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Simulation of semidilute suspensions of non-Brownian fibres in shear flow
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
Responsible organisation
2008 (English)In: Journal of Chemical Physics, ISSN 0021-9606, Vol. 128, no 2, 024901- p.Article in journal (Refereed) Published
Abstract [en]

Particle-level simulations are performed to study semidilute suspensions of monodispersed non-Brownian fibers in shear flow, with a Newtonian fluid medium. The incompressible three-dimensional Navier-Stokes equations are used to describe the motion of the medium, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous drag forces. The two-way coupling between the solids and the fluid phase is taken into account by enforcing momentum conservation. The model includes long-range and short-range hydrodynamic fiber-fiber interactions, as well as mechanical interactions. The simulations rendered the time-dependent fiber orientation distribution, whose time average was found to agree with experimental data in the literature. The viscosity and first normal stress difference was calculated from the orientation distribution using the slender body theory of Batchelor [J. Fluid Mech. 46, 813--829 (1971)], with corrections for the finite fiber aspect ratios. The viscosity was also obtained from direct computation of the shear stresses of the suspension for comparison. These two types of predictions compared well in the semidilute regime. At higher concentrations, however, a discrepancy was seen, most likely due to mechanical interactions, which are only accounted for in the direct computation method. The simulated viscosity determined directly from shear stresses was in good agreement with experimental data found in the literature. The first normal stress difference was found to be proportional to the square of the volume concentration of fibers in the semidilute regime. As concentrations approached the concentrated regime, the first normal stress difference became proportional to volume concentration.

Place, publisher, year, edition, pages
2008. Vol. 128, no 2, 024901- p.
Keyword [en]
fiber suspension, fiber orientation distribution, suspension microstructure, Jeffery orbit, hydrodynamic fiber interactions, suspension viscosity, first normal stress difference, shear flow, simulation
National Category
Chemical Engineering Other Engineering and Technologies
Identifiers
URN: urn:nbn:se:miun:diva-413DOI: 10.1063/1.2815766ISI: 000252450100036PubMedID: 18205469Scopus ID: 2-s2.0-38349164723Local ID: 5052OAI: oai:DiVA.org:miun-413DiVA: diva2:2040
Projects
Stochastic Modelling of Paper Structures
Available from: 2008-11-29 Created: 2008-11-13 Last updated: 2009-03-19Bibliographically approved
In thesis
1. Modelling and simulation of paper structure development
Open this publication in new window or tab >>Modelling and simulation of paper structure development
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

 

 

 

 

 

A numerical tool has been developed for particle-level simulations of fibre suspension flows, particularly forming of the fibre network structure of paper sheets in the paper machine. The model considers inert fibres of various equilibrium shapes, and finite stiffness, interacting with each other through normal, frictional, and lubrication forces, and with the surrounding fluid medium through hydrodynamic forces. Fibre–fluid interactions in the non-creeping flow regime are taken into account, and the two-way coupling between the solids and the fluid phases is included by enforcing momentum conservation between phases. The incompressible three-dimensional Navier–Stokes equations are employed tomodel themotion of the fluid medium.

The validity of the model has been tested by comparing simulation results with experimental data from the literature. It was demonstrated that the model predicts well the motion of isolated fibres in shear flow over a wide range of fibre flexibilities. It was also shown that the model predicts details of the orientation distribution of

 

multiple, straight, rigid fibres in a sheared suspension. Furthermore, model predictions of the shear viscosity and first normal stress difference were in fair agreement with experimental data found in the literature. Since the model is based solely on first principles physics, quantitative predictions could be made without any parameter fitting.

 

Based on these validations, a series of simulations have been performed to investigate the basic mechanisms responsible for the development of the stress tensor components for monodispersed, non-Brownian fibres suspended in a Newtonian fluid in shear flow. The effects of fibre aspect ratio, concentration, and inter-particle friction, as well as the tendency of fibre agglomeration, were examined in the nonconcentrated regimes. For the case of well dispersed suspensions, semi-empirical relationships were found between the aforementioned fibre suspension properties, and the steady state apparent shear viscosity, and the first/second normal stress differences.

 

Finally, simulations have been conducted for the development of paper structures in the forming section of the paper machine. The conditions used for the simulations were retrieved from pilot-scale forming trial data in the literature, and from real pulp fibre analyses. Dewatering was simulated by moving two forming fabrics toward each other through a fibre suspension. Effects of the jet-to-wire speed difference on the fibre orientation anisotropy, the mass density distribution, and three-dimensionality of the fibre network, were investigated. Simulation results showed that the model captures well the essential features of the forming effects on these paper structure parameters, and also posed newquestions on the conventional wisdom of the forming mechanics.

 

 

Place, publisher, year, edition, pages
Sundsvall: Department of Natural Sciences, Engineering and Mathematics, Mid Sweden University, 2008. 64 p.
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 60
Keyword
Forming, Fibre, Paper, Fibre suspension, Paper structure, Simulation, Rheology
National Category
Chemical Engineering Other Engineering and Technologies
Identifiers
urn:nbn:se:miun:diva-7003 (URN)978-91-86073-10-7 (ISBN)
Public defence
2008-10-28, O102, Mid Sweden University, Holmgatan 10, Sundsvall, 09:30 (English)
Opponent
Supervisors
Available from: 2008-11-12 Created: 2008-11-12 Last updated: 2009-03-19Bibliographically approved
2. Simulations of the Dynamics of Fibre Suspension Flows
Open this publication in new window or tab >>Simulations of the Dynamics of Fibre Suspension Flows
2007 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

A new model for simulating non-Brownian flexible fibres suspended in a Newtonian fluid has been developed. Special attention has been given to include realistic flow conditions found in the industrial papermaking process in the key features of the model; it is the intention of the author to employ the model in simulations of the forming section of the paper machine in future studies.

The model considers inert fibres of various shapes and finite stiffness, interacting with each other through normal, frictional and lubrication forces, and with the surrounding fluid medium through hydrodynamic forces. Fibre-fluid interactions in the non-creeping flow regime are taken into account, and the two-way coupling between the solids and the fluid phase is included by enforcing momentum conservation between phases. The incompressible three-dimensional Navier-Stokes equations are employed to model the motion of the fluid medium.

The validity of the model has been tested by comparing simulation results with experimental data from the literature. It was demonstrated that the model predicts the motion of isolated fibres in shear flow over a wide range of fibre flexibilities. It was also shown that the model predicts details of the orientation distribution of multiple straight, rigid fibres in a sheared suspension. Model predictions of the viscosity and first normal stress difference were in good agreement with experimental data found in the literature. Since the model is based solely on first-principles physics, quantitative predictions could be made without any parameter fitting.

Abstract [sv]

En ny modell för simulering av rörelserna hos icke-Brownska böjliga fibrer dispergerade i en Newtonsk vätska har utvecklats. Eftersom det är författarens avsikt att modellen skall kunna tillämpas vid simulering av arkformning under de förhållanden som råder i en modern pappersmaskin, har särskilt omsorg givits till att inkludera motsvarande flödesvillkor i modellens giltighetsområde.

Modellen hanterar fibrer av varierande form, massa och styvhet, som växelverkar sinsemellan via normal-, friktions- och smörjkrafter. Deras växelverkan med den omgivande vätskan sker via hydrodynamiska krafter vid finita Reynolds-tal. Den så kallade tvåvägskopplingen mellan fibrerna och vätskefasen har tagits i beaktande genom att kräva att rörelsemängden bevaras vid interaktionen mellan faserna. Vidare har Navier-Stokes ekvationer för inkompressibla vätskor använts för att beskriva mediets rörelser.

Modellens giltighet har undersökts genom att jämföra resultat från simuleringar med experimentella data från litteraturen. Det har påvisats att modellen förutsäger rörelsen hos ensamma fibrer i ett skjuvflöde, för vitt skilda fiberflexibiliteter. Det visades också att modellen förutsäger detaljer hos fiberorienteringsdistributionen i suspensioner utsatta för skjuvflöde. Det kunde också konstateras att modellens förutsägelser av fibersuspensioners viskositet och första normalspänningsdifferens under skjuvning väl överensstämde med experimentella data i litteraturen. Kvantitativa förutsägelser har kunnat göras utan någon parameteranpassning, då modellen bygger uteslutande på väletablerade fysikaliska samband inom klassisk mekanik och strömningslära.

Place, publisher, year, edition, pages
Sundsvall: Mid Sweden University, 2007
Series
Mid Sweden University licentiate thesis, ISSN 1652-8948 ; 25
Keyword
fibre, fibre suspension, simulation, paper, papermaking, forming, fibre orientation distribution, fibre flexibility, viscosity, first normal stress difference, fluid flow, simple shear flow, two-way coupling, three-dimensional
National Category
Chemical Engineering Other Engineering and Technologies
Identifiers
urn:nbn:se:miun:diva-53 (URN)5137 (Local ID)978-91-85317-62-2 (ISBN)5137 (Archive number)5137 (OAI)
Presentation
2007-09-19, O102, O-huset, Holmgatan 10, Sundsvall, 10:00 (English)
Opponent
Supervisors
Available from: 2008-01-07 Created: 2008-01-07 Last updated: 2009-07-10Bibliographically approved

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