Relevant bibliographies by topics / Weissenberg number

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Weissenberg number'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Weissenberg number"

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Hao, Jian, and Tsorng-Whay Pan. "Simulation for high Weissenberg number." Applied Mathematics Letters 20, no. 9 (September 2007): 988–93. http://dx.doi.org/10.1016/j.aml.2006.12.003.

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Keunings, Roland. "On the high Weissenberg number problem." Journal of Non-Newtonian Fluid Mechanics 20 (January 1986): 209–26. http://dx.doi.org/10.1016/0377-0257(86)80022-2.

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Evans, J. D. "Re-entrant corner flows of upper convected Maxwell fluids: the small and high Weissenberg number limits." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2076 (July 21, 2006): 3749–74. http://dx.doi.org/10.1098/rspa.2006.1737.

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We discuss here the steady planar flow of the upper convected Maxwell fluid at re-entrant corners in the singular limits of small and large Weissenberg number. The Weissenberg number is a parameter representing the dimensionless relaxation time and hence the elasticity of the fluid. Its value determines the strength of the fluid memory and thus the influence of elastic effects over viscosity. The small Weissenberg limit is that in which the elastic effects are small and the fluid's memory is weak. It is an extremely singular limit in which the behaviour of a Newtonian fluid is obtained in a main core region away from the corner and walls. Elastic effects are confined to boundary layers at the walls and core regions nearer to the corner. The actual asymptotic structure comprises a complicated four-region structure. The other limit of interest is the large Weissenberg limit (or high Weissenberg number problem) in which the elastic effects now dominate in the main regions of the flow. We explain how the transition in solution from Weissenberg order 1 flows to high Weissenberg flows is achieved, with the singularity in the stress field at the corner remaining the same but its effects now extending over larger length-scales. Implicit in this analysis is the absence of a lip vortex. We also show (for the main core region) that there is a small reduction in the velocity field at the corner and walls where it becomes smoother. This high Weissenberg number limit has a six-region local asymptotic structure and comment is made on its relevance to the case in which a lip vortex is present.
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Lin, Che-Yu, and Chao-An Lin. "Direct Numerical Simulations of Turbulent Channel Flow With Polymer Additives." Journal of Mechanics 36, no. 5 (August 6, 2020): 691–98. http://dx.doi.org/10.1017/jmech.2020.34.

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ABSTRACTDirect numerical simulations have been applied to simulate flows with polymer additives. FENE-P (finite-extensible-nonlinear-elastic-Peterlin) dumbbell model solving for the conformation tensor is adopted to investigate the influence of the polymer on the flowfield. Boundary treatments of the conformation tensor on the flowfield are examined first, where boundary condition based on the linear extrapolation scheme provides more accurate results with second-order accurate error norms. Further simulations of the turbulent channel flow at different Weissenberg numbers are also conducted to investigate the influence on drag reduction. Drag reduction increases in tandem with the increase of Weissenberg number and the increase saturates at Weτ~200, where the drag reduction is close to the maximum drag reduction (MDR) limit. At the regime of y+ > 5, the viscous layer thickens with the increase of the Weissenberg number showing a departure from the traditional log-law profile, and the velocity profiles approach the MDR line at high Weissenberg number. The Reynolds stress decreases in tandem with the increase of Weτ, whereas the levels of laminar stress and polymer stress act adversely. However, as the Weissenberg number increases, the proportion of the laminar stress in the total stress increases, and this contributes to the drag reduction of the polymer flow.
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Yu, Zhaosheng, Peng Wang, Jianzhong Lin, and Howard H. Hu. "Equilibrium positions of the elasto-inertial particle migration in rectangular channel flow of Oldroyd-B viscoelastic fluids." Journal of Fluid Mechanics 868 (April 11, 2019): 316–40. http://dx.doi.org/10.1017/jfm.2019.188.

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In this paper, the lateral migration of a neutrally buoyant spherical particle in the pressure-driven rectangular channel flow of an Oldroyd-B fluid is numerically investigated with a fictitious domain method. The aspect ratio of the channel cross-section considered is 1 and 2, respectively. The particle lateral motion trajectories are shown for the bulk Reynolds number ranging from 1 to 100, the ratio of the solvent viscosity to the total viscosity being 0.5, and a Weissenberg number up to 1.5. Our results indicate that the lateral equilibrium positions located on the cross-section midline, diagonal line, corner and channel centreline occur successively as the fluid elasticity is increased, for particle migration in square channel flow with finite fluid inertia. The transition of the equilibrium position depends strongly on the elasticity number (the ratio of the Weissenberg number to the Reynolds number) and weakly on the Reynolds number. The diagonal-line equilibrium position occurs at an elasticity number ranging from roughly 0.001 to 0.02, and can coexist with the midline and corner equilibrium positions. When the fluid inertia is negligibly small, particles migrate towards the channel centreline, or the closest corner, depending on their initial positions and the Weissenberg number, and the corner attractive area first increases and then decreases as the Weissenberg number increases. For particle migration in a rectangular channel with an aspect ratio of 2, the transition of the equilibrium position from the midline, ‘diagonal line’ (the line where two lateral shear rates are equal to each other), off-centre long midline and channel centreline takes place as the Weissenberg number increases at moderate Reynolds numbers. An off-centre equilibrium position on the long midline is observed for a large blockage ratio of 0.3 (i.e. the ratio of the particle diameter to the channel height is 0.3) at a low Reynolds number. This off-centre migration is driven by shear forces, unlike the elasticity-induced rapid inward migration, which is driven by the normal force (pressure or first normal stress difference).
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Miller, Joel C., and J. M. Rallison. "Instability of coextruded elastic liquids at high Weissenberg number." Journal of Non-Newtonian Fluid Mechanics 143, no. 2-3 (May 2007): 88–106. http://dx.doi.org/10.1016/j.jnnfm.2007.01.008.

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Lee, Daewoong, and Kyung Hyun Ahn. "Time–Weissenberg number superposition in planar contraction microchannel flows." Journal of Non-Newtonian Fluid Mechanics 210 (August 2014): 41–46. http://dx.doi.org/10.1016/j.jnnfm.2014.05.004.

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GOTO, Ikuhisa, Hikaru WAKI, Shuichi IWATA, Hideki MORI, and Tsutomu ARAGAKI. "Numerical analysis of viscoelastic flow at high Weissenberg number." Proceedings of the Fluids engineering conference 2000 (2000): 155. http://dx.doi.org/10.1299/jsmefed.2000.155.

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Huo, Xiaokai, and Wen-An Yong. "Global existence for viscoelastic fluids with infinite Weissenberg number." Communications in Mathematical Sciences 15, no. 4 (2017): 1129–40. http://dx.doi.org/10.4310/cms.2017.v15.n4.a10.

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Trebotich, David. "Toward a solution to the high Weissenberg number problem." PAMM 7, no. 1 (December 2007): 2100073–74. http://dx.doi.org/10.1002/pamm.200700989.

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Dissertations / Theses on the topic "Weissenberg number"

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Niethammer, Matthias Samuel [Verfasser]. "A Finite Volume Framework for Viscoelastic Flows at High Weissenberg Number / Matthias Samuel Niethammer." München : Verlag Dr. Hut, 2019. http://d-nb.info/1190421909/34.

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Wang, Xiaojun. "Well-posedness results for a class of complex flow problems in the high Weissenberg number limit." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27669.

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For simple fluids, or Newtonian fluids, the study of the Navier-Stokes equations in the high Reynolds number limit brings about two fundamental research subjects, the Euler equations and the Prandtl's system. The consideration of infinite Reynolds number reduces the Navier-Stokes equations to the Euler equations, both of which are dealing with the entire flow region. Prandtl's system consists of the governing equations of the boundary layer, a thin layer formed at the wall boundary where viscosity cannot be neglected. In this dissertation, we investigate the upper convected Maxwell(UCM) model for complex fluids, or non-Newtonian fluids, in the high Weissenberg number limit. This is analogous to the Newtonian fluids in the high Reynolds number limit. We present two well-posedness results. The first result is on an initial-boundary value problem for incompressible hypoelastic materials which arise as a high Weissenberg number limit of viscoelastic fluids. We first assume the stress tensor is rank-one and develop energy estimates to show the problem is locally well-posed. Then we show the more general case can be handled in the same spirit. This problem is closely related to the incompressible ideal magneto-hydrodynamics (MHD) system. The second result addresses the formulation of a time-dependent elastic boundary layer through scaling analysis. We show the well-posedness of this boundary layer by transforming to Lagrangian coordinates. In contrast to the possible ill-posedness of Prandtl's system in Newtonian fluids, we prove that in non-Newtonian fluids the stress boundary layer problem is well-posed.
Ph. D.
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Kaffel, Ahmed. "On the stability of plane viscoelastic shear flows in the limit of infinite Weissenberg and Reynolds numbers." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/77325.

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Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. Specifically, we study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet. The equation for stability is derived and solved numerically using the Chebyshev collocation spectral method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability. The numerical solutions are compared with the analysis of the long wave limit and excellent agreement is shown between the analytical and the numerical solutions. We found flows which are long wave stable, but nevertheless unstable to wave numbers in a certain finite range. While elasticity is ultimately stabilizing, this effect is not monotone; there are instances where a small amount of elasticity actually destabilizes the flow. The linear stability in the short wave limit of shear flows bounded by two parallel free surfaces is investigated. Unlike the plane Couette flow which has no short wave instability, we show that plane Poiseuille flow has two unstable eigenmodes localized near the free surfaces which can be combined into an even and an odd eigenfunctions. The derivation of the asymptotics of these modes shows that our numerical eigenvalues are in agreement with the analytic formula and that the difference between the two eigenvalues tends to zero exponentially with the wavenumber.
Ph. D.
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Martins, Adam Macedo. "Análise da qualidade de tensões obtidas na simulação de escoamentos de fluidos viscoelásticos usando a formulação log-conformação." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/156814.

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Uma das mais recentes abordagens propostas na literatura para tratar o problema do alto número de Weissenberg (We) é a Formulação Log-Conformação (FLC). Nesta formulação, a equação constitutiva viscoelástica utilizada é reescrita em termos de uma variável Ψ, que é o logaritmo do tensor conformação. Apesar do potencial de aplicação da FLC, pouca atenção tem sido dirigida para análise da acurácia da solução obtida para o campo de tensões quando se utiliza esta formulação. Assim, o objetivo do presente trabalho foi estudar a acurácia da solução obtida pela FLC na análise de escoamentos de fluidos viscoelásticos usando duas geometrias padrão de estudo: placas paralelas e cavidade quadrada com tampa móvel. Primeiramente, a FLC foi implementada no pacote de CFD OpenFOAM. Em seguida foram verificados os limites do número de Weissenberg na formulação numérica padrão (Welim,P), onde para a geometria de placas paralelas foi encontrado Welim,P = 0,3 e para a geometria da cavidade quadrada com tampa móvel foi encontrado Welim,P = 0,8. Depois o código implementado foi aplicado em ambas as geometrias, comparando-se a solução obtida pela FLC com aquela da formulação padrão na faixa de We < Welim,P. Os resultados obtidos na geometria de placas paralelas apresentaram boa concordância com a solução padrão e solução analítica. Para a geometria da cavidade quadrada com tampa móvel, que não possui solução analítica, boa concordância dos resultados também foi observada em comparação com a solução padrão. Posteriormente foram comparados os resultados obtidos pela FLC na faixa de We > Welim,P. Na geometria de placas paralelas, além da boa concordância com a solução analítica, obteve-se convergência em todos os casos estudados neste trabalho, com o maior número de Weissenberg utilizado sendo igual a 8 Os resultados da geometria da cavidade quadrada com tampa móvel também apresentaram boa concordância em comparação com dados da literatura, porém a convergência foi obtida até para We = 2. Com respeito à comparação das formulações numéricas com a solução analítica, feita apenas na geometria de placas paralelas, foi observado um erro máximo de 7,57% na solução padrão e de 12,33% na FLC. Em relação à análise da qualidade das tensões usando os resíduos da equação constitutiva viscoelástica como critério de acurácia, foi verificado nas duas geometrias que os valores de tensão obtidos usando a FLC são menos acurados que aqueles obtidos pela formulação explícita no tensor das tensões nos casos em que esta última converge. Também foi observado que a acurácia diminui com o aumento do We. Esse efeito pôde ser melhor notado na geometria de placas paralelas. Uma razão para a perda de acurácia da tensão provavelmente ocorre devido à natureza matemática da transformação algébrica inversa de Ψxx para τxx. O novo solver implementado neste trabalho apresentou convergência e soluções corretas para as duas geometrias, logo foi implementado corretamente. Ele também potencializa o solver de partida viscoelastiFluidFoam ao estender simulações para uma faixa maior do número de Weissenberg.
A recent approach proposed in the literature to deal with the High Weissenberg Number Problem is the Log-Conformation formulation (LCF). In this formulation the viscoelastic constitutive equation is rewritten in terms of the logarithm of the conformation tensor Ψ. Despite the great potential application of the LCF, little attention has been given in the literature to the accuracy of the obtained stress fields. The purpose of this work was to study the solution obtained by LCF in the analysis of viscoelastic flows using two benchmark geometries: parallel plates and lid driven cavity. Firstly, the LCF was implemented in the OpenFOAM CFD package. Then, the limits of Weissenberg number for the standard numerical formulation (Welim,P) were verified, obtaining Welim,P = 0.3 for the parallel plates and Welim,P = 0.8 for the lid driven cavity. When comparing the solution obtained by the LCF with that of the standard formulation in a range of We < Welim,P, the results obtained for the parallel plates geometry showed good agreement with the standard solution and the analytical solution. For the lid driven cavity geometry, for which there is not analytical solution, good agreement with the standard solution was also observed. For We > Welim,P in the parallel plates geometry, in addition to the good agreement with the analytical solution, it was possible to obtain convergence in all the cases studied in this work, with the largest number of Weissenberg used being equal to 8 The results of the lid driven cavity geometry also presented good agreement in comparison with literature data, but convergence was obtained up to We = 2. With respect to the comparison of the numerical formulations with the analytical solution for the parallel plates geometry, a maximum error of 7.57% was observed in the standard solution and of 12.33% in the LCF. When using the residues of the viscoelastic constitutive equation as a criterion of accuracy, it was verified that for the two geometries the stress values obtained using the LCF were less accurate than those obtained by the explicit formulation in the stress tensor. It has also been observed that accuracy decreases with increasing of We. One reason for the loss of stress accuracy probably occurs because of the mathematical nature of the inverse algebraic transformation from Ψxx to τxx. The new solver implemented in this work presented convergence and correct solutions for the two geometries, so it was implemented correctly. It also potentiates the viscoelastiFluidFoam starting solver by extending simulations to a larger range of Weissenberg number.
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Searle, Toby William. "Purely elastic shear flow instabilities : linear stability, coherent states and direct numerical simulations." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28991.

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Recently, a new kind of turbulence has been discovered in the flow of concentrated polymer melts and solutions. These flows, known as purely elastic flows, become unstable when the elastic forces are stronger than the viscous forces. This contrasts with Newtonian turbulence, a more familiar regime where the fluid inertia dominates. While there is little understanding of purely elastic turbulence, there is a well-established dynamical systems approach to the transition from laminar flow to Newtonian turbulence. In this project, I apply this approach to purely elastic flows. Laminar flows are characterised by ordered, locally-parallel streamlines of fluid, with only diffusive mixing perpendicular to the flow direction. In contrast, turbulent flows are in a state of continuous instability: tiny differences in the location of fluid elements upstream make a large difference to their later locations downstream. The emerging understanding of the transition from a laminar to turbulent flow is in terms of exact coherent structures (ECS) — patterns of the flow that occur near to the transition to turbulence. The problem I address in this thesis is how to predict when a purely elastic flow will become unstable and when it will transition to turbulence. I consider a variety of flows and examine the purely elastic instabilities that arise. This prepares the ground for the identification of a three-dimensional steady state solution to the equations, corresponding to an exact coherent structure. I have organised my research primarily around obtaining a purely elastic exact coherent structure, however, solving this problem requires a very accurate prediction of the exact solution to the equations of motion. In Chapter 2 I start from a Newtonian ECS (travelling wave solutions in two-dimensional flow) and attempt to connect it to the purely elastic regime. Although I found no such connection, the results corroborate other evidence on the effect of elasticity on travelling waves in Poiseuille flow. The Newtonian plane Couette ECS is sustained by the Kelvin-Helmholtz instability. I discover a purely elastic counterpart of this mechanism in Chapter 3, and explore the non-linear evolution of this instability in Chapter 4. In Chapter 5 I turn to a slightly different problem, a (previously unexplained) instability in a purely elastic oscillatory shear flow. My numerical analysis supports the experimental evidence for instability of this flow, and relates it to the instability described in Chapter 3. In Chapter 6 I discover a self-sustaining flow, and discuss how it may lead to a purely elastic 3D exact coherent structure.
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Dey, Anita Anup. "Experimental Study on Viscoelastic Fluid-Structure Interactions." 2017. https://scholarworks.umass.edu/masters_theses_2/502.

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It is well known that when a flexible or flexibly-mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. If the same flexible object is placed in non-Newtonian flows, however, the structure's response is still unknown. The main objective of this thesis is to introduce a new field of viscoelastic fluid-structure interactions by showing that the elastic instabilities that occur in the flow of viscoelastic fluids can drive the motion of a flexible structure placed in its path. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable at infinitesimal Reynolds numbers due to the onset of a purely elastic flow instability. This instability occurs in the absence of nonlinear effects of fluid inertia and the Reynolds number of the flows studied here are in the order of 10-4. When such an elastic flow instability occurs in the vicinity of a flexible structure, the fluctuating fluid forces exerted on the structure grow large enough to cause a structural instability which in turn feeds back into the fluid resulting in a flow instability. Nonlinear periodic oscillations of the flexible structure are observed which have been found to be coupled to the time-dependent growth and decay of viscoelastic stresses in the wake of the structure. Presented in this thesis are the results of an investigation of the interaction occurring in the flow of a viscoelastic wormlike micelle solution past a flexible rectangular sheet. The structural geometries studied include: flexible sheet inclinations at 20°, 45° and 90° and flexible sheet widths of 5mm and 2.5mm. By varying the flow velocity, the response of the flexible sheet has been characterized in terms of amplitude and frequency of oscillations. Steady and dynamic shear rheology and filament stretching extensional rheology measurements are conducted in order to characterize the viscoelastic wormlike micelle solution. Bright field images show the deformation of the flexible sheet during an unstable oscillation while flow-induced birefringence images highlight the viscoleastic fluid stresses produced in the wake of the flexible sheet.
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Arun, Dalal Swapnil. "A Numerical Study of Droplet Dynamics in Viscoelastic Flows." Thesis, 2016. http://etd.iisc.ernet.in/handle/2005/2702.

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The polymers are integral part of vast number of products used in day to day life due to their anomalous viscoelastic behaviour. The remarkable flow behaviour exhibited by the polymeric fluids including rod climbing, extrudate swell, tube-less siphon, viscoelastic jet, elastic recoil and sharkskin instability is attributed to the complex microstructures in the polymeric liquids that arise due to the interactions of long chain polymer molecules with each other and with the surrounding fluid particles. The significance of polymer in transportation, packaging, pharmaceutical, chemical, biomedical, textiles, food and polymer processing industries highlights the requirement to comprehend the complex rheology of polymeric fluids. First, we investigate the flow features exhibited by different shear thinning vis-coelastic fluids in rectangular cavities over a wide range of depth to width ratio. We have developed a viscoelastic flow solver in order to perform numerical simulations of highly elastic flow of viscoelastic fluids. In particular, we discuss the simulations of flows of constant viscosity Boger and shear thinning viscoelastic fluids in the complex flow problems using different constitutive equations. The effects of elasticity and inertia on the flow behaviour of two shear thinning vis-coelastic fluids modeled using Giesekus and linear PTT constitutive equations in rectangular cavities is studied. The size of the primary eddies and critical aspect ratio over which the corner eddies merge to yield a second primary eddy in deep cavities is discussed. We demonstrate that the flow in the shallow and deep cavities can be characterized using Weissenberg number, defined based on the shear rate, and Deborah number, specified based on the convective time scale, respectively. The study of flow in driven cavities is important in understanding of the mixing process during synthesis of blends and composites. Next, we study two phase polymeric flow in confined geometries. Nowadays, polymer processing industries prefer to develop newer polymer with the desired material properties mechanically by mixing and blending of different polymer components instead of chemically synthesizing fresh polymer. The microstructure of blends and emulsions following drop deformation, breakup and coalescence during mixing determines its macroscopic interfacial rheology. We developed a two phase viscoelastic flow solver using volume conserving sharp interface volume-of-fluid (VOF) method for studying the dynamics of single droplet subjected to the complex flow fields. We investigated the effects of drop and matrix viscoelasticity on the motion and deformation of a droplet suspended in a fully developed channel flow. The flow behaviour exhibited by Newtonian-Newtonian, viscoelastic-Newtonian, Newtonian-viscoelastic and viscoelastic-viscoelastic drop-matrix systems is presented. The difference in the drop dynamics due to presence of constant viscosity Boger fluid and shear thinning viscoelastic fluid is represented using FENE-CR and linear PTT constitutive equations, respectively. The presence of shear thinning viscoelastic fluid either in the drop or the matrix phase suppresses the drop deformation due to stronger influence of matrix viscoelasticity as compared to the drop elasticity. The shear thinning viscoelastic drop-matrix system further restricts the drop deformation and it displays non-monotonic de-formation. The constant viscosity Boger fluid droplet curbs the drop deformation and exhibits flow dynamics identical to the shear thinning viscoelastic droplet, thus indicating that the nature of the drop viscoelasticity has little influence on the flow behaviour. The matrix viscoelasticity due to Boger fluid increases drop deformation and displays non-monotonic deformation. The drop deformation is further enhanced in the case of Boger fluid in viscoelastic drop-matrix system. Interestingly, the pressure drop due to the presence of viscoelastic drop in a Newtonian matrix is lower than the single phase flow of Newtonian fluid. We also discuss the effects of inertia, surface tension, drop to matrix viscosity ratio and the drop size on these drop-matrix systems. Finally, we investigate the emulsion rheology by studying the motion of a droplet in the square lid driven cavity flow. The viscoelastic effects due to constant viscosity Boger fluid and shear thinning viscoelastic fluid are illustrated using FENECR and Giesekus rheological relations, respectively. The presence of viscoelasticity either in drop or matrix phase boosts the drop deformation with the drop viscoelasticity displaying intense deformation. The drop dynamics due to the droplet viscoelasticity is observed to be independent of the nature of vis-coelastic fluid. The shear thinning viscoelastic matrix has a stronger influence on the drop deformation and orientation compared to the Boger fluid matrix. The different blood components, cells and many materials of industrial importance are viscoelastic in nature. Thus, the present study has significant applications in medical diagnostics, drug delivery, manufacturing and processing industries, study of biological flows, pharmaceutical research and development of lab-on-chip devices.
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Book chapters on the topic "Weissenberg number"

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Gooch, Jan W. "Weissenberg Number." In Encyclopedic Dictionary of Polymers, 808. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_12776.

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Renardy, M. "High Weissenberg Number Asymptotics and Corner Singularities in Viscoelastic Flows." In IUTAM Symposium on Non–Linear Singularities in Deformation and Flow, 13–20. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4736-1_2.

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"Weissenberg number (new)." In Encyclopedic Dictionary of Polymers, 1063. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-30160-0_12528.

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"6. High Weissenberg Number Asymptotics." In Mathematical Analysis of Viscoelastic Flows, 47–55. Society for Industrial and Applied Mathematics, 2000. http://dx.doi.org/10.1137/1.9780898719413.ch6.

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"Defeating the High Weissenberg Number Problem." In Computational Rheology, 173–99. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2002. http://dx.doi.org/10.1142/9781860949425_0007.

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Yu, Bo, and Yasuo Kawaguchi. "Effect of Weissenberg Number on the Flow Structure: DNS Study of the Drag-Reducing Giesekus Fluid Flow With MINMOD Scheme." In Engineering Turbulence Modelling and Experiments 5, 617–26. Elsevier, 2002. http://dx.doi.org/10.1016/b978-008044114-6/50059-4.

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Winterbottom, Michael. "M. Weissenberger (ed., tr., ann.), Sopatri Quaestionum divisio—SopatrosStreitfälle. Gliederung und Ausarbeitung kontroverser Reden, Königshausen & Neumann (Würzburg, 2010)." In Papers on Quintilian and Ancient Declamation, edited by Antonio Stramaglia, Francesca Romana Nocchi, and Giuseppe Russo, 347–50. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198836056.003.0036.

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M. Weissenberger’ s Sopatri Quaestionum divisio—Sopatros: Streitfälle. Gliederung und Ausarbeitung kontroverser Reden (2010) is the first modern edition of a text important for the history of declamation in antiquity. It employs the material amassed in D. C. Innes and M. Winterbottom, Sopatros the Rhetor (1988) to produce a revised text that enormously improves on that of Walz in Rhetores Graeci 8 (1835), and includes a German translation and full notes. This review commends this achievement, but notes that the book is not much more easy to use than Innes and Winterbottom, the inconvenience of which Weissenberger deplores. The reviewer remarks on Weissenberger’s neglect of Sopatros’ prose rhythm, lists a number of passages where the text is still in doubt, and offers some new emendations. He ends: ‘Readers of Weissenberger’s…monumental book will need to be pretty knowledgeable…but they will be richly rewarded.’
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CLERMONT, J. R., and M. E. DE LA LANDE. "THE MAIN FLOW OF A MEMORY INTEGRAL FLUID IN AN AXISYMMETRIC CONTRACTION AT HIGH WEISSENBERG NUMBERS." In Theoretical and Applied Rheology, 268–70. Elsevier, 1992. http://dx.doi.org/10.1016/b978-0-444-89007-8.50104-0.

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Conference papers on the topic "Weissenberg number"

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Junio da Silva Furlan, Laison, Matheus Tozo de Araujo, Leandro Franco de Souza, Analice Costacurta Brandi, and Marcio Teixeira de Mendonca. "Stability Analysis of Viscoelastic Fluid Flows for the High Weissenberg Number." In 25th International Congress of Mechanical Engineering. ABCM, 2019. http://dx.doi.org/10.26678/abcm.cobem2019.cob2019-2036.

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Carreira, Beatriz Liara, Analice Costacurta Brandi, Laison Junio da Silva Furlan, Matheus Tozo de Araujo, and Leandro Franco de Souza. "Log-Conformation and Square Root-Conformation Transformations in High Weissenberg Number Flows." In 25th International Congress of Mechanical Engineering. ABCM, 2019. http://dx.doi.org/10.26678/abcm.cobem2019.cob2019-1949.

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Ashrafi, N., M. Mohamadali, and M. Najafi. "High Weissenberg Number Stress Boundary Layer for the Upper Convected Maxwell Fluid." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-36544.

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The classic Blassius problem of steady boundary-layer flow of the upper convected Maxwell over a flat plate in a moving fluid is studied. According to scaling parameters the equations represent the viscoelastic stress boundary layer. By means of an exact similarity transformation, the non-linear viscoelastic momentum and constitutive equations transform into a system of highly nonlinear coupled ordinary differential equations. Numerical solution may be achieved by a variable stepping method for the initial-value problem. The stepping numerical method chosen fifth order Runge-Kutta for solving the resulting nonlinear algebraic equations at each step. It is seen that there is a stress boundary layer and there is no velocity boundary layer.
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Majidi, Sahand, and Ashkan Javadzadegan. "Numerical Simulation of Confined Swirling Flows of Oldroyd Fluids." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78340.

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The effect of a fluid’s elasticity has been investigated on the vortex breakdown phenomenon in confined swirling flow. Assuming that the fluid obeys upper-convected Maxwell model as its constitutive equation, the finite volume method together with a collocated mesh was used to calculate the velocity profiles and streamline pattern inside a typical lid-driven swirling flow at different Reynolds and Weissenberg numbers. The flow was to be steady and axisymmetric. Based on the results obtained in this work, it can be concluded that fluid’s elasticity has a strong effect on the secondary flow completely reversing its direction of rotation depending on the Weissenberg number. Even in swirling flows with low ratio of elasticity to inertia, vortex breakdown is postponed to higher Reynolds numbers. Also, the effect of retardation ratio on the flow structure of viscoelastic fluid with the Weissenberg number being constant was surveyed. Based on our results, by decreasing the retardation ratio the flow becomes Newtonian like.
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Jafari, Azadeh, Michel O. Deville, and Nicolas Fiétier. "Spectral Elements Analysis for Viscoelastic Fluids at High Weissenberg Number Using Logarithmic conformation Tensor Model." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990912.

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Zhang, Xin, Xili Duan, Yuri Muzychka, and Zongming Wang. "Predicting Drag Reduction in Turbulent Pipe Flow With Relaxation Time of Polymer Additives." In 2018 12th International Pipeline Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/ipc2018-78701.

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This paper presents an experimental study on drag reduction induced by PEO (Polyethylene oxide) in a fully turbulent pipe flow. The objective of this work is to develop a correlation to predict drag reduction using the relaxation time of the polymer additives under dilute solution conditions, i.e., the polymer concentration is less than the overlap concertation. This paper discusses the meaning of relaxation time of polymers, and why the Weissenberg number, a dimensionless number that is related to the relaxation time and shear rate, is independent on the concentration in the dilute solution. Experimental data of drag reduction in a pipe flow are obtained from measurements using a flow loop. A correlation to predict drag reduction with the Weissenberg number and polymer concentration is established and a good agreement is shown between the predicted values and experimental data. The new correlation using the Weissenberg number and polymer concentration is shown to cost less to develop than one using the Reynolds number, in which larger pipes or higher flow rates are required.
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Ashrafi, Nariman. "Stability of Viscoelastic Channel Flow." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41830.

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The nonlinear stability and bifurcation of the one-dimensional channel (Poiseuille) flow is examined for a Johnson-Segalman fluid. The velocity and stress are represented by orthonormal functions in the transverse direction to the flow. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. The stability picture is dramatically influenced by the viscosity ratio. The range of shear rate or Weissenberg number for which the base flow is unstable increases from zero as the fluid deviates from the Newtonian limit as decreases. Typically, two turning points are observed near the critical Weissenberg numbers. The transient response is heavily influenced by the level of inertia. It is found that the flow responds oscillatorily. When the Reynolds number is small, and monotonically at large Reynolds number when elastic effects are dominated by inertia.
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Kawase, Tomohiro, Takahiro Tsukahara, and Yasuo Kawaguchi. "Parametric Study of Viscoelastic Turbulence Within an Obstructed Channel Flow." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-25019.

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The behavior of viscoelastic flow behind a two-dimensional slits was examined using direct numerical simulations (DNS). We performed DNS at five different conditions with changing the Reynolds number and the Weissenberg number, to investigate the parametric dependence of several characters of the viscoelastic flows (e.g., Toms effect and Barus effect) accompanied by the separation and reattachment. In the present conditions, the drag reduction rate was achieved from 15.1% to 19.7%. It was found that the wall-normal viscoelastic stress mainly enhanced the Barus effect in the present geometry and the streamwise viscoelastic force caused an increase of the drag. We found that, at a Weissenberg number higher than a certain level, the drag reduction rate should be decreased despite the reduced turbulent frictional drag. Moreover, we observed that, in the Newtonian flow, the spanwise vortices were dominant in a downstream region of the slits, while the streamwise vortices were dominant there in the case of the viscoelastic flow.
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Zhang, Meng, Wu Zhang, Zhengwei Wu, Weihua Cai, Zhiying Zheng, Yicheng Chen, and Chaofeng Lan. "Instabilities of Pre-Stretched Viscoelastic Flow in Microfluidic Cross-Slot Devices." In ASME 2019 6th International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/mnhmt2019-4120.

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Abstract In this paper we experimentally studied the instabilities of pre-stretched viscoelastic fluid in cross-slot devices. We first investigate the instability of the flow in a standard cross-slot at different Weissenberg numbers without pre-stretch. It is found the viscoelastic flow is transformed from the steady symmetric state to the instabilities states including the steady asymmetric state and the non-periodically oscillated asymmetric state. This is due to the extension of the polymer in the viscoelastic fluid at the stagnation point stretched by the extensional flow in the cross-slot. We then modified the cross-slot channel in which the viscoelastic fluid is pre-stretched before entering the crossroad region. Due to the pre-stretch, elastic energy is pre-stored in the polymer, and the energy required to fully extend the polymer is also different with those extending from equilibrium state. As a result, the flow remains in the steady asymmetric state in all tested Weissenberg number condition.
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Siginer, Dennis A. "Heat Transfer Asymptote in Laminar Tube Flows of Non-Linear Viscoelastic Fluids." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-23224.

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The fully developed thermal field in constant pressure gradient driven laminar flow of a class of nonlinear viscoelastic fluids with instantaneous elasticity in straight pipes of arbitrary contour ∂D with constant wall flux is investigated. The nonlinear fluids considered are constitutively represented by a class of single mode, non-affine constitutive equations. The driving forces can be large. Asymptotic series in terms of the Weissenberg number Wi are employed to expand the field variables. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D0. The analytical method presented is capable of predicting the velocity and temperature fields in tubes with arbitrary cross-section. Heat transfer enhancement due to shear-thinning is identified together with the enhancement due to the inherent elasticity of the fluid. The latter is to a very large extent the result of secondary flows in the cross-section but there is a component due to first normal stress differences as well. Increasingly large enhancements are computed with increasing elasticity of the fluid as compared to its Newtonian counterpart. Order of magnitude larger enhancements are possible even with slightly viscoelastic fluids. The coupling between inertial and viscoelastic nonlinearities is crucial to enhancement. Isotherms for the temperature field are discussed for non-circular contours such as the ellipse and the equilateral triangle together with the behavior of the average Nusselt number Nu, a function of the Reynolds Re, the Prandtl Pr and the Weissenberg Wi numbers. Analytical evidence for the existence of a heat transfer asymptote in laminar flow of viscoelastic fluids in non-circular contours is given for the first time. Nu becomes asymptotically independent from elasticity with increasing Wi, Nu = f (Pe,Wi) → Nu = f(Pe). This asymptote is the counterpart in laminar flows in non-circular tubes of the heat transfer asymptote in turbulent flows of viscoelastic fluids in round pipes. A different asymptote corresponds to different cross-sectional shapes in straight tubes. The change of type of the vorticity equation governs the trends in the behavior of Nu with increasing Wi and Pe. The implications on the heat transfer enhancement is discussed in particular for slight deviations from Newtonian behavior where a rapid rise in enhancement seems to occur as opposed to the behavior for larger values of the Weissenberg number where the rate of increase is much slower. The asymptotic independence of Nu from elasticity with increasing Wi is related to the extent of the supercritical region controlled by the interaction of the viscoelastic Mach number M and the Elasticity number E, which mitigates and ultimately cancels the effect of the increasingly strong secondary flows with increasing Wi to level off the enhancement. The physics of the interaction of the effects of the Elasticity E, Viscoelastic Mach M, Reynolds Re and Weissenberg Wi numbers on generating the heat transfer enhancement is discussed.
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