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Journal articles on the topic 'Viscoelastic fluids'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 June 2024

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1

Guillopé, Colette, and Jean-Claude Saut. "Existence and stability of steady flows of weakly viscoelastic fluids." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 119, no. 1-2 (1991): 137–58. http://dx.doi.org/10.1017/s0308210500028377.

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SynopsisWe consider steady flows of viscoelastic fluids for which the extrastress tensor is given by a differential constitutive equation and is such that the retardation time is large (weakly viscoelastic fluids).We show the existence of a unique viscoelastic steady flow close to a given Newtonian flow and investigate its linear stability.As an example, we consider the Bénard problem for viscoelastic fluids and we prove that there exists a nontrivial linearly stable flow of a weakly viscoelastic fluid in a container heated from below.

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2

Song, Jinhyeuk, Jaekyeong Jang, Taehoon Kim, and Younghak Cho. "Particle Separation in a Microchannel with a T-Shaped Cross-Section Using Co-Flow of Newtonian and Viscoelastic Fluids." Micromachines 14, no. 10 (2023): 1863. http://dx.doi.org/10.3390/mi14101863.

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In this study, we investigated the particle separation phenomenon in a microchannel with a T-shaped cross-section, a unique design detailed in our previous study. Utilizing a co-flow system within this T-shaped microchannel, we examined two types of flow configuration: one where a Newtonian fluid served as the inner fluid and a viscoelastic fluid as the outer fluid (Newtonian/viscoelastic), and another where both the inner and outer fluids were Newtonian fluids (Newtonian/Newtonian). We introduced a mixture of three differently sized particles into the microchannel through the outer fluid and

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3

Li, Chuanbin, Boyang Qin, Arvind Gopinath, Paulo E. Arratia, Becca Thomases, and Robert D. Guy. "Flagellar swimming in viscoelastic fluids: role of fluid elastic stress revealed by simulations based on experimental data." Journal of The Royal Society Interface 14, no. 135 (2017): 20170289. http://dx.doi.org/10.1098/rsif.2017.0289.

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Many important biological functions depend on microorganisms' ability to move in viscoelastic fluids such as mucus and wet soil. The effects of fluid elasticity on motility remain poorly understood, partly because the swimmer strokes depend on the properties of the fluid medium, which obfuscates the mechanisms responsible for observed behavioural changes. In this study, we use experimental data on the gaits of Chlamydomonas reinhardtii swimming in Newtonian and viscoelastic fluids as inputs to numerical simulations that decouple the swimmer gait and fluid type in order to isolate the effect of

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4

Peiffer, D. G. "Polymerizable viscoelastic fluids." Journal of Polymer Science Part A: Polymer Chemistry 28, no. 3 (1990): 619–27. http://dx.doi.org/10.1002/pola.1990.080280313.

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5

Niedziela, D., A. Latz, and O. Iliev. "Simulations of Viscoelastic Polymer Solution Flows." NAFEMS International Journal of CFD Case Studies 6 (March 2007): 15–25. http://dx.doi.org/10.59972/d8hd7bkp.

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Many natural and synthetic fluids are viscoelastic materials i.e. the stress at a certain fluid particle depends upon the history of the deformation experienced by that particle. Polymer melts and most polymer solutions are examples of such liquids. Simulation of the flow of these fluids is therefore of great interest for the plastic industry. Viscoelastic fluids are examples of non - Newtonian fluids. While the Newtonian fluids are characterised by a constant viscosity (i.e., constant ratio between shear stress and the rate of strain), the non-Newtonian fluids require more complicated constit

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6

Bizhani, M., and E. Kuru. "Particle Removal From Sandbed Deposits in Horizontal Annuli Using Viscoelastic Fluids." SPE Journal 23, no. 02 (2017): 256–73. http://dx.doi.org/10.2118/189443-pa.

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Summary This paper presents results of an experimental study on how fluid viscoelastic properties would influence the particle removal from the sandbed deposited in horizontal annuli. Water and two different viscoelastic fluids were used for bed-erosion experiments. The particle-image-velocimetry (PIV) technique was used to measure the local fluid velocity at the fluid/sandbed interface, allowing for accurate estimation of the fluid-drag forces and the turbulence stresses. It was found that polymer fluids needed to exert higher level drag forces (than those of water) on the sandbed to start mo

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7

Makarynska, Dina, Boris Gurevich, Jyoti Behura, and Mike Batzle. "Fluid substitution in rocks saturated with viscoelastic fluids." GEOPHYSICS 75, no. 2 (2010): E115—E122. http://dx.doi.org/10.1190/1.3360313.

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Heavy oils have high densities and extremely high viscosities, and they exhibit viscoelastic behavior. Traditional rock physics based on Gassmann theory does not apply to materials saturated with viscoelastic fluids. We use an effective-medium approach known as coherent potential approximation (CPA) as an alternative fluid-substitution scheme for rocks saturated with viscoelastic fluids. Such rocks are modeled as solids with elliptical fluid inclusions when fluid concentration is small and as suspensions of solid particles in the fluid when the solid concentration is small. This approach is co

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8

Xu, Zhengming, Xianzhi Song, and Zhaopeng Zhu. "Development of Elastic Drag Coefficient Model and Explicit Terminal Settling Velocity Equation for Particles in Viscoelastic Fluids." SPE Journal 25, no. 06 (2020): 2962–83. http://dx.doi.org/10.2118/201194-pa.

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Summary Viscoelastic fluids are frequently used as drilling or fracturing fluids to enhance cuttings or proppant transport efficiency. The solid transport performance of these fluids largely depends on the settling behaviors of suspended particles. Different from viscoinelastic fluids, the elastic and viscous characteristics of viscoelastic fluids both affect particle settling behaviors. In this study, to separately quantify the contribution degrees of the shear viscosity and fluid elasticity on the terminal settling velocity, we decompose the total drag force into a viscous drag force and an

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9

Yasappan, Justine, Ángela Jiménez-Casas, and Mario Castro. "Asymptotic Behavior of a Viscoelastic Fluid in a Closed Loop Thermosyphon: Physical Derivation, Asymptotic Analysis, and Numerical Experiments." Abstract and Applied Analysis 2013 (2013): 1–20. http://dx.doi.org/10.1155/2013/748683.

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Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian) fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial mani

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10

Cho, Mira, Sun Ok Hong, Seung Hak Lee, Kyu Hyun, and Ju Min Kim. "Effects of Ionic Strength on Lateral Particle Migration in Shear-Thinning Xanthan Gum Solutions." Micromachines 10, no. 8 (2019): 535. http://dx.doi.org/10.3390/mi10080535.

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Viscoelastic fluids, including particulate systems, are found in various biological and industrial systems including blood flow, food, cosmetics, and electronic materials. Particles suspended in viscoelastic fluids such as polymer solutions migrate laterally, forming spatially segregated streams in pressure-driven flow. Viscoelastic particle migration was recently applied to microfluidic technologies including particle counting and sorting and the micromechanical measurement of living cells. Understanding the effects on equilibrium particle positions of rheological properties of suspending vis

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11

Chen, Dilin, Jie Li, Haiwen Chen, Lai Zhang, Hongna Zhang, and Yu Ma. "Electroosmotic Flow Behavior of Viscoelastic LPTT Fluid in a Microchannel." Micromachines 10, no. 12 (2019): 881. http://dx.doi.org/10.3390/mi10120881.

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In many research works, the fluid medium in electroosmosis is considered to be a Newtonian fluid, while the polymer solutions and biological fluids used in biomedical fields mostly belong to the non-Newtonian category. Based on the finite volume method (FVM), the electroosmotic flow (EOF) of viscoelastic fluids in near-neutral (pH = 7.5) solution considering four ions (K+, Cl−, H+, OH−) is numerically studied, as well as the viscoelastic fluids’ flow characteristics in a microchannel described by the Linear Phan-Thien–Tanner (LPTT) constitutive model under different conditions, including the e

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12

Poole, R. J. "Three-dimensional viscoelastic instabilities in microchannels." Journal of Fluid Mechanics 870 (May 7, 2019): 1–4. http://dx.doi.org/10.1017/jfm.2019.260.

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Whereas the flow of simple single-phase Newtonian fluids tends to become more complex as the characteristic length scale in the problem (and hence the Reynolds number) increases, for complex elastic fluids such as dilute polymer solutions the opposite holds true. Thus small-scale, so-called ‘microfluidic’ flows of complex fluids can exhibit rich dynamics in situations where the ‘equivalent’ flow of Newtonian fluids remains linear and predictable. In the recent study of Qin et al. (J. Fluid Mech., vol. 864, 2019, R2) of the flow of a dilute polymeric fluid past a $50~\unicode[STIX]{x03BC}\text{

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13

Wang, Fang, and Yu Wang. "A Finite Difference Method for Solving Unsteady Fractional Oldroyd-B Viscoelastic Flow Based on Caputo Derivative." Advances in Mathematical Physics 2023 (April 29, 2023): 1–22. http://dx.doi.org/10.1155/2023/8963904.

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In this paper, the effect of a fractional constitutive model on the rheological properties of fluids and its application in numerical simulation are investigated, which is important to characterize the rheological properties of fluids and physical characteristics of materials more accurately. Based on this consideration, numerical simulation and analytical study of unsteady fractional Oldroyd-B viscoelastic flow are carried out. In order to improve the degree of accuracy, the mixed partial derivative including the fractional derivative in the differential equation is converted effectively by i

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14

Joseph, D. D., and T. Y. Liao. "Potential flows of viscous and viscoelastic fluids." Journal of Fluid Mechanics 265 (April 25, 1994): 1–23. http://dx.doi.org/10.1017/s0022112094000741.

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Potential flows of incompressible fluids admit a pressure (Bernoulli) equation when the divergence of the stress is a gradient as in inviscid fluids, viscous fluids, linear viscoelastic fluids and second-order fluids. We show that in potential flow without boundary layers the equation balancing drag and acceleration is the same for all these fluids, independent of the viscosity or any viscoelastic parameter, and that the drag is zero when the flow is steady. But, if the potential flow is viewed as an approximation to the actual flow field, the unsteady drag on bubbles in a viscous (and possibl

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15

Jamil, Muhammad, and Najeeb Alam Khan. "Slip Effects on Fractional Viscoelastic Fluids." International Journal of Differential Equations 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/193813.

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Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions , by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter is . Furthermore, th

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16

Li, Gaojin, Eric Lauga, and Arezoo M. Ardekani. "Microswimming in viscoelastic fluids." Journal of Non-Newtonian Fluid Mechanics 297 (November 2021): 104655. http://dx.doi.org/10.1016/j.jnnfm.2021.104655.

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17

Badmaev, B. B., B. B. Damdinov, and T. S. Dembelova. "Viscoelastic relaxation in fluids." Bulletin of the Russian Academy of Sciences: Physics 79, no. 10 (2015): 1301–5. http://dx.doi.org/10.3103/s1062873815100044.

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18

Zhou, Hong, Wei Kang, Arthur Krener, and Hongyun Wang. "Observability of viscoelastic fluids." Journal of Non-Newtonian Fluid Mechanics 165, no. 7-8 (2010): 425–34. http://dx.doi.org/10.1016/j.jnnfm.2010.01.025.

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19

Shinohara, Akira, Chengjun Pan, Zhenfeng Guo, et al. "Viscoelastic Conjugated Polymer Fluids." Angewandte Chemie International Edition 58, no. 28 (2019): 9581–85. http://dx.doi.org/10.1002/anie.201903148.

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20

Loginova, Marianna E., and Farit A. Agzamov. "Viscoelastic systems for well construction." Kazakhstan journal for oil & gas industry 4, no. 1 (2022): 58–68. http://dx.doi.org/10.54859/kjogi104413.

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One of the most important factors ensuring the required quality of well cementing is the use of effective flushing fluids (spacers). Among these fluids are viscoelastic systems (VES), which provide the best displacement of the drilling fluid during the cementing process. The article discusses the mechanism of polymerization of viscoelastic systems when using polyacrylamide cross-linked with polyvalent metal cations and the prospects for using these systems for oil and gas wells cementing. Models of the viscoelastic systems flow and their differences due to the presence of normal stresses

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21

Mostafa, D. M. "Linear Stability of Magneto Viscoelastic Walter’s B ′ Type with Heat and Mass Transfer." Advances in High Energy Physics 2022 (May 23, 2022): 1–10. http://dx.doi.org/10.1155/2022/6577512.

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In this paper, the couple influence of axial magnetic field and the heat and mass transfer on two rotating cylinders of Walter’s B ′ viscoelastic fluids by using the potential flow theory of viscoelastic fluid has been investigated. The normal mode method is used to compute the growth rate of disturbance. The influence of gravity is ignored at the interface, while the effect of surface tension is present in the analysis. The effect of the parameters on the stability is studied. It is found that the rotation of the inner cylinder induces stability. Furthermore, the viscoelastic ratio of fluids

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22

Yamamoto, Takehiro, Takanori Suga, Kiyoji Nakamura, and Noriyasu Mori. "The Gas Penetration Through Viscoelastic Fluids With Shear-Thinning Viscosity in a Tube." Journal of Fluids Engineering 126, no. 2 (2004): 148–52. http://dx.doi.org/10.1115/1.1669402.

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The penetration of a long gas bubble through a viscoelastic fluid in a tube was studied. Experiments were carried out for two Newtonian and five polymeric solutions to investigate the relation between the coating film thickness and rheological properties of the test fluids. The polymeric solutions are viscoelastic fluids having shear-thinning viscosity. A bubble of air was injected into a tube filled with a test fluid to form hydrodynamic coating on a tube wall. The film thickness was evaluated by hydrodynamic fractional coverage m. The fractional coverage was characterized using the capillary

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23

Huang, Jingting, Liqiong Chen, Shuxuan Li, Jinghang Guo, and Yuanyuan Li. "Numerical Study for the Performance of Viscoelastic Fluids on Displacing Oil Based on the Fractional-Order Maxwell Model." Polymers 14, no. 24 (2022): 5381. http://dx.doi.org/10.3390/polym14245381.

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In the study of polymer flooding, researchers usually ignore the genetic stress properties of viscoelastic fluids. In this paper, we investigate the process of viscoelastic fluid flooding the remaining oil in the dead end. This work uses the fractional-order Maxwell in the traditional momentum equation. Furthermore, a semi-analytic solution of the flow control equation for fractional-order viscoelastic fluids is derived, and the oil-repelling process of viscoelastic fluids is simulated by a secondary development of OpenFOAM. The results show that velocity fractional-order derivative α signific

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24

Hsu, C. H., S. Y. Hu, K. Y. Kung, C. C. Kuo, and C. C. Chang. "A Study on the Flow Patterns of a Second Grade Viscoe-Lastic Fluid Past a Cavity in a Horizontal Channel." Journal of Mechanics 29, no. 2 (2012): 207–15. http://dx.doi.org/10.1017/jmech.2012.143.

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AbstractThis paper studies the behavior of second grade viscoelastic fluid past a cavity in a horizontal channel. The effects of Reynolds number, fluid elasticity and the aspect ratio of the cavity on the flow field are simulated numerically. The equations are converted into the vorticity and stream function equations. The solution is obtained by the finite difference method.The behavior of viscoelastic fluids is quite different from the Newtonian fluid, due to the effects of fluid elasticity. Only one flow pattern appears when the Newtonian fluid past the cavity. However, three kinds of flow

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25

Jegatheeswaran, Sinthuran, Farhad Ein-Mozaffari, and Jiangning Wu. "Laminar mixing of non-Newtonian fluids in static mixers: process intensification perspective." Reviews in Chemical Engineering 36, no. 3 (2020): 423–36. http://dx.doi.org/10.1515/revce-2017-0104.

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AbstractStatic mixers are widely used in various industrial applications to intensify the laminar mixing of non-Newtonian fluids. Non-Newtonian fluids can be categorized into (1) time-independent, (2) time-dependent, and (3) viscoelastic fluids. Computational fluid dynamics studies on the laminar mixing of viscoelastic fluids are very limited due to the complexity in incorporating the multiple relaxation times and the associated stress tensor into the constitutive equations. This review paper provides recommendations for future research studies while summarizing the key research contributions

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26

Alves, M. A., P. J. Oliveira, and F. T. Pinho. "Numerical Methods for Viscoelastic Fluid Flows." Annual Review of Fluid Mechanics 53, no. 1 (2021): 509–41. http://dx.doi.org/10.1146/annurev-fluid-010719-060107.

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Complex fluids exist in nature and are continually engineered for specific applications involving the addition of macromolecules to a solvent, among other means. This imparts viscoelasticity to the fluid, a property responsible for various flow instabilities and major modifications to the fluid dynamics. Recent developments in the numerical methods for the simulation of viscoelastic fluid flows, described by continuum-level differential constitutive equations, are surveyed, with a particular emphasis on the finite-volume method. This method is briefly described, and the main benchmark flows cu

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27

Procopio, Giuseppe, and Massimiliano Giona. "Modal Representation of Inertial Effects in Fluid–Particle Interactions and the Regularity of the Memory Kernels." Fluids 8, no. 3 (2023): 84. http://dx.doi.org/10.3390/fluids8030084.

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This article develops a modal expansion (in terms of functions exponentially decaying with time) of the force acting on a micrometric particle and stemming from fluid inertial effects (usually referred to as the Basset force) deriving from the application of the time-dependent Stokes equation to model fluid–particle interactions. One of the main results is that viscoelastic effects induce the regularization of the inertial memory kernels at t=0, eliminating the 1/t-singularity characterizing Newtonian fluids. The physical origin of this regularization stems from the finite propagation velocity

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28

Takamatsu, Kenji, and Takashi Kanai. "A Fast and Practical Method for Animating Particle-Based Viscoelastic Fluids." International Journal of Virtual Reality 10, no. 1 (2011): 29–35. http://dx.doi.org/10.20870/ijvr.2011.10.1.2798.

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This paper proposes a practical technique for fast animation of materials such as viscoelastic fluids. A fast animation of such materials is desperately desirable especially for real-time applications such as games. We compute the behavior of viscoelastic fluids approximately instead of the exact simulation by combining two well-established approaches, Smoothed- Particle Hydrodynamics and Shape Matching. This enables fast and stable computations. A combination is done by a simple linear interpolation of velocities. A variety of materials between a fluid and an elastic solid can be represented

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29

Hashimoto, H. "Viscoelastic Squeeze Film Characteristics With Inertia Effects Between Two Parallel Circular Plates Under Sinusoidal Motion." Journal of Tribology 116, no. 1 (1994): 161–66. http://dx.doi.org/10.1115/1.2927034.

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In this paper, viscoelastic squeeze film characteristics subjected to fluid inertia effects are investigated theoretically in the case of parallel circular type squeeze films. In the development of modified lubrication equations, the nonlinear Maxwell model combining the Rabinowitsch model and Maxwell model is used as a constitutive equation for the viscoelastic fluids, and the inertia term in the momentum equation is approximated by the mean value averaged over the film thickness. Applying the modified lubrication equation to parallel circular type squeeze films under sinusoidal motion, the v

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30

Xu, Zhi, Shuai Yu, Rong Fu, Ji Wang, and Yujun Feng. "pH-Responsive Viscoelastic Fluids of a C22-Tailed Surfactant Induced by Trivalent Metal Ions." Molecules 28, no. 12 (2023): 4621. http://dx.doi.org/10.3390/molecules28124621.

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pH-responsive viscoelastic fluids are often achieved by adding hydrotropes into surfactant solutions. However, the use of metal salts to prepare pH-responsive viscoelastic fluids has been less documented. Herein, a pH-responsive viscoelastic fluid was developed by blending an ultra-long-chain tertiary amine, N-erucamidopropyl-N, N-dimethylamine (UC22AMPM), with metal salts (i.e., AlCl3, CrCl3, and FeCl3). The effects of the surfactant/metal salt mixing ratio and the type of metal ions on the viscoelasticity and phase behavior of fluids were systematically examined by appearance observation and

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31

Wu, Dianguo, Yiwen Shi, Kun Lv, et al. "Tunable Viscoelastic Properties of Sodium Polyacrylate Solution via CO2-Responsive Switchable Water." Molecules 26, no. 13 (2021): 3840. http://dx.doi.org/10.3390/molecules26133840.

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Upon stimulus by CO2, CO2-switchable viscoelastic fluids experience a deliberate transition between non-viscous and highly viscous solution states. Despite attracting considerable recent attention, most such fluids have not been applied at a large- scale due to their high costs and/or complex synthesis processes. Here, we report the development of CO2-switchable viscoelastic fluids using commercially available sodium polyacrylate (NaPAA) and N,N-dimethyl ethanol amine (DMEA)-based switchable water. Upon bubbling CO2, into the solutions under study, DMEA molecules are protonated to generate qua

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32

Mavko, Gary. "Relaxation shift in rocks containing viscoelastic pore fluids." GEOPHYSICS 78, no. 3 (2013): M19—M28. http://dx.doi.org/10.1190/geo2012-0272.1.

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The interaction of pore stiffness with pore fluid moduli leads to shifts in viscoelastic relaxation times of the overall rock relative to those of the fluids alone. Crack-based and fluid substitution models indicate that stiff pores cause little shift, whereas thin, soft cracks can shift relaxation times by several orders of magnitude toward lower frequencies (longer relaxation times). Pore stiffness also causes a shift in apparent temperature dependence of rock viscoelasticity toward higher temperatures when cracks are present. As with more conventional fluid substitution problems, quantifyin

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33

El, Mohamed Fahmy. "Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids." Zeitschrift für Naturforschung A 56, no. 6-7 (2001): 416–39. http://dx.doi.org/10.1515/zna-2001-0602.

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Abstract The stability of the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent of the viscosity and viscoelasticity, and to be dependent on t

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Patel, Mahesh Chandra, Mohammed Abdalla Ayoub, Mazlin Bt Idress, and Anirbid Sircar. "Development of a Novel Surfactant-Based Viscoelastic Fluid System as an Alternative Nonpolymeric Fracturing Fluid and Comparative Analysis with Traditional Guar Gum Gel Fluid." Polymers 15, no. 11 (2023): 2444. http://dx.doi.org/10.3390/polym15112444.

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Surfactant-based viscoelastic (SBVE) fluids have recently gained interest from many oil industry researchers due to their polymer-like viscoelastic behaviour and ability to mitigate problems of polymeric fluids by replacing them during various operations. This study investigates an alternative SBVE fluid system for hydraulic fracturing with comparable rheological characteristics to conventional polymeric guar gum fluid. In this study, low and high surfactant concentration SBVE fluid and nanofluid systems were synthesized, optimized, and compared. Cetyltrimethylammonium bromide and counterion i

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35

Hidema, Ruri. "Elastic Instability of Viscoelastic Fluids." Seikei-Kakou 30, no. 8 (2018): 411–14. http://dx.doi.org/10.4325/seikeikakou.30.411.

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36

Lei, Youan, Chuanxi Xiong, Hong Guo, Junlong Yao, Lijie Dong, and Xiaohong Su. "Controlled Viscoelastic Carbon Nanotube Fluids." Journal of the American Chemical Society 130, no. 11 (2008): 3256–57. http://dx.doi.org/10.1021/ja710014q.

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37

TOMITA, Yukio, and Toshio SHINBO. "Unstable flow of viscoelastic fluids." Transactions of the Japan Society of Mechanical Engineers Series B 53, no. 487 (1987): 858–64. http://dx.doi.org/10.1299/kikaib.53.858.

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Perrotti, Louis, Noel J. Walkington, and Daren Wang. "Numerical approximation of viscoelastic fluids." ESAIM: Mathematical Modelling and Numerical Analysis 51, no. 3 (2017): 1119–44. http://dx.doi.org/10.1051/m2an/2016053.

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39

Chakraborty, A. K., and A. B. Metzner. "Sink Flows of Viscoelastic Fluids." Journal of Rheology 30, no. 1 (1986): 29–41. http://dx.doi.org/10.1122/1.549896.

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40

Allen, E., and P. H. T. Uhlherr. "Nonhomogeneous Sedimentation in Viscoelastic Fluids." Journal of Rheology 33, no. 4 (1989): 627–38. http://dx.doi.org/10.1122/1.550030.

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41

Pontrelli, Giuseppe. "Mathematical modelling for viscoelastic fluids." Nonlinear Analysis: Theory, Methods & Applications 30, no. 1 (1997): 349–57. http://dx.doi.org/10.1016/s0362-546x(96)00293-3.

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42

Kordonskii, V. I., S. A. Demchuk, and V. A. Kuz’min. "Viscoelastic properties of magnetorheological fluids." Journal of Engineering Physics and Thermophysics 72, no. 5 (1999): 841–44. http://dx.doi.org/10.1007/bf02699403.

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43

Rajagopal, K. R. "Swirling flows of viscoelastic fluids." Computers & Structures 30, no. 1-2 (1988): 143–49. http://dx.doi.org/10.1016/0045-7949(88)90222-2.

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Li, W. H., G. Chen, and S. H. Yeo. "Viscoelastic properties of MR fluids." Smart Materials and Structures 8, no. 4 (1999): 460–68. http://dx.doi.org/10.1088/0964-1726/8/4/303.

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45

TOMITA, Yukio, and Toshio SHIMBO. "Unstable flow of viscoelastic fluids." JSME international journal 30, no. 266 (1987): 1257–65. http://dx.doi.org/10.1299/jsme1987.30.1257.

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Giorgi, C., and A. Morro. "Extremum principles for viscoelastic fluids." International Journal of Engineering Science 29, no. 7 (1991): 807–17. http://dx.doi.org/10.1016/0020-7225(91)90003-l.

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47

Durning, C. J. "Differential sorption in viscoelastic fluids." Journal of Polymer Science: Polymer Physics Edition 23, no. 9 (1985): 1831–55. http://dx.doi.org/10.1002/pol.1985.180230909.

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48

Lin, Fang-Hua, Chun Liu, and Ping Zhang. "On hydrodynamics of viscoelastic fluids." Communications on Pure and Applied Mathematics 58, no. 11 (2005): 1437–71. http://dx.doi.org/10.1002/cpa.20074.

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Claracq, J�r�me, J�r�me Sarrazin, and Jean-Pierre Montfort. "Viscoelastic properties of magnetorheological fluids." Rheologica Acta 43, no. 1 (2004): 38–49. http://dx.doi.org/10.1007/s00397-003-0318-7.

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ELFRING, GWYNN J., ON SHUN PAK, and ERIC LAUGA. "Two-dimensional flagellar synchronization in viscoelastic fluids." Journal of Fluid Mechanics 646 (March 8, 2010): 505–15. http://dx.doi.org/10.1017/s0022112009994010.

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Abstract:

Experimental studies have demonstrated that spermatozoa synchronize their flagella when swimming in close proximity. In a Newtonian fluid, it was shown theoretically that such synchronization arises passively due to hydrodynamic forces between the two swimmers if their waveforms exhibit a front–back geometrical asymmetry. Motivated by the fact that most biological fluids possess a polymeric microstructure, here we address synchronization in a viscoelastic fluid analytically. Using a two-dimensional infinite sheet model, we show that the presence of polymeric stresses removes the geometrical as

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