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Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-2346-7063
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Chemical Science and Engineering (CHE), Centres, Wallenberg Wood Science Center.
2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 738, 563-590 p.Article in journal (Refereed) Published
Abstract [en]

The basic dynamics of a prolate spheroidal particle suspended in shear flow is studied using lattice Boltzmann simulations. The spheroid motion is determined by the particle Reynolds number (Re-p) and Stokes number (St), estimating the effects of fluid and particle inertia, respectively, compared with viscous forces on the particle. The particle Reynolds number is defined by Re-p = 4Ga(2)/nu, where G is the shear rate, a is the length of the spheroid major semi-axis and nu is the kinematic viscosity. The Stokes number is defined as St = alpha . Re-p, where alpha is the solid-to-fluid density ratio. Here, a neutrally buoyant prolate spheroidal particle (St = Re-p) of aspect ratio (major axis/minor axis) r(p) = 4 is considered. The long-term rotational motion for different initial orientations and Re-p is explained by the dominant inertial effect on the particle. The transitions between rotational states are subsequently studied in detail in terms of nonlinear dynamics. Fluid inertia is seen to cause several bifurcations typical for a nonlinear system with odd symmetry around a double zero eigenvalue. Particle inertia gives rise to centrifugal forces which drives the particle to rotate with the symmetry axis in the flow-gradient plane (tumbling). At high Re-p, the motion is constrained to this planar motion regardless of initial orientation. At a certain critical Reynolds number, Re-p = Re-c, a motionless (steady) state is created through an infinite-period saddle-node bifurcation and consequently the tumbling period near the transition is scaled as vertical bar Re-p - Re-c vertical bar(-1/2). Analyses in this paper show that if a transition from tumbling to steady state occurs at Re-p = Re-c, then any parameter beta (e. g. confinement or particle spacing) that influences the value of Re-c, such that Re-p = Re-c as beta = beta(c), will lead to a period that scales as vertical bar beta - beta c vertical bar(-1/2) and is independent of particle shape or any geometric aspect ratio in the flow.

Place, publisher, year, edition, pages
2014. Vol. 738, 563-590 p.
Keyword [en]
complex fluids, multiphase and particle-laden flows, nonlinear dynamical systems
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-140130DOI: 10.1017/jfm.2013.599ISI: 000328486400024Scopus ID: 2-s2.0-84910138134OAI: oai:DiVA.org:kth-140130DiVA: diva2:689665
Note

QC 20140121

Available from: 2014-01-21 Created: 2014-01-17 Last updated: 2017-12-06Bibliographically approved
In thesis
1. The influence of inertia on the rotational dynamics of spheroidal particles suspended in shear flow
Open this publication in new window or tab >>The influence of inertia on the rotational dynamics of spheroidal particles suspended in shear flow
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Dispersed particle flows occur in many industrial, biological and geophysical applications. The knowledge of how these flow behave can for example lead to improved material processes, better predictions of vascular diseases or more accurate climate models. These particle flows have certain properties that depend on single particle motion in fluid flows and especially how they are distributed both in terms of spatial position and, if they are non-spherical, in terms of orientation. Much is already known about the motion of perfectly spherical particles. For non-spherical particles, apart from their translation, it is important to know the the rotational motion due to local velocity gradients. Such studies have usually been restricted by the assumption that particles are extremely small compared to fluid length scales. In this limit, both inertia of the particle and inertia of the fluid can be neglected for the particle motion. This thesis gives a complete picture of how a spheroidal particle (a particle described by a rotation of an ellipse around one of its principal axes) behave in a linear shear flow when including both fluid and particle inertia, using numerical simulations. It is observed that this very simple problem possess very interesting dynamical behavior with different stable rotational states appearing as a competition between the two types of inertia. The effect of particle inertia leads to a rotation where the mass of the particle is concentrated as far away from the rotational axis as possible, i.e.\ a rotation around the minor axis. Typically, the effect of fluid inertia is instead that it tries to force the particle in a rotation where the streamlines of the flow remain as straight as possible. The first effect of fluid inertia is thus the opposite of particle inertia and instead leads to a particle rotation around the major axis. Depending on rotational state, the particles also affect the apparent viscosity of the particle dispersion. The different transitions and bifurcations between rotational states are characterized in terms of non-linear dynamics, which reveal that the particle motion probably can be described by some reduced model. The results in this theses provides fundamental knowledge and is necessary to understand flows containing non-spherical particles.

Abstract [sv]

Flöden med dispergerade partiklar påträffas i många industriella, biologiska och geofysiska tillämpningar. Kunskap om hur dessa flöden beter sig kan bl.a. leda till förbättrade materialprocesser, bättre förutsägelser om hjärt- och kärlsjukdomar eller mer noggranna väderprognoser. Dessa flödens egenskaper beror på hur enskilda partiklar rör sig i en fluid och speciellt hur de är fördelade både i termer av position och, om de är icke-sfäriska, i termer av orientering. Mycket är redan känt om rörelsen av perfekt sfäriska partiklar. För icke-sfäriska partiklar är det inte bara translationen som är av intresse utan det är även viktigt att veta hur partiklarna roterar till följd av lokala hastighetsgradienter. Sådana studier har tidigare varit begränsade av antagandet att partiklarna är extremt små jämfört med fluidens typiska längdskalor. I denna gräns kan både partikelns och fluidens tröghet antas försumbar. Den här avhandlingen ger en komplett bild av hur en sfäroidisk partikel (en partikel som beskrivs av en rotation av en ellips runt en av dess huvudaxlar) beter sig i ett linjärt skjuvflöde när tröghetseffekter inkluderas. Resultaten har erhållits genom numeriska simuleringar. Det visar sig att detta enkla problem är väldigt rikt på olika dynamiska beteenden med flera stabila rotationstillstånd som uppstår tilll följd av både partikel- och fluidtröghet. Inverkan av partikeltröghet leder till en rotation där massan av partikeln är koncentrerad så långt ifrån rotationsaxeln som möjligt, d.v.s. en rotation runt lillaxeln. Den typiska inverkan av fluidtröghet är istället att fluiden försöker påtvinga partikeln en rotation där strömlinjer förblir så raka som möjligt. Primärt leder detta till att partikeln istället roterar runt storaxeln. Beroende på rotationstillstånd, så har partikeln även olika inverkan på den märkbara viskositeten av partikeldispersionen. De olika övergångarna och bifurkationerna mellan rotationstillstånd är karaktäriserade i termer av icke-linjär dynamik, vilket visar på att partikelrörelserna förmodligen kan beskrivas med en reducerad modell. Resultaten i denna avhandling är därför fundamental kunskap och ett nödvändigt steg mot att förstå beteendet av flöden med dispergerade, icke-sfäriska partiklar.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. x, 86 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2014:11
Keyword
Fluid mechanics, dispersed particle flows, inertia, non-spherical particles, non-linear dynamics
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-143663 (URN)978-91-7595-093-8 (ISBN)
Presentation
2014-04-24, D3, Lindstedtsvägen 5, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20140328

Available from: 2014-03-28 Created: 2014-03-26 Last updated: 2014-03-28Bibliographically approved
2. Angular dynamics of non-spherical particles in linear flows related to production of biobased materials
Open this publication in new window or tab >>Angular dynamics of non-spherical particles in linear flows related to production of biobased materials
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Dispersed particle flows are encountered in many biological, geophysical but also in industrial situations, e.g. during processing of materials. In these flows, the particles usually are non-spherical and their angular dynamics play a crucial role for the final material properties. Generally, the angular dynamics of a particle is dependent on the local flow in the frame-of-reference of this particle. In this frame, the surrounding flow can be linearized and the linear velocity gradient will determine how the particle rotates. In this thesis, the main objective is to improve the fundamental knowledge of the angular dynamics of non-spherical particles related to two specific biobased material processes.

Firstly, the flow of suspended cellulose fibers in a papermaking process is used as a motivation. In this process, strong shear rates close to walls and the size of the fibers motivates the study of inertial effects on a single particle in a simple shear flow. Through direct numerical simulations combined with a global stability analysis, this flow problem is approached and all stable rotational states are found for spheroidal particles with aspect ratios ranging from moderately slender fibers to thin disc-shaped particles.

The second material process of interest is the production of strong cellulose filaments produced through hydrodynamic alignment and assembly of cellulose nanofibrils (CNF). The flow in the preparation process and the small size of the particles motivates the study of alignment and rotary diffusion of CNF in a strain flow. However, since the particles are smaller than the wavelength of visible light, the dynamics of CNF is not easily captured with standard optical techniques. With a new flow-stop experiment, rotary diffusion of CNF is measured using Polarized optical microscopy. This process is found to be quite complicated, where short-range interactions between fibrils seem to play an important role. New time-resolved X-ray characterization techniques were used to target the underlying mechanisms, but are found to be limited by the strong degradation of CNF due to the radiation.

Although the results in this thesis have limited direct applicability, they provide important fundamental stepping stones towards the possibility to control fiber orientation in flows and can potentially lead to new tailor-made materials assembled from a nano-scale.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. 134 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2016:14
Keyword
Fluid mechanics, dispersed particle flows, inertia, non-linear dynamics, rotary diffusion, characterization techniques
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-193124 (URN)978-91-7729-139-8 (ISBN)
Public defence
2016-10-28, F2, Lindstedsvägen 26, Stockholm, 10:30 (English)
Opponent
Supervisors
Note

QC 20160929

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2016-09-29Bibliographically approved

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