Suspensions with a tunable effective viscosity: a numerical study

2012 ◽  
Vol 693 ◽  
pp. 345-366 ◽  
Author(s):  
L. Jibuti ◽  
S. Rafaï ◽  
P. Peyla
Keyword(s):  
Effective Viscosity ◽  
Volume Fraction ◽  
Numerical Study ◽  
Spherical Particles ◽  
Dimensionless Number ◽  
Particle Rotation ◽  
Concentrated Suspensions ◽  
Sheared Suspensions ◽  
Neutrally Buoyant ◽  
Universal Behaviour

AbstractIn this paper, we conduct a numerical investigation of sheared suspensions of non-colloidal spherical particles on which a torque is applied. Particles are mono-dispersed and neutrally buoyant. Since the torque modifies particle rotation, we show that it can indeed strongly change the effective viscosity of semi-dilute or even more concentrated suspensions. We perform our calculations up to a volume fraction of 28 %. And we compare our results to data obtained at 40 % by Yeo and Maxey (Phys. Rev. E, vol. 81, 2010, p. 62501) with a totally different numerical method. Depending on the torque orientation, one can increase (decrease) the rotation of the particles. This results in a strong enhancement (reduction) of the effective shear viscosity of the suspension. We construct a dimensionless number $\Theta $ which represents the average relative angular velocity of the particles divided by the vorticity of the fluid generated by the shear flow. We show that the contribution of the particles to the effective viscosity can be suppressed for a given and unique value of $\Theta $ independently of the volume fraction. In addition, we obtain a universal behaviour (i.e. independent of the volume fraction) when we plot the relative effective viscosity divided by the relative effective viscosity without torque as a function of $\Theta $. Finally, we show that a modified Faxén law can be equivalently established for large concentrations.

A Parametric Numerical Study of Radiative Transfer in Thermotropic Materials

2013 ◽  
Author(s):  
Adam C. Gladen ◽  
Susan C. Mantell ◽  
Jane H. Davidson
Keyword(s):  
Particle Size ◽  
Radiative Transfer ◽  
Optical Thickness ◽  
Parametric Study ◽  
Volume Fraction ◽  
Numerical Study ◽  
Anisotropic Scattering ◽  
Index Of Refraction ◽  
Spherical Particles ◽  
Size Parameter

A thermotropic material is modeled as an absorbing, thin slab containing anisotropic scattering, monodisperse, spherical particles. Monte Carlo ray tracing is used to solve the governing equation of radiative transfer. Predicted results are validated by comparison to the measured normal-hemispherical reflectance and transmittance of samples with various volume fraction and relative index of refraction. A parametric study elucidates the effects of particle size parameter, scattering albedo, and optical thickness on the normal-hemispherical transmittance, reflectance, and absorptance. The results are interpreted for a thermotropic material used for overheat protection of a polymer solar absorber. For the preferred particle size parameter of 2, the optical thickness should be less than 0.3 to ensure high transmittance in the clear state. To significantly reduce the transmittance and increase the reflectance in the translucent state, the optical thickness should be greater than 2.5 and the scattering albedo should be greater than 0.995. For optical thickness greater than 5, the reflectance is asymptotic and any further reduction in transmittance is through increased absorptance. A case study is used to illustrate how the parametric study can be used to guide the design of thermotropic materials. Low molecular weighted polyethylene in poly(methyl methacrylate) is identified as a potential thermotropic material. For this material and a particle radius of 200 nm, it is determined that the volume fraction and thickness should equal 10% and 1 mm, respectively.

Heat transfer across sheared suspensions: role of the shear-induced diffusion

2013 ◽  
Vol 724 ◽  
pp. 527-552 ◽  
Author(s):  
Bloen Metzger ◽  
Ouamar Rahli ◽  
Xiaolong Yin
Keyword(s):  
Thermal Diffusivity ◽  
Volume Fraction ◽  
Spherical Particles ◽  
Transient Temperature ◽  
Particle Diffusion ◽  
Driving Mechanism ◽  
Average Particle ◽  
Particle Rotation ◽  
Effective Thermal Diffusivity ◽  
Couette Cell

AbstractSuspensions of non-Brownian spherical particles undergoing shear provide a unique system where mixing occurs spontaneously at low Reynolds numbers. Through a combination of experiments and simulations, we investigate the effect of shear-induced particle diffusion on the transfer of heat across suspensions. The influence of particle size, particle volume fraction and applied shear are examined. By applying a heat pulse to the inner copper wall of a Couette cell and analysing its transient temperature decay, the effective thermal diffusivity of the suspension, $\alpha $, is obtained. Using index matching and laser-induced fluorescence imaging, we measured individual particle trajectories and calculated their diffusion coefficients. Simulations that combined a lattice Boltzmann technique to solve for the flow and a passive Brownian tracer algorithm to solve for the transfer of heat are in very good agreement with experiments. Fluctuations induced by the presence of particles within the fluid cause a significant enhancement (${\gt }200\hspace{0.167em} \% $) of the suspension transport properties. The effective thermal diffusivity was found to be linear with respect to both the Péclet number ($\mathit{Pe}= \dot {\gamma } {d}^{2} / {\alpha }_{0} \leq 100$) and the solid volume fraction ($\phi \leq 40\hspace{0.167em} \% $), leading to a simple correlation $\alpha / {\alpha }_{0} = 1+ \beta \phi \mathit{Pe}$ where $\beta = 0. 046$ and ${\alpha }_{0} $ is the thermal diffusivity of the suspension at rest. In our Couette cell, the enhancement was found to be optimum for a volume fraction, $\phi \approx 40\hspace{0.167em} \% $, above which, due to steric effects, both the particle diffusion motion and of the effective thermal diffusion dramatically decrease. No such correlation was found between the average particle rotation and the thermal diffusivity of the suspension, suggesting that the driving mechanism for enhanced transport is the translational particle diffusivity. Movies are available with the online version of the paper.

scholarly journals On the effect of coalescence on the rheology of emulsions

2019 ◽  
Vol 880 ◽  
pp. 969-991 ◽  
Author(s):  
Francesco De Vita ◽  
Marco Edoardo Rosti ◽  
Sergio Caserta ◽  
Luca Brandt
Keyword(s):  
Disperse Phase ◽  
Effective Viscosity ◽  
Volume Fraction ◽  
Numerical Study ◽  
Extensional Flow ◽  
Interface Tension ◽  
Flow Topology ◽  
Volume Fractions ◽  
Rotational Components ◽  
The Matrix

We present a numerical study of the rheology of a two-fluid emulsion in dilute and semidilute conditions. The analysis is performed for different capillary numbers, volume fractions and viscosity ratios under the assumption of negligible inertia and zero buoyancy force. The effective viscosity of the system increases for low values of the volume fraction and decreases for higher values, with a maximum for approximately 20 % concentration of the disperse phase. When the dispersed fluid has lower viscosity, the normalised effective viscosity becomes smaller than 1 for high enough volume fractions. To single out the effect of droplet coalescence on the rheology of the emulsion we introduce an Eulerian force which prevents merging, effectively modelling the presence of surfactants in the system. When the coalescence is inhibited the effective viscosity is always greater than 1 and the curvature of the function representing the emulsion effective viscosity versus the volume fraction becomes positive, resembling the behaviour of suspensions of deformable particles. The reduction of the effective viscosity in the presence of coalescence is associated with the reduction of the total surface of the disperse phase when the droplets merge, which leads to a reduction of the interface tension contribution to the total shear stress. The probability density function of the flow topology parameter shows that the flow is mostly a shear flow in the matrix phase, with regions of extensional flow when the coalescence is prohibited. The flow in the disperse phase, instead, always shows rotational components. The first normal stress difference is positive, except for the smallest viscosity ratio considered, whereas the second normal difference is negative, with their ratio being constant with the volume fraction. Our results clearly show that the coalescence efficiency strongly affects the system rheology and that neglecting droplet merging can lead to erroneous predictions.

scholarly journals Dipolophoresis in concentrated suspensions of ideally polarizable spheres

2019 ◽  
Vol 875 ◽  
Author(s):  
Siamak Mirfendereski ◽  
Jae Sung Park
Keyword(s):  
Large Scale ◽  
Volume Fraction ◽  
Local Maximum ◽  
Close Packing ◽  
Density Fluctuations ◽  
Distribution Functions ◽  
Spherical Particles ◽  
Concentrated Suspensions ◽  
Induced Charge ◽  
Pair Distribution Functions

The dynamics of ideally polarizable spherical particles in concentrated suspensions under the effects of nonlinear electrokinetic phenomena is analysed using large-scale numerical simulations. Particles are assumed to carry no net charge and considered to undergo the combination of dielectrophoresis and induced-charge electrophoresis termed dipolophoresis. Chaotic motion and resulting hydrodynamic diffusion are known to be driven by the induced-charge electrophoresis, which dominates the dielectrophoresis. Up to a volume fraction $\unicode[STIX]{x1D719}\approx 35\,\%$, the particle dynamics seems to be hindered by the increase in the magnitude of excluded volume interactions with concentration. However, a non-trivial suspension behaviour is observed in concentrated regimes, where the hydrodynamic diffusivity starts to increase with the volume fraction at $\unicode[STIX]{x1D719}\approx 35\,\%$, before reaching a local maximum, and then drastically decreases on approaching random close packing. Similar non-trivial behaviours are observed in the particle velocity and number-density fluctuations around volume fractions at which the non-trivial behaviour of the hydrodynamic diffusion is observed. We explain these non-trivial behaviours as a consequence of particle contacts, which are related to the dominant mechanism of particle pairings. The particle contacts are classified into attractive and repulsive classes by the nature of contacts, and in particular, the strong repulsive contact becomes predominant at $\unicode[STIX]{x1D719}>20\,\%$. Moreover, this transition is visible in the pair distribution functions, which also reveal the change in the suspension microstructure in concentrated regimes. It appears that strong and massive repulsive contacts along the direction perpendicular to an electric field promote the non-trivial suspension behaviours observed in concentrated regimes.

Shape effects on turbulent modulation by large nearly neutrally buoyant particles

2012 ◽  
Vol 712 ◽  
pp. 41-60 ◽  
Author(s):  
Gabriele Bellani ◽  
Margaret L. Byron ◽  
Audric G. Collignon ◽  
Colin R. Meyer ◽  
Evan A. Variano
Keyword(s):  
Single Phase ◽  
Volume Fraction ◽  
Spatial Scales ◽  
Spherical Particles ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Particle Rotation ◽  
Turbulent Statistics ◽  
Small Scales ◽  
Shape Effects

AbstractWe investigate dilute suspensions of Taylor-microscale-sized particles in homogeneous isotropic turbulence. In particular, we focus on the effect of particle shape on particle–fluid interaction. We conduct laboratory experiments using a novel experimental technique to simultaneously measure the kinematics of fluid and particle phases. This uses transparent particles having the same refractive index as water, whose motion we track via embedded optical tracers. We compare the turbulent statistics of a single-phase flow to the turbulent statistics of the fluid phase in a particle–laden suspension. Two suspensions are compared, one in which the particles are spheres and the other in which they are prolate ellipsoids with aspect ratio 2. We find that spherical particles at volume fraction ${\phi }_{v} = 0. 14\hspace{0.167em} \% $ reduce the turbulent kinetic energy (TKE) by 15 % relative to the single-phase flow. At the same volume fraction (and slightly smaller total surface area), ellipsoidal particles have a much smaller effect: they reduce the TKE by 3 % relative to the single-phase flow. Spectral analysis shows the details of TKE reduction and redistribution across spatial scales: spherical particles remove energy from large scales and reinsert it at small scales, while ellipsoids remove relatively less TKE from large scales and reinsert relatively more at small scales. Shape effects are far less evident in the statistics of particle rotation, which are very similar for ellipsoids and spheres. Comparing these with fluid enstrophy statistics, we find that particle rotation is dominated by velocity gradients on scales much larger than the particle characteristic length scales.

The influence of inertia on the rheology of a periodic suspension of neutrally buoyant rigid ellipsoids

2015 ◽  
Vol 781 ◽  
pp. 506-549 ◽  
Author(s):  
Mohsen Daghooghi ◽  
Iman Borazjani
Keyword(s):  
Normal Stress ◽  
Reynolds Stress ◽  
Intrinsic Viscosity ◽  
Volume Fraction ◽  
Normal Stress Difference ◽  
Numerical Results ◽  
Spherical Particles ◽  
Stress Difference ◽  
Neutrally Buoyant ◽  
Normal Difference

We investigate the rheological properties of a suspension of neutrally buoyant rigid ellipsoids by fluid–structure interaction simulations of a particle in a periodic domain under simple shear using the curvilinear immersed-boundary (CURVIB) method along with a quaternion–angular velocity technique to calculate the dynamics of the particle’s motion. We calculate all the different terms of particle stress for the first time for non-spherical particles, i.e. in addition to the stresslet, we calculate the acceleration and Reynolds stress, which are typically ignored in previous similar works. Furthermore, we derive analytical expressions for all these terms to verify the numerical results and deduce the effect of inertia by comparing our numerical results with the analytical solution. The effect of particle Reynolds number ($\mathit{Re}$), volume fraction (${\it\phi}$), and the shape of particles has been studied on all mechanisms of stress generation, the intrinsic viscosity, and normal stress differences of the suspension for the range$0.008\leqslant {\it\phi}\leqslant 0.112$and$0.01\leqslant \mathit{Re}\leqslant 10.0$. We found that inertia increases the shear and the second normal difference of the stresslet (dominant term of the particle stress), and decreases the first normal difference that is generated due to the strain field. The contribution of acceleration stress to the total stress is found to be important in the second normal stress difference, with a cycle-average comparable to the stresslet component. We also discovered that the contribution of Reynolds stress in the first normal stress difference becomes important even when inertia is as low as$\mathit{Re}\sim O(0.1)$, and its value can be even greater than the stresslet when inertia increases, i.e. Reynolds stresses cannot be ignored for non-spherical particles. For concentrations in the range from dilute to semi-dilute, the effect of inertia on the intrinsic viscosity of a suspension is found to be comparable to the volume fraction. Furthermore, our calculations show that for a dilute concentration and the low-inertia regime ($\mathit{Re}<1.0$), the intrinsic viscosity of a suspension consisting of ellipsoids with an aspect ratio of five can be 20 % higher than its Stokesian analytical value.

scholarly journals Microstructure and rheology of finite inertia neutrally buoyant suspensions

2014 ◽  
Vol 749 ◽  
pp. 431-459 ◽  
Author(s):  
Hamed Haddadi ◽  
Jeffrey F. Morris
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Volume Fraction ◽  
Spherical Particles ◽  
Simple Shear Flow ◽  
Flow Reynolds Number ◽  
Boltzmann Method ◽  
Neutrally Buoyant ◽  
Boltzmann Model ◽  
Scale Shear

AbstractThe microstructure and rheological properties of suspensions of neutrally buoyant hard spherical particles in Newtonian fluid under finite inertia conditions are studied using the lattice-Boltzmann method (LBM), which is based on a discrete Boltzmann model for the fluid and Newtonian dynamics for the particles. The suspensions are subjected to simple-shear flow and the properties are studied as a function of Reynolds number and volume fraction, $\phi $. The inertia is characterized by the particle-scale shear flow Reynolds number $\mathit{Re}= {(\rho \dot{\gamma }a^{2})/\mu }$, where $a$ is the particle radius, $\dot{\gamma }$ is the shear rate and $\rho $ and $\mu $ are the density and viscosity of the fluid, respectively. The influences of inertia and of the volume fraction are investigated for $0.005\leqslant \mathit{Re}\leqslant 5$ and$0.1\leqslant \phi \leqslant 0.35$. The flow-induced microstructure is studied using the pair distribution function $g(\boldsymbol {r})$. Different stress mechanisms, including those due to surface tractions (stresslet), acceleration and the Reynolds stress due to velocity fluctuations are computed and their influence on the first and second normal stress differences, the particle pressure and the viscosity of the suspensions are detailed. The probability density functions (PDFs) of linear and angular accelerations are also presented.

Dilute suspension of neutrally buoyant particles in viscoelastic turbulent channel flow

2019 ◽  
Vol 875 ◽  
pp. 286-320 ◽  
Author(s):  
Amir Esteghamatian ◽  
Tamer A. Zaki
Keyword(s):  
Channel Flow ◽  
Volume Fraction ◽  
Qualitative Difference ◽  
Turbulent Channel Flow ◽  
Polymer Chains ◽  
Spherical Particles ◽  
Lower Probability ◽  
Fluid Field ◽  
The Individual ◽  
Neutrally Buoyant

Direct numerical simulations of viscoelastic turbulent channel flow laden with neutrally buoyant spherical particles are performed. Two FENE-P viscoelastic and one Newtonian fluid are examined, and for each the particle-laden configuration is contrasted to a reference condition without seeding. The size of the particles is larger than the dissipation length scale, and their presence enhances drag in a manner that is intrinsically different in the viscoelastic and Newtonian flows. While the particles effectively suppress the turbulence activity, they significantly enhance the polymer stresses. The polymer chains are markedly stretched in the vicinity of the particles, altering the correlation between the turbulence and polymer work that is commonly observed in single-phase viscoelastic turbulence. At the lower elasticity, the particles enhance the cycle of hibernating and active turbulence and, in turn, their migration and volume-fraction profiles are qualitatively altered by the intermittency of the turbulence. Particle–fluid momentum transfer is investigated by estimating the local fluid field on a trimmed spherical shell around the individual particles. And by comparing the particle microstructures, a lower probability of particle alignment in the streamwise direction is observed in the viscoelastic configuration. This effect is attributed to a qualitative difference in the conditionally averaged velocity fields in the vicinity of the particles in the Newtonian and viscoelastic flows.

scholarly journals Effect of Nanostructure on Thermal Conductivity of Nanofluids

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Saba Lotfizadeh ◽  
Themis Matsoukas
Keyword(s):  
Thermal Conductivity ◽  
Colloidal Particles ◽  
Volume Fraction ◽  
Numerical Study ◽  
Hollow Spheres ◽  
Structural Features ◽  
Solid Particles ◽  
Spherical Particles ◽  
Colloidal Gel ◽  
The One

The presence of colloidal particles is known to increase the thermal conductivity of base fluids. The shape and structure of the solid particles are important in determining the magnitude of enhancement. Spherical particles—the only shape for which analytic theories exist—produce the smallest enhancement. Nonspherical shapes, including clusters formed by colloidal aggregation, provide substantially higher enhancements. We conduct a numerical study of the thermal conductivity of nonspherical structures dispersed in a liquid at fixed volume fraction in order to identify structural features that promote the conduction of heat. We find that elongated structures provide high enhancements, especially if they are long enough to create a solid network (colloidal gel). Cross-linking further enhances thermal transport by directing heat in multiple directions. The most efficient structure is the one formed by hollow spheres consisting of a solid shell and a core filled by the fluid. In both dispersed and aggregated forms, hollow spheres provide enhancements that approach the theoretical limit set by Maxwell’s theory.

scholarly journals Tunable fall velocity of a dense ball in oscillatory cross-sheared concentrated suspensions

2014 ◽  
Vol 746 ◽  
Author(s):  
Frédéric Blanc ◽  
Elisabeth Lemaire ◽  
François Peters
Keyword(s):  
Strain Amplitude ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Small Strain ◽  
Concentrated Suspensions ◽  
Particle Volume ◽  
Fall Velocity ◽  
Brownian Particles ◽  
Ball Velocity ◽  
Neutrally Buoyant

AbstractThe fall velocity of a dense large ball in a suspension of neutrally buoyant non-Brownian particles subjected to horizontal oscillatory shear is studied. As the strain amplitude is increased, the velocity increases up to a maximum value before decreasing to the value that it would have in a resting suspension. The higher the frequency is, the stronger the effect is. The falling ball velocity can be largely increased in the presence of the oscillatory cross-shear flow. For instance, for a particle volume fraction of $\varPhi =0.47$ it reaches four times the value it has in the unsheared suspension. At small strain amplitudes, it turns out that the velocity of the falling ball is determined by a balance between the steady drag flow, which drives the apparent suspension viscosity toward a high value, and the oscillatory cross-shear, which lessens it. A simple model is proposed to explain the experimental observations at small strain amplitude. The velocity decrease observed at larger amplitude is not completely understood yet.

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