628 research outputs found

    Methods for suspensions of passive and active filaments

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    Flexible filaments and fibres are essential components of important complex fluids that appear in many biological and industrial settings. Direct simulations of these systems that capture the motion and deformation of many immersed filaments in suspension remain a formidable computational challenge due to the complex, coupled fluid--structure interactions of all filaments, the numerical stiffness associated with filament bending, and the various constraints that must be maintained as the filaments deform. In this paper, we address these challenges by describing filament kinematics using quaternions to resolve both bending and twisting, applying implicit time-integration to alleviate numerical stiffness, and using quasi-Newton methods to obtain solutions to the resulting system of nonlinear equations. In particular, we employ geometric time integration to ensure that the quaternions remain unit as the filaments move. We also show that our framework can be used with a variety of models and methods, including matrix-free fast methods, that resolve low Reynolds number hydrodynamic interactions. We provide a series of tests and example simulations to demonstrate the performance and possible applications of our method. Finally, we provide a link to a MATLAB/Octave implementation of our framework that can be used to learn more about our approach and as a tool for filament simulation

    Shape evolution of long flexible fibers in viscous flows

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    The present work studies numerically the dynamics and shape evolution of long flexible fibers suspended in a Newtonian viscous cellular flow using a particle-level fiber simulation technique. The fiber is modeled as a chain of massless rigid cylindrical segments connected by ball and socket joints; one-way coupling between the fibers and the flow is considered while Brownian motion is neglected. The effect of stiffness, equilibrium shape, and aspect ratio of the fibers on the shape evolution of the fibers are analyzed. Moreover, the influence of fiber stiffness and their initial positions and orientations on fiber transport is investigated. For the conditions considered, the results show that the fiber curvature field resembles that of the flow streamline. It is found that the stiffer fibers experience not only a quicker relaxation phase, in which they transient from their initial shape to their "steady-state shape," but they also regain their equilibrium shape to a larger extent. The findings also demonstrate that even a small deviation of fiber shape from perfectly straight impacts significantly the early-stage evolution of the fiber shape and their bending behavior. Increasing the fiber aspect ratio, when other parameters are kept fixed, leads the fiber to behave more flexible, and it consequently deforms to a larger extent to adjust to the shape of the flow streamlines. In agreement with the available experimental results, the fiber transport studies show that either the fiber becomes trapped within the vortices of the cellular array or it moves across the vortical arrays while exhibiting various complex shapes

    3D computational simulation and experimental characterization of polymeric stochastic network materials : case studies in reinforced eucalyptus office paper and nanofibrous materials

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    The properties of stochastic fibrous materials like paper and nanowebs are highly dependent on those fibers from which the network structure is made. This work contributes to a better understanding of the effect of fiber properties on the network structural properties, using an original 3D fibrous material model with experimental validation, and its application to different fibrous materials used in reinforced Eucalyptus office paper and nanofibrous networks. To establish the relationships between the fiber and the final structural material properties, an experimental laboratorial plan has been executed for a reinforced fibrous structure, and a physical based 3D model has been developed and implemented. The experimental plan was dedicated to an important Portuguese material: the reinforced Eucalyptus based office paper. Office paper is the principal Portuguese paper industry product. This paper is mainly produced from Eucalyptus globulus bleached kraft pulp with a small incorporation of a softwood pulp to increase paper strength. It is important to access the contribution of different reinforcement pulp fibers with different biometry and coarseness to the final paper properties. The two extremes of reinforcement pulps are represented by a Picea abies kraft softwood pulp, usually considered the best reinforcement fiber, and the Portuguese pine Pinus pinaster kraft pulp. Fiber flexibility was determined experimentally using the Steadman and Luner method with a computerized acquisition device. When comparing two reinforcement fibers, the information about fiber flexibility and biometry is determinant to predict paper properties. The values presented correspond to the two extremes of fibers available as reinforcement fibers, regarding wall thickness, beating ability and flexibility values. Pinus pinaster has the thickest fiber wall, and consequently it is less flexible than the thinner wall fibers: Pinus sylvestris and Picea abies. Experimental results for the evolutions of paper properties, like paper apparent density, air permeability, tensile and tear strength, together with fiber flexibility for the two reinforcement fibers, constitute valuable information, also applicable for other reinforcement fibers, with fiber walls dimensions in this range. After having quantified the influence of fiber flexibility, we identified that this is as a key physical property to be included in our structural model. Therefore, we chose to develop a 3D network model that includes fiber bending in the z direction as an important parameter. The inclusion of fiber flexibility was done for the first time by Niskanen, in a model known as the KCL-Pakka model. We propose an extension of this model, with improvements on the fiber model, as well as an original computational implementation. A simulator has been developed from scratch and the results have been validated experimentally using handmade laboratory structures made from Eucalyptus fibers (hardwood fibers), and also Pinus pinaster, Pinus Sylvestris and Picea abies fibers, which are representative reinforcement fibers. Finally, the model was modified and extended to obtain an original simulator to nanofibrous materials, which is also an important innovation. In the network model developed in this work, the structure is formed by the sequential deposition of fibers, which are modeled individually. The model includes key papermaking fiber properties like morphology, flexibility, and collapsibility and process operations such as fiber deposition, network forming or densification. For the first time, the model considers the fiber microstructure level, including lumen and fiber wall thickness, with a resolution up to 0.05ÎŒm for the paper material case and 0.05nm for the nanofibrous materials. The computational simulation model was used to perform simulation studies. In the case of paper materials, it was used to investigate the relative influence of fiber properties such as fiber flexibility, dimensions and collapsibility. The developed multiscale model gave realistic predictions and enabled us to link fiber microstructure and paper properties. In the case of nanofibrous materials, the 3D network model was modified and implemented for Polyamide-6 electrospun and cellulose nanowebs. The influence of computational fiber flexibility and dimensions was investigated. For the Polyamide-6 electrospun network experimental results were compared visually with simulation results and similar evolutions were observed. For cellulose nanowebs the simulation study used literature data to obtain the input information for the nanocellulose fibers. The design of computer experiments was done using a space filling design, namely the Latin hypercube sampling design, and the simulations results were organized and interpreted using regression trees. Both the experimental characterization, and computational modeling, contributed to study the relationships between the polymeric fibers and the network structure formed.As propriedades de materiais estocĂĄsticos constituĂ­dos por fibras, tais como o papel ou nanoredes polimĂ©ricas, dependem fortemente das fibras a partir das quais a estrutura em rede se forma. Este trabalho contribui para uma melhor compreensĂŁo da influĂȘncia das propriedades das fibras nas propriedades estruturais das redes, utilizando um modelo original 3D para materiais constituĂ­dos por fibras, com validação experimental, bem como a sua aplicação aos materiais utilizados no papel de escritĂłrio de Eucalyptus, com fibras de reforço, e a redes de nanofibras. Para estabelecer as relaçÔes entre a fibra e as propriedades estruturais do material, executou-se um planeamento experimental para uma estrutura fibrosa reforçada, e desenvolveu-se e implementou-se um modelo 3D de base fĂ­sica. O plano experimental teve como objecto um material relevante em Portugal: o papel de escritĂłrio de Eucalyptus com fibras de reforço. O papel de escritĂłrio Ă© o produto principal da indĂșstria de papel Portuguesa. Este tipo de papel Ă© produzido a partir da pasta kraft branqueada de Eucalyptus globulus, com incorporação de uma pequena quantidade de pasta de reforço, “softwood”, para melhorar a resistĂȘncia do papel. É importante avaliar a contribuição de diferentes fibras de reforço, com biometria e massas linear distinta, nas diferentes propriedades finais do papel. Os dois extremos das fibras de reforço estĂŁo representados pela pasta kraft de Picea abies, usualmente considerada a melhor fibra de reforço, e a pasta kraft Portuguesa de Pinus pinaster. A flexibilidade da fibra determinou-se experimentalmente utilizando o mĂ©todo de Steadman e Luner, com um dispositivo de aquisição automatizado. A informação relativa Ă  flexibilidade e biometria da fibra Ă© fundamental para inferir sobre as propriedades do papel. Os valores determinados correspondem a valores dos extremos, paras as fibras de reforço disponĂ­veis no mercado, no que diz respeito a espessura de parede, refinabilidade e valores de flexibilidade. Pode considerar-se a fibra de Pinus pinaster num extremo, sendo a fibra de paredes mais espessas, e consequentemente menos flexĂ­vel que as fibras de paredes mais finas: Pinus sylvestris e Picea abies. Desta forma, os resultados experimentais obtidos para estas fibras, relativos Ă  evolução de propriedades do papel, nomeadamente densidade, permeabilidade ao ar, resistĂȘncia Ă  tracção e ao rasgamento, entre outros, constituem informação importante que pode ser aplicada a outras fibras de reforço, que se situem nesta gama. Como consequĂȘncia lĂłgica da identificação da flexibilidade da fibra como uma propriedade fĂ­sica determinante, e apĂłs a quantificação experimental, a escolha do modelo de papel recaiu sobre um modelo que inclui a flexibilidade como propriedade chave. Assim, desenvolvemos um modelo 3D que inclui a flexĂŁo das fibras na direcção transversal, isto Ă©, a direcção da espessura do papel, tambĂ©m reconhecida como direcção da coordenada z. A inclusĂŁo da flexibilidade da fibra baseia-se no modelo de Niskanen, conhecido como o modelo KCL-Pakka. Apresenta-se uma extensĂŁo deste modelo, com modificaçÔes no modelo da fibra, bem como uma implementação computacional original. Desenvolveu-se um simulador para matĂ©rias em rede, que se validou com resultados experimentais. Efectuaram-se, tambĂ©m, as modificaçÔes necessĂĄrias para obter um simulador para nanomateriais, o que constitui uma inovação relevante. No modelo deste trabalho, desenvolvido para materiais fibrosos em rede, as fibras modelam-se individualmente e a estrutura forma-se sequencialmente pela sua deposição e conformação Ă  estrutura existente. O modelo inclui propriedades das fibras determinantes, tais como morfologia, flexibilidade e colapsabilidade. Bem como etapas do processo, nomeadamente a deposição das fibras e a formação da rede, isto Ă©, a densificação da estrutura. De uma forma original, o modelo da fibra inclui a espessura do lĂșmen e da parede da fibra, com uma resolução de 0.05ÎŒm para as fibras do papel e 0.05nm no caso das nanofibras. O modelo computacional desenvolvido utilizou-se na realização de estudos de simulação. No caso dos materiais papeleiros, utilizou-se para investigar a influĂȘncia das propriedades das fibras, tendo-se obtido previsĂ”es realistas. No caso dos nanomateriais, o modelo foi modificado e implementado para as fibras electrofiadas de Poliamida-6 e redes de nanocelulose. O plano de experiencias computacionais utilizou uma distribuição no espaço “Latin hypercube” e os resultados das simulaçÔes organizaram-se recorrendo a ĂĄrvores de regressĂŁo. Tanto a caracterização experimental, como a modelação computacional, contribuĂ­ram com valiosa informação para o estudo das relaçÔes entre as fibras polimĂ©ricas e as estruturas em rede por elas formadas

    Axial Variations and Entry Effects in a Pressure Screen

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    Pressure screens are used for contaminant removal and fibre length fractionation in the production of pulp and paper products. Axial variations and entry effects in the screen are known to occur and these variations have not been adequately quantified. This thesis describes a fundamental study of the axial variations of several factors that occur within an industrial pressure screen; namely, pulp consistency, fibre length distribution, rotor pressure pulse, and feed annulus tangential velocity. Axial variations of pulp consistency in the screen annulus and the accept chamber of the screen were studied using an internal radial sampling method. Localised pulp samples were taken and evaluated and common measures of screen performance such as fibre passage ratio and fractionation efficiency were calculated along the screen. Consistency generally increased along the length of the screen although under certain conditions the consistency toward the front of the screen was lower than the feed consistency. A two passage ratio model that incorporated forward and reverse passage ratio was derived to elucidate the flow of both fibre and fluid through the screen and their effects on overall screen performance. The passage of fibre through the screen decreased with screen length which generally had a positive effect on the fractionation efficiency toward the back of the screen. The passage of individual fibre length fractions was also studied and it was found that long fibre had a much lower passage than short fibre which caused the average fibre length in the annulus to increase. Rotor induced pressure pulse variations along the screen length were also investigated. The magnitude of the pressure pulse was significantly lower (up to 40 %) at the rear of the screen. The variation in pressure caused by the rotor is due to a Venturi effect and the shape of the rotor. The relative velocity of the fluid and the rotor, called the slip factor, also directly affects the size of the pressure pulse in the annulus. The slip factor decreases along the length of the screen due to the increase in tangential velocity of the fluid. Pressure pulse data was also used to estimate the instantaneous aperture velocity and back-flush ratio. The instantaneous aperture velocity was calculated to vary considerably from the superficial aperture velocity by up to 5 m/s in the forward direction and 10 m/s in the reverse direction. Computational Fluid Dynamics (CFD) was used to model tangential velocity changes in simplified screen annuli with axial through flow. For a smooth screen rotor the mean tangential velocity increased over the entire length of the annulus without reaching a maximum value. A step and bump rotor were modelled and the shape of the pressure pulses showed good agreement with experimentally measured pulses. The mean tangential velocity and the entrance length were found to be heavily dependant on the screen rotor used

    A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number

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    This contribution provides a general framework to use Lagrange multipliers for the simulation of low Reynolds number fiber dynamics based on Bead Models (BM). This formalism provides an efficient method to account for kinematic constraints. We illustrate, with several examples, to which extent the proposed formulation offers a flexible and versatile framework for the quantitative modeling of flexible fibers deformation and rotation in shear flow, the dynamics of actuated filaments and the propulsion of active swimmers. Furthermore, a new contact model called Gears Model is proposed and successfully tested. It avoids the use of numerical artifices such as repulsive forces between adjacent beads, a source of numerical difficulties in the temporal integration of previous Bead Models.Comment: 41 pages, 15 figure

    Orientation and rotational diffusion of fibers in semidilute suspension

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    The dynamics of fiber orientation is of great interest for efforts to predict the microstructure and material properties of a suspension flow system. In this research a fiber-level, hybrid simulation method, LBM‒EBF (coupled lattice‒Boltzmann method with the external boundary force method) is undertaken to advance the current understanding of the hydrodynamic interaction induced rotational diffusion mechanism for rigid fibers in semidilute suspension of low Reynolds number flow. The LBM‒EBF simulations correctly predict the orbit constant distribution of fibers in a sheared semidilute suspension flow. It is demonstrated that an anisotropic, weak rotary diffusion model can fit the orbit constant distribution very well, but it can not describe the asymmetry in Stokes flow observed in semidilute suspension. The rotational diffusion process is then characterized with a three dimensional spatial tensor representation of the rotational diffusivity. A scalar measure of the rotational diffusion‒'scalar Folgar‒Tucker constant', C[subscript I], is extracted from this tensor. The study provides substantial numerical evidence that the range of C[subscript I] (0.0038 to 0.0165) obtained by Folgar&Tucker (J. reinf. plast. and comp, v.3, 1984) in a semidilute regime is overly diffusive, and that the correct magnitude is of O(10⁻⁎). The study reveals that the interactions among fibers become more frequent with either the decrease of fiber aspect-ratio, r[subscript p] (keeping nLÂł constant, where n is the fiber number density, and L is the fiber length) or with the increase of nLÂł (keeping r[subscript p] constant) in the semidilute regime, which in consequence causes an increase in C[subscript I]. The rheological properties of sheared semidilute suspension are also computed with direct LBM‒EBF simulations. The LBM‒EBF investigation is extended to characterize the fiber orientation in a linearly contracting channel similar to a paper machine 'headbox'. It is found that the rotational diffusion is the predominant term over the strain rate in the semidilute regime for a low Reynolds number flow, and it results in a decreasing trend of rotational Peclet number, Pe, along the contraction centerline. Lastly, in order to improve the numerical consistency of the existing LBM‒EBF approach, a modification to the body force term in the LB equation is suggested, which can recover the exact macroscopic hydrodynamics from the mesoscale.Ph.D.Committee Chair: Cyrus, Aidun; Committee Member: Breedveld, Victor; Committee Member: Ghiaasiaan, Mostafa S.; Committee Member: Salant, Richard F.; Committee Member: Vuduc, Richar
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