosity vs shear rate behavior. All the models are based on the assumption that aggregation of particles is due to surface forces of arbitrary nature and disaggregation is due to viscous stresses. The models differ from each other by the methods of taking into account hydrodynamic interaction of aggregates. Some modifications of the models are considered and different methods of the aggregates yield stress evaluation are compared. It is shown that two models (one of them is based on the mean field theory and the other utilizes the free cell theory) correspond to the diluted suspensions and the third one (based on the lubrication theory) can be applied to the suspensions of high concentration and low concentration as well.

Experimental study on solid particle dynamics in shear flow

Uniform shear flow of suspensions is generated between two vertical parallel belts with adjustable speeds. Two cameras at right angles are used to track the three-dimensional motion of solid particles. The experiments were carried out with three particle sizes, four carrier fluids and five shear rates. The experiments are illustrated for suspensions of spheres of 12.6-mm dia, with a relative density in fluid ϱ S/ϱ F = 1.166, and concentration α S = 5 vol.%. Opaque particles are introduced in the optically transparent mixture of particles having the same refractive index as the carrying fluid. The paper presents the apparatus, the high-speed video recording of the interior of the flow field, and the image analysis. The recorded data provide the necessary information to identify the flow regime, to determine single particle dynamics, the inertial shear stresses and kinetic energy, to measure the density distribution functions for parameters attached to neighboring particles, as well as to find significant correlations for the assembly of particles within a control volume. The results will be used to better understand the transport processes at particle scale and improve the macroscopic modeling.

Structure of Thixotropic Suspensions in Shear Flow. III. Time-Dependent Behavior

The time-dependent viscosity of bentonite-water suspensions was studied experimentally in Couette flow for various transitions between constant shear rates. It was found that after a sudden change in the shear rate the time dependence of the viscosity can be described by η(t)=A exp[−(t/τ1)4.0]+B exp(−t/τ2)+C, with τ2>τ1. In general, the characteristic times: 1) become longer as the differences in shear rates become smaller; 2) decrease with increasing concentration; 3) show little temperature effect for a 20°C temperature change. A theory for the time-dependent behavior is given which can reproduce the essential features of the experimental results.

Structure of thixotropic suspensions in shear flow: II. Optical properties

A theory of the opacity of bentonite-water suspensions as a function of the shear rate is given. The experimental opacity behavior confirms previous theoretical predictions of the aggregate size distribution. The extinction coefficient of bentonite was determined at two wavelengths.

Structure of thixotropic suspensions in shear flow: I. Mechanical properties

A theory for the steady state viscosity η of thixotropic clay-water suspensions is given. The numerical results of this analysis can be approximated by u + u2/10 = K/γ̇ where u = (ηr − 1)/C, γ̇ is the shear rate, η∞ is the viscosity for γ̇ → ∞, ηr =η/η∞, and K and C are parameters depending on concentration and temperature. For large shear rates this expression reduces to the Bingham behavior ηr = 1 + τ0/η∞γ̇, where τ0 is the Bingham yield stress. Experiments on a Wyoming bentonite at various concentrations and temperatures give good agreement with the theoretically predicted behavior. The comparison of experimental and analytical results yields the cohesive force per particle and the ratio of the major and minor dimensions of the bentonite particles.