Steady shear rheology of a viscous emulsion in the presence of finite inertia at moderate volume fractions: sign reversal of normal stress differences

2016 ◽  
Vol 805 ◽  
pp. 494-522 ◽  
Author(s):  
Priyesh Srivastava ◽  
Abhilash Reddy Malipeddi ◽  
Kausik Sarkar
Keyword(s):  
Reynolds Number ◽  
Normal Stress ◽  
Capillary Number ◽  
Volume Fraction ◽  
Small Range ◽  
Sign Reversal ◽  
Interfacial Stresses ◽  
Number Range ◽  
Shear Rheology ◽  
Normal Stress Differences

The shear rheology of an emulsion of viscous drops in the presence of finite inertia is investigated using direct numerical simulation. In the absence of inertia, emulsions display a non-Newtonian rheology with positive first and negative second normal stress differences. However, recently it was discovered that a small amount of drop-level inertia alters their signs – the first normal stress difference becomes negative and the second one becomes positive, each in a small range of capillary numbers (Li & Sarkar,J. Rheol., vol. 49, 2005, pp. 1377–1394). Sign reversal was shown numerically and analytically, but only in the limit of a dilute emulsion where drop–drop interactions were neglected. Here, we compute the rheology of a density- and viscosity-matched emulsion, accounting for the interactions in the volume fraction range of 5 %–27 % and Reynolds number range of 0.1–10. The computed rheological properties (effective shear viscosity and first and second normal stress differences) in the Stokes limit match well with previous theoretical (Choi–Schowalter in the dilute limit) and simulated results (for concentrated systems) using the boundary element method. The two distinct components of the rheology arising from the interfacial stresses at the drop surface and the perturbative Reynolds stresses are investigated as functions of the drop Reynolds number, capillary number and volume fraction. The sign change is caused by the increasing drop inclination in the presence of inertia, which in turn directly affects the interfacial stresses. Increase of the volume fraction or capillary number increases the critical Reynolds number for sign reversals due to enhanced alignment of the drops with the flow directions. The effect of increasing the volume fraction on the rheology is explained by relating it to interactions and specifically to the contact pair-distribution function computed from the simulation. The excess stresses are seen to show an approximately linear behaviour with the Reynolds number in the range of 0.1–5, while with the capillary number and volume fraction, the variation is weakly quadratic.

Simulations of Droplet Collisions in Shear Flow

2012 ◽  
Author(s):  
Orest Shardt ◽  
J. J. Derksen ◽  
Sushanta K. Mitra
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Capillary Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Simple Shear Flow ◽  
Number Range ◽  
Droplet Collisions ◽  
Critical Capillary Number ◽  
Boltzmann Method

When droplets collide in a shear flow, they may coalesce or remain separate after the collision. At low Reynolds numbers, droplets coalesce when the capillary number does not exceed a critical value. We present three-dimensional simulations of droplet coalescence in a simple shear flow. We use a free-energy lattice Boltzmann method (LBM) and study the collision outcome as a function of the Reynolds and capillary numbers. We study the Reynolds number range from 0.2 to 1.4 and capillary numbers between 0.1 and 0.5. We determine the critical capillary number for the simulations (0.19) and find that it is does not depend on the Reynolds number. The simulations are compared with experiments on collisions between confined droplets in shear flow. The critical capillary number in the simulations is about a factor of 25 higher than the experimental value.

scholarly journals Negative normal stress differences N1–N2 in a low concentration capillary suspension

Soft Matter ◽  
2018 ◽  
Vol 14 (17) ◽  
pp. 3254-3264 ◽  
Author(s):  
Irene Natalia ◽  
Nicole Zeiler ◽  
Moritz Weiß ◽  
Erin Koos
Keyword(s):  
Normal Stress ◽  
Volume Fraction ◽  
Solid Concentration ◽  
Particle Suspensions ◽  
Fluid System ◽  
Low Concentration ◽  
Capillary Suspensions ◽  
Normal Stress Differences ◽  
Capillary Attraction ◽  
Two Fluid

Negative normal stress differences are reported in capillary suspensions, i.e. particle suspensions in a two-fluid system that creates strong capillary attraction, at a solid concentration of 25%. This volume fraction has heretofore been too low to show such normal stress differences.

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 $.

scholarly journals Normal stress differences in dense suspensions

2018 ◽  
Vol 857 ◽  
pp. 200-215 ◽  
Author(s):  
Ryohei Seto ◽  
Giulio G. Giusteri
Keyword(s):  
Normal Stress ◽  
Simple Shear ◽  
Volume Fraction ◽  
Hydrodynamic Lubrication ◽  
Contact Forces ◽  
Simple Shear Flow ◽  
First Normal Stress Difference ◽  
Dense Suspensions ◽  
Normal Stress Differences ◽  
Dynamics Simulations

The presence and the microscopic origin of normal stress differences in dense suspensions under simple shear flows are investigated by means of inertialess particle dynamics simulations, taking into account hydrodynamic lubrication and frictional contact forces. The synergic action of hydrodynamic and contact forces between the suspended particles is found to be the origin of negative contributions to the first normal stress difference $N_{1}$ , whereas positive values of $N_{1}$ observed at higher volume fractions near jamming are due to effects that cannot be accounted for in the hard-sphere limit. Furthermore, we found that the stress anisotropy induced by the planarity of the simple shear flow vanishes as the volume fraction approaches the jamming point for frictionless particles, while it remains finite for the case of frictional particles.

Numerical Modelling of Nanofluid Heat Transfer Inside a Microchannel Heat Sink

2012 ◽  
Author(s):  
Benjamin Rimbault ◽  
Cong Tam Nguyen ◽  
Nicolas Galanis
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Sink ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Convective Heat Transfer Coefficient ◽  
Microchannel Heat Sink ◽  
Pumping Power ◽  
Particle Volume ◽  
Number Range

The problem of laminar flow and heat transfer of water-based nanofluids inside a 3D-microchannel heat sink was numerically investigated, considering temperature-dependent fluids properties. Results, obtained for the 250–2000 Reynolds number range, show that an important enhancement of surface convective heat transfer coefficient can be achieved by increasing the particle volume fraction. For given Reynolds number and particle fraction, a highest heat transfer enhancement is obtained using CuO-water nanofluid. However, the use of nanofluids considerably increases the wall friction and consequently the pumping power. The ‘heat transferred to fluid/pumping power’ ratio was calculated for nanofluids. For given Reynolds number and particle volume fraction, such a ratio was found lowest for CuO-water nanofluid, while alumina-water nanofluids provide similar results.

On the Thermal Characteristics of Two-Phase, Liquid-Liquid, Non-Boiling Droplet Flow in Minichannels

2011 ◽  
Author(s):  
Marc Mac Giolla Eain ◽  
Vanessa Egan ◽  
Jeff Punch
Keyword(s):  
Reynolds Number ◽  
Capillary Number ◽  
Thermal Characteristics ◽  
Flow Regimes ◽  
Two Phase ◽  
Flux Boundary Condition ◽  
Number Range ◽  
Droplet Flow ◽  
Micro Fluidics ◽  
Phase Liquid

Two-phase flow regimes offer numerous advantages over traditional single phase flows, resulting in a wide variety of uses in diverse applications such as electronics cooling, heat exchange systems, pharmacology and biological micro-fluidics. This paper experimentally investigates the enhanced heat transfer rates attainable with two-phase liquid-liquid non-boiling droplet flow. A custom experimental facility was constructed, allowing the flow to be analysed in a minichannel geometry subjected to a constant heat flux boundary condition. Parameters of Reynolds number, Capillary number, droplet length and droplet spacing were varied during the course of the experimentation. The experiments were conducted over the Reynolds number range of 46 ≤ Re ≤ 71.8 and a Capillary number range of 0.00849 ≤ Ca ≤ 0.0102. The flow passed through a capillary of 1.5mm internal diameter and 0.25mm wall thickness. Local Nusselt numbers were obtained at the entrance region through the use of infrared thermography. Enhancements of 144% over fully developed Poiseuille flow were encountered. The findings of this paper highlight the thermal characteristics of two-phase liquid-liquid flow regimes and are of practical relevance to applications in both the thermal management and biological micro-fluidics industries.

Combined Effects of Nanofluid and Geometrical Structures of a Parallel Plate Channel With Semicircle Corrugations on Flow Characteristics and Thermal-Hydraulic Performance

2020 ◽  
Vol 12 (4) ◽  
Author(s):  
Raheem K. Ajeel ◽  
Wan Saiful-Islam Wan Salim
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Volume Fraction ◽  
Numerical Study ◽  
Hydraulic Performance ◽  
Geometrical Structures ◽  
Fluid Medium ◽  
Number Range ◽  
Corrugated Channel ◽  
Smooth Channel

Abstract The combination of corrugated surface and nanofluid techniques can boost thermo-hydraulic performance with the ability to make thermal systems more effective and reliable. In this numerical study, the combined effect of different structures of a semicircle-corrugated channel is investigated and examined, as well as different types of nanofluids on thermal and hydraulic performance in the Reynolds number range from 10,000 to 30,000. With respect to the fluid medium, four kinds of nanoparticles Al2O3, CuO, SiO2, and ZnO are used and investigated. The volume fraction of nanoparticles and the diameter of the particles are in the range of 0–0.08 and 20–80 nm, respectively. The findings show that the geometrical structures of the tested channel have a great effect to improve heat transfer enhancement, approvingly around 2.3–3.7 times that of the smooth channel. Furthermore, the outcomes show a dramatic increase in the heat transfer coefficient as the volume fractions of nanoparticles and Reynolds number are increased, and with the decline of particle size, but it accompanied with the increase of shear stress. Among the nanofluids used here, SiO2–water offers the highest enhancement of heat transfer. For all forms tested here, the rib shape of a semicircle-corrugated channel displays the best thermal-hydraulic performance of 2.84 at a volume fraction of 0.08 and Re = 10,000.

Investigation of the convective heat transfer and friction factor of magnetic Ni nanofluids within cylindrical pipes

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
M. Abdelkader ◽  
H. Ameur ◽  
Y. Menni
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Constant Heat Flux ◽  
Particle Volume ◽  
Number Range

The current paper reports the results of numerical research on the magnetic Ni nanofluid flowing in a tube, developing turbulent flows under constant heat flux conditions. The numerical investigations are conducted for a Reynolds number range from 3,000 to 22,000, and a particle concentration range of 0% to 0.6%. The effects of the Reynolds number on the friction factor and Nusselt number are computed and compared satisfactorily with the experimental results of the literature. The classical correlations of Gnielinski, Notter – Rouse, and Pak and Cho are verified by predicting the Nusselt number of the Ni nanofluid. The obtained results revealed an enhancement in the heat transfer with the increase of magnetic Ni particle volume fraction and Reynolds number.

Normal stresses in concentrated non-Brownian suspensions

2013 ◽  
Vol 715 ◽  
pp. 239-272 ◽  
Author(s):  
T. Dbouk ◽  
L. Lobry ◽  
E. Lemaire
Keyword(s):  
Normal Stress ◽  
Pore Pressure ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Particle Volume Fraction ◽  
Radial Profile ◽  
Normal Stresses ◽  
Particle Volume ◽  
Wide Range ◽  
Normal Stress Differences

AbstractWe present an experimental approach used to measure both normal stress differences and the particle phase contribution to the normal stresses in suspensions of non-Brownian hard spheres. The methodology consists of measuring the radial profile of the normal stress along the velocity gradient direction in a torsional flow between two parallel discs. The values of the first and the second normal stress differences, ${N}_{1} $ and ${N}_{2} $, are deduced from the measurement of the slope and of the origin ordinate. The measurements are carried out for a wide range of particle volume fractions (between 0.2 and 0.5). As expected, ${N}_{2} $ is measured to be negative but ${N}_{1} $ is found to be positive. We discuss the validity of the method and present numerous tests that have been carried out in order to validate our results. The experimental setup also allows the pore pressure to be measured. Then, subtracting the pore pressure from the total stress, ${\mbrm{\Sigma} }_{\mathbf{22} } $, the contribution of the particles to the normal stress ${ \mbrm{\Sigma} }_{\mathbf{22} }^{\mathbi{p}} $ is obtained. Most of our results compare well with the different experimental and numerical data present in the literature. In particular, our results show that the magnitude of the particle stress tensor component and their dependence on the particle volume fraction used in the suspension model balance proposed by Morris & Boulay (J. Rheol., vol. 43, 1999, p. 1213) are suitable.

Dense suspensions in rotating-rod flows: normal stresses and particle migration

2011 ◽  
Vol 686 ◽  
pp. 5-25 ◽  
Author(s):  
François Boyer ◽  
Olivier Pouliquen ◽  
Élisabeth Guazzelli
Keyword(s):  
Shear Rate ◽  
Normal Stress ◽  
Volume Fraction ◽  
Particle Migration ◽  
Balance Model ◽  
Normal Stresses ◽  
Dense Suspensions ◽  
Normal Stress Differences ◽  
Neutrally Buoyant ◽  
Dependent Behaviour

AbstractNormal stress differences are measured in dense suspensions of neutrally buoyant non-Brownian spheres dispersed in a Newtonian fluid. Rotating-rod rheometry is used to characterize the suspension normal stresses which are responsible for a rod-dipping phenomenon. These normal stress differences are seen to strongly increase above a volume fraction of approximately 22 %. During the course of the experiments, a new time-dependent behaviour is also observed: the dip is filled with increasing times. This time evolution is found to be related to particle migration from regions of high shear rate to regions of low shear rate. The behaviour is compared with the predictions of a suspension balance model in which the particle migration flux is related to the normal stresses of the suspension.

Sign in / Sign up

Export Citation Format

Share Document