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Numerical study of particle suspensions in Newtonian and non-Newtonian fluids
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Kufa Univ, Coll Engn, Al Najaf, Iraq..
2019 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Numerisk studie av partikelsuspensioner i Newtonska och icke-Newtonska vätskor (Swedish)
Abstract [en]

Solid or deformable particles suspended in a viscous fluid are of scientific and technological interest in a broad range of applications. Pyroclastic flows from volcanoes, sedimentation flows in river bed, food industries, oil-well drilling, as well as blood flow in the human body and the motion of suspended micro-organisms in water (like plankton) are among the possible examples. Often, in these particulate flows, the carrier fluid might exhibit an inelastic or a visco-elastic non-Newtonian behavior. Understanding the behavior of these suspensions is a very difficult task. Indeed, the complexities and challenges of multiphase flows are mainly due to the large number of governing parameters such as the physical properties of the particles (e.g., shape, size, stiffness, density difference with suspended fluid, solid volume fraction), the large set of interactions among particles and the properties of the carrier fluid (Newtonian or non-Newtonian); variations of each of these parameters may provide substantial quantitative and qualitative changes in the behavior of the suspension and affect the overall dynamics in several and sometimes surprising ways. The aim of this work is therefore to provide a deeper understanding of the behavior of particle suspensions in laminar Newtonian and non-Newtonian (inelastic and/or visco-elastic) fluid flows for a wide range of different parameters. To this purpose, particle-resolved direct numerical simulations of spherical particles are performed, using an efficient and accurate numerical tool. The code is based on the Immersed Boundary Method (IBM) for the fluid-solid interactions with lubrication, friction and collision models for the close range particle-particle (particle-wall) interactions. Both inelastic (Carreau and power-law), and visco-elastic models (Oldroyd-B and Giesekus) are employed to investigate separately the shear-thinning, shear-thickening, viscoelastic and combined shear-thinning visco-elastic features of the most commonly encountered non-Newtonian fluids. Moreover, a fully Eulerian numerical algorithm based on the one-continuum formulation is used to examine the case of an hyper-elastic neo-Hookean deformable particle suspended in a Newtonian flows.

Firstly, we have investigated suspensions of solid spheres in Newtonian, shear thinning and shear thickening fluids in the simple shear flow created by two walls moving in opposite directions, considering various solid volume fractions and particle Reynolds numbers, thus including inertial effects. The results show that that the non-dimensional relative viscosity of of the suspension and the mean value of the local shear-rate can be well predicted by homogenization theory, more accurately for lower particle concentrations. Moreover, we show that in the presence of inertia, the effective viscosity of these suspensions deviates from that of Stokesian suspensions.

We also examine the role of fluid elasticity, shear-thinning and combined shear-thinning visco-elastic effects on the simple linear Couette shear flow of neutrally-buoyant rigid spherical particles. It is found that the effective viscosity grows monotonically with the solid volume fraction and that all the Non-Newtonian cases exhibit a lower effective viscosity than the Newtonian ones; in addition, we show that elastic effects dominate at low elasticity whereas shear thinning is predominant at high applied shear rates. These variations in the effective viscosity are mainly due to changes in the particle-induced shear stress component.

We then study the settling of spherical particles in quiescent wall-bounded Newtonian and shear-thinning fluids at three different solid volume fractions. We find that the mean settling velocities decrease with the particle concentration as a consequence of the hindering effect and thatthe mean settling speed is always larger in the shear thinning fluid than in the Newtonian one, due to the reduction of the local fluid viscosity around the particles which leads to a lower drag force acting on the particles.

Finally, the inertial migration of hyper-elastic deformable particle in laminar pipe flows is also investigated. We consider different flow rates and various levels of particle elasticity. We observe that the particle deforms and experiences a lateral movement while traveling downstream through the pipe, always finding a stable position at the pipe centerline.

Abstract [sv]

Suspensioner av solida eller deformerbara partiklar iviskösa vätskor är av vetenskapligt och teknologiskt intresse för ett stortspann av applikationer. Några typiska exempel inkluderar pyroklastiskaflöden från vulkaner, sedimenterande flöden i flodbäddar,livsmedelsindustrin, oljebrunnsborrning, blodflödet i människokroppen samtrörelsen hos mikroorganismer (till exempel plankton) i havet. I dessapartikelflöden kan den bärande vätskan ha ett icke-elastiskt ellerviskoelastiskt icke-Newtonskt beteende. Att förstå beteendet hos dessasuspensioner är en mycket svår uppgift. Komplexiteten hos, och utmaningenmed, multifasflöden beror till största delen på det stora antal styrandeparametrar. Dessa inkluderar de fysikaliska partikelegenskaperna (tillexempel form, storlek, styvhet, densitetsskillnad mot det bärande medietsamt volymfraktion), den stora mängden interaktioner mellan partiklarnasamt egenskaperna hos den bärande fluiden (Newtonsk eller icke-Newtonsk).Variationer i vardera av dessa parametrar kan leda till stora kvantitativaoch kvalitativa förändringar i suspensionens beteende och kan påverka denövergripande dynamiken på många, ibland överraskande, sätt. Målet meddenna avhandling är därför att ge en djupare förståelse avpartikelsuspensioner i laminära, Newtonska och icke-Newtonska(icke-elastiska och/eller visko-elasiska), flöden för ett stort spann avparametrar. För detta används ett effektivt och precist simuleringsverktygsom tillåter partikelupplösta, numeriska simuleringar av sfäriskapartiklar. Koden är baserad på Immersed boundary-metodiken (IBM) förfluid-strukturinteraktion med lubrikations-, friktions- ochkollisionsmodeller för partikel-partikel- och partikel-vägginteraktioner.Både icke-elastiska (Carreau och power-law) och viskoelastiska (Oldroyd-Boch Giesekus) modeller betraktades för att, i isolering, undersökaeffekterna av skjuvförtunnande, skjuvförtjockande, viskoelasticitet samtkombinationen av skjuvförtunning och viskoelastik, vilka vanligen förekommerhos icke-Newtonska fluider. Därutöver användes en Eulerisk numeriskalgoritm baserad på en en-kontinuumformulering för att undersöka fallet meden hyperelastisk, neo-Hookisk och deformerbar partikel i en Newtonsk vätska.

Till att börja med undersöks suspensioner av solida sfärer i Netwonska,skjuvförtunnande samt skjuvförtjockande fluider i ett skjuvflöde genereratmellan två väggar som rör sig i motsatt riktning. Varierandevolymfraktioner (av partiklar) och partikel-Reynoldstal (dvs inkluderandeav fluidtröghet) betraktas. Resultaten visar att den dimensionslösarelativa viskositeten hos suspensionen och medelvärdet av den lokalaskjuvhastigheten kan väl förutsägas av homogeniseringsteori, speciellttillförlitligt vid låga partikelkoncentrationer. Därutöver visas att deneffektiva viskositeten hos dessa suspensioner avviker från suspensioner iStokesflöde när flödeströghet inkluderas.

Därutöver undersöktes rollen hos elasticitet, skjuvförtunnande samtkombinerad skjuvförtunnande och viskoelasticitet i det bärande mediet påett linjärt Couetteflöde med densitetsmatchade, rigida och sfäriskapartiklar. Den effektiva viskositeten växer monotont medpartikelvolymfraktionen och alla icke-Newtonska fall uppvisar en lägreeffektiv viskositet än de motsvarande Newtonska fallen. Det visas även attelastiska effekter dominerar vid låg elasticitet medan skjuvförtunnandeeffekter dominerar vid höga skjuvhastigheter. Dessa variationer i effektivviskositet beror främst på förändringar i den partikelinduceradekomponenten av skjuvspänningen.

Efter detta studeras sedimentering av sfäriska partiklar i ettstillastående flöde mellan två väggar. Både Newtonska och skjuvförtunnandevätskor betraktas vid tre olika partikelvolymfraktioner. Det visas attmedelvärdet av sedimenteringshastigheten minskar med partikelkoncentrationpå grund av den hindrande effekten av omgivande partiklar. Därutöver ärmedelsedimentationshastigheten alltid större i en skjuvförtunnande än enNewtonsk vätska på grund av reduktionen i lokal fluidviskositet runtpartiklarna, vilket leder till en lägre motståndskraft.

Slutligen undersöks även tröghetsinducerad migration av hyperelastiska ochdeformerbara partiklar i ett laminärt rörflöde. Olika flöden och nivåer avelasticitet hos partikeln betraktas. Partikeldeformation och lateralrörelse observeras för partiklarna när de rör sig nedströms längs röret,vilket leder till att partiklarna alltid finner en stabil position vidrörets centerlinje.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2019. , p. 66
Series
TRITA-MEK, ISSN 0348-467X ; 2019;55
Keywords [en]
inertial suspensions, rheology, non-Newtonian fluids, visco-elastic, sedimentation, deformable particle, hyper-elastic.
Keywords [sv]
tröghetsbehäftad suspension, reologi, icke-Newtonska fluider, vis- koelastik, sedimentering, deformerbara partiklar, hyperelastik
National Category
Physical Sciences
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-263657ISBN: 978-91-7873-385-9 (print)OAI: oai:DiVA.org:kth-263657DiVA, id: diva2:1368941
Public defence
2019-12-06, Ångdomen (Rumsnr: 5209), Osquars backe 31, KTHB, våningsplan 2, KTH Campus, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
EU, European Research Council, ERC-2013-CoG-616186
Note

QC 20191114

Available from: 2019-11-14 Created: 2019-11-08 Last updated: 2019-11-14Bibliographically approved
List of papers
1. Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids
Open this publication in new window or tab >>Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids
2018 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 852, p. 329-357Article in journal (Refereed) Published
Abstract [en]

We present a numerical study of non-colloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an immersed boundary method. We consider a linear Couette configuration to explore a wide range of solid volume fractions (0.1 <= Phi <= 0.4) and particle Reynolds numbers (0.1 <= Re<INF>p</INF><INF></INF> <= 10). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal Phi. This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare the latter's mean value with the values estimated from the homogenisation theory of Chateau et al. (J. Rheol., vol. 52, 2008, pp. 489-506), indicating a reasonable agreement in the Stokesian regime. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the Re<INF>p</INF>. The wide spectrum of the local shear rate and its dependency on Phi and Re<INF>p</INF> point to the deficiencies of the mean value of the local shear rates in estimating the rheology of these non-colloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these non-colloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, O(Re<INF>p</INF>) similar to 10.

Place, publisher, year, edition, pages
Cambridge University Press, 2018
Keywords
particle/fluid flow, rheology, suspensions
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-233414 (URN)10.1017/jfm.2018.532 (DOI)000440857700001 ()2-s2.0-85051202483 (Scopus ID)
Funder
EU, European Research Council, ERC-2013-CoG-616186
Note

QC 20180821

Available from: 2018-08-21 Created: 2018-08-21 Last updated: 2019-11-08Bibliographically approved
2. Interface-resolved simulations of particle suspensions in visco-elastic carrier fluids
Open this publication in new window or tab >>Interface-resolved simulations of particle suspensions in visco-elastic carrier fluids
(English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Refereed) Submitted
Abstract [en]

We study the rheology of a suspension of neutrally buoyant rigid particles subject touniform shear in different kinds of non-Newtonian fluids, chosen in order to disentanglethe effect of elasticity and shear thinning on the macroscopic system behavior. In par-ticular, we adopt the inelastic Carreau, viscoelastic Oldroyd-B and Giesekus models forthe carrier fluid. The rheology of the suspension is analyzed for a wide range of particlevolume fractions, Weissenberg and Reynolds numbers, comparing the results with thoseobtained for a Newtonian carrier fluid. We report here that the effective viscosity per-taining all the non-Newtonian cases is always lower than that of the suspension in theNewtonian carrier fluid and grows monotonically with the solid volume fraction. Theshear-thinning viscoelastic Giesekus fluid behaves similarly to the Oldroyd-B fluid at lowWeissenberg numbers and to the Carreau fluid at high Weissenberg numbers, indicatingthat elastic effects dominate at low Weissenberg and shear thinning is predominant athigh Weissenberg number. These variations in the effective viscosity are mainly due tochanges in the particle induced shear stress component. These data show that, at highshear rates, a viscoelastic carrier fluid can be modelled as a simple shear-thinning fluidfor which theoretical closures exists, while new models are needed at low Weissenbergnumbers to account for elastic effects such as decreased particle stress. Finally, when theinertia is increased, the suspension effective viscosity grows with the particle Reynoldsnumber at the same rate as in a Newtonian fluid for the Oldroyd-B case, while in ashear-thinning fluid the growth is less than in the Newtonian fluid. Also in the presenceof inertia, therefore, the shear-thinning behaviour dominates the suspension dynamics atrelatively high values of the imposed shear rate and elasticity effects saturate.

Keywords
particle/fluid flow, rheology, suspensions, Visco-elastic
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-263654 (URN)
Funder
EU, European Research Council, ERC-2013-CoG-616186
Note

QC 20191210

Available from: 2019-11-07 Created: 2019-11-07 Last updated: 2019-12-10Bibliographically approved
3. Sedimentation of finite-size particles in quiescent wall-bounded shear-thinning and Newtonian fluids
Open this publication in new window or tab >>Sedimentation of finite-size particles in quiescent wall-bounded shear-thinning and Newtonian fluids
(English)In: Journal of International Journal of Multiphase Flow, ISSN 0301-9322Article in journal (Refereed) Submitted
Abstract [en]

We study the sedimentaion of finite-size particles in a quiescent wall-boundedNewtonian and shear-thinning fluids. The problem is studied numerically bymeans of direct numerical simulations with the presence of the particles ac-counted for with an immersed boundary method. The supensions are Non-Brownian rigid spherical particles with particle to fluid density ratio ρ p /ρ f =1.5; three different solid volume fractions Φ = 1%, 5% and 20% are considered.The Archimedes number is kept constant to Ar = 36 for all shear-thinning fluidcases, while it is changed to Ar = 97 for the Newtonian fluid to reproduce thesame terminal velocity of a single particle sedimenting in the shear-thinningfluid. We show that the mean settling velocities decrease with the particle con-centration as a consequence of the hindering effect and that the mean settlingspeed is always larger in the shear thinning fluid than in the Newtonian one.This is due to the decrease of the mean viscosity of the fluid which leads to alower drag force acting on the particles. We show that particles tend to formaggregates in the middle of the channel in a shear-thinning fluid, preferentiallypositioning in the wake of neighboring particles or aside them, resulting in lowerlevels of fluctuation in the gravity direction than in a Newtonian fluid.

Keywords
non-Newtonian fluids, sedimentation, particle/fluid flow
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-263655 (URN)
Funder
EU, European Research Council, ERC-2013-CoG-616186
Note

QC 201912010

Available from: 2019-11-07 Created: 2019-11-07 Last updated: 2019-12-10Bibliographically approved
4. Inertial migration of a deformable particle in pipe flow
Open this publication in new window or tab >>Inertial migration of a deformable particle in pipe flow
2019 (English)In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 4, no 10, article id 104201Article in journal (Refereed) Published
Abstract [en]

We perform fully Eulerian numerical simulations of an initially spherical hyperelastic particle suspended in a Newtonian pressure-driven flow in a cylindrical straight pipe. We study the full particle migration and deformation for different Reynolds numbers and for various levels of particle elasticity, to disentangle the interplay of inertia and elasticity on the particle focusing. We observe that the particle deforms and undergoes a lateral displacement while traveling downstream through the pipe, finally focusing at the pipe centerline. We note that the migration dynamics and the final equilibrium position are almost independent of the Reynolds number, while they strongly depend on the particle elasticity; in particular, the migration is faster as the elasticity increases (i.e., the particle is more deformable), with the particle reaching the final equilibrium position at the centerline in shorter times. Our simulations show that the results are not affected by the particle initial conditions, position, and velocity. Finally, we explain the particle migration by computing the total force acting on the particle and its different components, viscous and elastic.

Place, publisher, year, edition, pages
American Physical Society, 2019
Keywords
deformable particle, hyper-elastic
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-263656 (URN)10.1103/PhysRevFluids.4.104201 (DOI)000489589700003 ()2-s2.0-85074434642 (Scopus ID)
Funder
EU, European Research Council, ERC-2013-CoG-616186
Note

QC 20191115

Available from: 2019-11-07 Created: 2019-11-07 Last updated: 2019-11-15Bibliographically approved

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