scholarly journals Confined flow of suspensions modelled by a frictional rheology

2014 ◽  
Vol 759 ◽  
pp. 197-235 ◽  
Author(s):  
Brice Lecampion ◽  
Dmitry I. Garagash
Keyword(s):  
Shear Stress ◽  
Friction Coefficient ◽  
Normal Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Numerical Predictions ◽  
Dry Granular Flow ◽  
Neutrally Buoyant ◽  
Constitutive Parameters ◽  
Axial Development

AbstractWe investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al. (Phys. Rev. Lett., vol. 107 (18), 2011, 188301). The friction coefficient (shear stress over particle normal stress) and solid volume fraction are taken as functions of the dimensionless viscous number $I$ defined as the ratio between the fluid shear stress and the particle normal stress. We clarify the contributions of the contact and hydrodynamic interactions on the evolution of the friction coefficient between the dilute and dense regimes reducing the phenomenological constitutive description to three physical parameters. We also propose an extension of this constitutive framework from the flowing regime (bounded by the maximum flowing solid volume fraction) to the fully jammed state (the random close packing limit). We obtain an analytical solution of the fully developed flow in channel and pipe for the frictional suspension rheology. The result can be transposed to dry granular flow upon appropriate redefinition of the dimensionless number $I$. The predictions are in excellent agreement with available experimental results for neutrally buoyant suspensions, when using the values of the constitutive parameters obtained independently from stress-controlled rheological measurements. In particular, the frictional rheology correctly predicts the transition from Poiseuille to plug flow and the associated particles migration with the increase of the entrance solid volume fraction. We also numerically solve for the axial development of the flow from the inlet of the channel/pipe toward the fully developed state. The available experimental data are in good agreement with our numerical predictions, when using an accepted phenomenological description of the relative phase slip obtained independently from batch-settlement experiments. The solution of the axial development of the flow notably provides a quantitative estimation of the entrance length effect in a pipe for suspensions when the continuum assumption is valid. Practically, the latter requires that the predicted width of the central (jammed) plug is wider than one particle diameter. A simple analytical expression for development length, inversely proportional to the gap-averaged diffusivity of a frictional suspension, is shown to encapsulate the numerical solution in the entire range of flow conditions from dilute to dense.

Suspensions in a tilted trough: second normal stress difference

2011 ◽  
Vol 686 ◽  
pp. 26-39 ◽  
Author(s):  
Étienne Couturier ◽  
François Boyer ◽  
Olivier Pouliquen ◽  
Élisabeth Guazzelli
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Volume Fraction ◽  
Behavioural Change ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
Rigid Spheres ◽  
First Normal Stress Difference ◽  
Second Normal Stress Difference ◽  
Neutrally Buoyant

AbstractWe measure the second normal-stress difference in suspensions of non-Brownian neutrally buoyant rigid spheres dispersed in a Newtonian fluid. We use a method inspired by Wineman & Pipkin (Acta Mechanica, vol. 2, 1966, pp. 104–115) and Tanner (Trans. Soc. Rheol., vol. 14, 1970, pp. 483–507), which relies on the examination of the shape of the suspension free surface in a tilted trough flow. The second normal-stress difference is found to be negative and linear in shear stress. The ratio of the second normal-stress difference to shear stress increases with increasing volume fraction. A clear behavioural change exhibiting a strong (approximately linear) growth in the magnitude of this ratio with volume fraction is seen above a volume fraction of 0.22. By comparing our results with previous data obtained for the same batch of spheres by Boyer, Pouliquen & Guazzeli (J. Fluid Mech., 2011, doi:10.1017/jfm.2011.272), the ratio of the first normal-stress difference to the shear stress is estimated and its magnitude is found to be very small.

scholarly journals Quantification of shear viscosity and wall slip velocity of highly concentrated suspensions with non-Newtonian matrices in pressure driven flows

2021 ◽  
Author(s):  
Patrick Wilms ◽  
Jan Wieringa ◽  
Theo Blijdenstein ◽  
Kees van Malssen ◽  
Reinhard Kohlus
Keyword(s):  
Shear Stress ◽  
Liquid Phase ◽  
Shear Rate ◽  
Shear Viscosity ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Wall Slip ◽  
Flow Index ◽  
Concentrated Suspensions

AbstractThe rheological characterization of concentrated suspensions is complicated by the heterogeneous nature of their flow. In this contribution, the shear viscosity and wall slip velocity are quantified for highly concentrated suspensions (solid volume fractions of 0.55–0.60, D4,3 ~ 5 µm). The shear viscosity was determined using a high-pressure capillary rheometer equipped with a 3D-printed die that has a grooved surface of the internal flow channel. The wall slip velocity was then calculated from the difference between the apparent shear rates through a rough and smooth die, at identical wall shear stress. The influence of liquid phase rheology on the wall slip velocity was investigated by using different thickeners, resulting in different degrees of shear rate dependency, i.e. the flow indices varied between 0.20 and 1.00. The wall slip velocity scaled with the flow index of the liquid phase at a solid volume fraction of 0.60 and showed increasingly large deviations with decreasing solid volume fraction. It is hypothesized that these deviations are related to shear-induced migration of solids and macromolecules due to the large shear stress and shear rate gradients.

Impact of viscosity variation on oblique flow of Cu–H2O nanofluid

2017 ◽  
Vol 232 (5) ◽  
pp. 622-631 ◽  
Author(s):  
R Tabassum ◽  
Rashid Mehmood ◽  
O Pourmehran ◽  
NS Akbar ◽  
M Gorji-Bandpy
Keyword(s):  
Heat Flux ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Solid Volume Fraction ◽  
Local Heat ◽  
Skin Friction Coefficient ◽  
Viscosity Parameter ◽  
Local Heat Flux

The dynamic properties of nanofluids have made them an area of intense research during the past few decades. In this article, flow of nonaligned stagnation point nanofluid is investigated. Copper–water based nanofluid in the presence of temperature-dependent viscosity is taken into account. The governing nonlinear coupled ordinary differential equations transformed by partial differential equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg integration technique. Effects of variable viscosity parameter on velocity and temperature profiles of pure fluid and copper–water nanofluid are analyzed, discussed, and presented graphically. Streamlines, skin friction coefficients, and local heat flux of nanofluid under the impact of variable viscosity parameter, stretching ratio, and solid volume fraction of nanoparticles are also displayed and discussed. It is observed that an increase in solid volume fraction of nanoparticles enhances the magnitude of normal skin friction coefficient, tangential skin friction coefficient, and local heat flux. Viscosity parameter is found to have decreasing effect on normal and tangential skin friction coefficients whereas it has a positive influence on local heat flux.

Heatline and Massline Visualization of Hydromagnetic Double Diffusive Convective Flow of Nanofluid Within a Porous Trapezoidal Cavity

2021 ◽  
Vol 10 (2) ◽  
pp. 270-284
Author(s):  
Bikash C. Saha ◽  
T. R. Mahapatra ◽  
Dulal Pal
Keyword(s):  
Aspect Ratio ◽  
Convective Flow ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Temperature Fields ◽  
Computational Domain ◽  
Aspect Ratios ◽  
Numerical Predictions ◽  
Double Diffusive

Double diffusive convective flow of nanofluid within a porous trapezoidal cavity of various aspect ratios consisting of Al2O3 nanoparticle in the presence of applied magnetic field in the direction perpendicular to the parallel top and bottom walls is analysed. The side walls of the cavity are maintained at constant temperature and concentration while its horizontal walls are insulated and impermeable. The irregular physical domain of the problem is transformed to a regular unit square computational domain. The governing equations have been solved by second order of finite difference method (FDM). Based upon numerical predictions, the effects of pertinent parameters such as Rayleigh number, Darcy number, aspect ratio, solid volume fraction and inclination angle on the flow and temperature fields and the heat transfer performance of the enclosure are examined. It is found that the intensity of heat and mass transfer increases with the increase in the Darcy number and aspect ratio. It is also observed that as the solid volume fraction increases there is increase in the average Nusselt number but reverse effect is observed on the average Sherwood number.

scholarly journals Heat transfer analysis of nanofluid flow through backward facing step

2020 ◽  
Vol 307 ◽  
pp. 01010 ◽  
Author(s):  
Ahlem Boudiaf ◽  
Fetta Danane ◽  
Youb Khaled Benkahla ◽  
Walid Berabou ◽  
Mahdi Benzema ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Thermal Characteristics ◽  
Heat Transfer Analysis ◽  
Backward Facing Step ◽  
Nanofluid Flow ◽  
Numerical Predictions ◽  
Flow Through ◽  
Volume Method

This paper presents the numerical predictions of hydrodynamic and thermal characteristics of nanofluid flow through backward facing step. The governing equations are solved through the finite volume method, as described by Patankar, by taking into account the associated boundary conditions. Empirical relations were used to give the effective dynamic viscosity and the thermal conductivity of the nanofluid. Effects of different key parameters such as Reynolds number, nanoparticle solid volume fraction and nanoparticle solid diameter on the heat transfer and fluid flow are investigated. The results are discussed in terms of the average Nusselt number and streamlines.

Microstructural theory and the rheology of concentrated colloidal suspensions

2012 ◽  
Vol 713 ◽  
pp. 420-452 ◽  
Author(s):  
Ehssan Nazockdast ◽  
Jeffrey F. Morris
Keyword(s):  
Normal Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Perturbation Expansion ◽  
Colloidal Suspensions ◽  
Simple Shear Flow ◽  
Fluid Viscosity ◽  
Analytical Prediction ◽  
Regular Perturbation ◽  
Normal Stress Differences

AbstractA theory for the analytical prediction of microstructure of concentrated Brownian suspensions of spheres in simple-shear flow is developed. The computed microstructure is used in a prediction of the suspension rheology. A near-hard-sphere suspension is studied for solid volume fraction $\phi \leq 0. 55$ and Péclet number $Pe= 6\lrm{\pi} \eta \dot {\gamma } {a}^{3} / {k}_{b} T\leq 100$; $a$ is the particle radius, $\eta $ is the suspending Newtonian fluid viscosity, $\dot {\gamma } $ is the shear rate, ${k}_{b} $ is the Boltzmann constant and $T$ is absolute temperature. The method developed determines the steady pair distribution function $g(\mathbi{r})$, where $\mathbi{r}$ is the pair separation vector, from a solution of the Smoluchowski equation (SE) reduced to pair level. To account for the influence of the surrounding bath of particles on the interaction of a pair, an integro-differential form of the pair SE is developed; the integral portion represents the forces due to the bath which drive the pair interaction. Hydrodynamic interactions are accounted for in a pairwise fashion, based on the dominant influence of pair lubrication interactions for concentrated suspensions. The SE is modified to include the influence of shear-induced relative diffusion, and this is found to be crucial for success of the theory; a simple model based on understanding of the shear-induced self-diffusivity is used for this property. The computation of the microstructure is split into two parts, one specific to near-equilibrium ($Pe\ll 1$), where a regular perturbation expansion of $g$ in $Pe$ is applied, and a general-$Pe$ solution of the full SE. The predicted microstructure at low $Pe$ agrees with prior theory for dilute conditions, and becomes increasingly distorted from the equilibrium isotropic state as $\phi $ increases at fixed $Pe\lt 1$. Normal stress differences are predicted and the zero-shear viscosity predicted agrees with simulation results obtained using a Green–Kubo formulation (Foss & Brady, J. Fluid Mech., vol. 407, 2000, pp. 167–200). At $Pe\geq O(1)$, the influence of convection results in a progressively more anisotropic microstructure, with the contact values increasing with $Pe$ to yield a boundary layer and a wake. Agreement of the predicted microstructure with observations from simulations is generally good and discrepancies are clearly noted. The predicted rheology captures shear thinning and shear thickening as well as normal stress differences in good agreement with simulation; quantitative agreement is best at large $\phi $.

Experimental Analysis on Shear Behavior of Sand-Concrete Interface

2012 ◽  
Vol 204-208 ◽  
pp. 893-898
Author(s):  
Chun Feng Zhao ◽  
Bao Lai Yu ◽  
Cheng Zhao
Keyword(s):  
Shear Stress ◽  
Friction Coefficient ◽  
Normal Stress ◽  
Maximum Shear Stress ◽  
Relative Displacement ◽  
Shear Behavior ◽  
Tangential Displacement ◽  
Interface Shear ◽  
Direct Shear Tests ◽  
Concrete Interface

In order to study the shear behavior of sand-concrete structure interface, shear stress and relative displacement curves were obtained through a series of direct shear tests, in the procedure of which the roughness of interfaces was quantified into 3 grades and the stress history can be achieved by loading the sand to an initial normal stress and then unloading to a normal stress to shear. Through analyzing the curves, several conclusions can be obtained as follows: Shear stress increases with the initial normal stress and roughness at the same tangential displacement. The initial shear modulus can be improved in case of the increase of initial normal stress and roughness. The friction coefficient can be obtained by fitting the curve of the maximum shear stress and normal stress corresponded to Mohr-Coulomb Criterion linearly. The friction coefficient of sand-concrete interface increases with roughness as well as its increase range.

scholarly journals CFD Study for the Flow Behaviour of Nanofluid Flow over Flat Plate

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Heat Transfer Coefficient ◽  
Friction Coefficient ◽  
Wall Shear Stress ◽  
Base Fluid ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Average Heat Transfer Coefficient ◽  
Average Heat

Computation fluid dynamics (CFD) modelling of laminar heat transfer behaviour of three types of nanofluids over flat plate are studied. In the modelling the two dimensional under laminar model is used. The base fluid is pure water and the volume fraction of nanoparticles in the base fluid is 0, 1, 2, 3, and 4%. The applied Reynolds number range considered is 997.1 ≤ Re ≤ 9971. For modelling of the physical properties of the nanofluid, single phase approach is used. The effect of the volume fraction and the type of nanoparticles on the physical properties has been evaluated and presented. Then, the analysis the flow behaviour of these three nanofluids is conducted by presenting the effect of increasing the nanoparticles concentration on the velocity profile, wall shear stress, skin friction coefficient, and average heat transfer coefficient. The results show that the type of nanoparticles is an important parameter for the heat transfer enhancement as each type has shown dissimilar behaviour in this study. Moreover, a polynomial correlation has been obtained to present the relation of the wall shear stress, skin friction coefficient and average heat transfer coefficient as a function of the volume fraction for the three nanofluids.

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.

Prediction of Conjugate Heat Transfer in a Solid–Liquid System: Inclusion of Buoyancy and Surface Tension Forces in the Liquid Phase

1989 ◽  
Vol 111 (3) ◽  
pp. 690-698 ◽  
Author(s):  
J. R. Keller ◽  
T. L. Bergman
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Steady State ◽  
Conjugate Heat Transfer ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Fluid Motion ◽  
Numerical Predictions ◽  
Solid Liquid ◽  
Surface Tension Forces

Numerical predictions have been obtained for steady-state conjugate heat transfer in an open rectangular cavity. For the geometry considered, fluid motion is driven by augmenting buoyancy and surface tension forces. Predictions of the steady-state solid volume fraction and various solid thicknesses were obtained for a high Prandtl number fluid characterized by various Rayleigh and Marangoni (Ma) numbers. Due to numerical difficulties associated with large surface tension effects, a limited range of Ma was investigated (Ma≤250). The predictions show that surface tension induced flow can affect the solid geometry and, ultimately, freezing or melting rates. Specifically, the solid–liquid interface shape is altered, the steady-state solid volume fraction is decreased, and the solid thickness at the top surface is smaller, compared to the pure buoyancy-driven case. The dimensionless solid volume fraction and solid thicknesses are related to the governing dimensionless parameters of the problem. Finally, predictions are made for high Marangoni number flows (Ma>>250) to demonstrate the potential governing influence of surface tension effects in phase-change systems.

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