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Shakeri P, Jung M, Seemann R. Scaling purely elastic instability of strongly shear thinning polymer solutions. Phys Rev E 2022; 105:L052501. [PMID: 35706259 DOI: 10.1103/physreve.105.l052501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Accepted: 05/10/2022] [Indexed: 06/15/2023]
Abstract
Flow of viscoelastic polymer solutions in curved channels exhibits instability caused by the elastic nature of polymers even at low Reynolds numbers. However, scaling of the onset of this purely elastic instability in semidilute polymer solutions has not been previously reported. Here we experimentally investigate the flow of highly elastic polymer solutions above their overlap concentrations using pressure measurements and particle image velocimetry. We demonstrate that the onset of instability can be scaled by including shear dependent rheological properties of the polymer solutions in the nonlinear stability analysis. As a result, a universal criterion as function of normalized polymer concentration is provided for scaling the onset of purely elastic instability in the semidilute regime regardless of the type and molecular weight of the polymer.
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Affiliation(s)
- Pegah Shakeri
- Experimental Physics, Saarland University, 66123 Saarbrücken, Germany and Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Michael Jung
- Experimental Physics, Saarland University, 66123 Saarbrücken, Germany and Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Ralf Seemann
- Experimental Physics, Saarland University, 66123 Saarbrücken, Germany and Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
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Yang H, Yao G, Wen D. Efficient mixing enhancement by orthogonal injection of shear-thinning fluids in a micro serpentine channel at low Reynolds numbers. Chem Eng Sci 2021. [DOI: 10.1016/j.ces.2020.116368] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Mandal R, Chakrabarti B, Chakraborty D, Dasgupta C. Complex dynamics of a sheared nematic fluid. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:134002. [PMID: 31778974 DOI: 10.1088/1361-648x/ab5caa] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Nonlinearities in constitutive equations of extended objects in shear flow lead to novel phenomena, e.g. 'rheochaos' in solutions of wormlike micelles and 'elastic turbulence' in polymer solutions. Since both phenomena involve anisotropic objects, their contributions to the deviatoric stress are likely to be similar. However, these two fields have evolved rather independently and an attempt at connecting these fields is still lacking. We show that a minimal model in which the anisotropic nature of the constituting objects is taken into account by a nematic alignment tensor field reproduces several statistical features found in rheochaos and elastic turbulence. We numerically analyse the full non-linear hydrodynamic equations of a sheared nematic fluid under shear stress and strain rate controlled situations, incorporating spatial heterogeneity only in the gradient direction. For a certain range of imposed stress and strain rates, this extended dynamical system shows signatures of spatiotemporal chaos and transient shear banding. In the chaotic regime the power spectra of the order parameter stress, velocity fluctuations and the total injected power show power law behavior and the total injected power shows a non-gaussian, skewed probability distribution. These dynamical features bear resemblance to elastic turbulence phenomena observed in polymer solutions. The scaling behavior is independent of the choice of shear rate/stress controlled method.
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Affiliation(s)
- Rituparno Mandal
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany. Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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Carenza LN, Gonnella G, Lamura A, Negro G, Tiribocchi A. Lattice Boltzmann methods and active fluids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:81. [PMID: 31250142 DOI: 10.1140/epje/i2019-11843-6] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Accepted: 05/24/2019] [Indexed: 05/24/2023]
Abstract
We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.
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Affiliation(s)
- Livio Nicola Carenza
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - Giuseppe Gonnella
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy.
| | - Antonio Lamura
- Istituto Applicazioni Calcolo, CNR, Via Amendola 122/D, 70126, Bari, Italy
| | - Giuseppe Negro
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - Adriano Tiribocchi
- Center for Life Nano Science@La Sapienza, Istituto Italiano di Tecnologia, 00161, Roma, Italy
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Malm AV, Waigh TA. Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry. Sci Rep 2017; 7:1186. [PMID: 28442789 PMCID: PMC5430809 DOI: 10.1038/s41598-017-01303-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2015] [Accepted: 03/29/2017] [Indexed: 12/11/2022] Open
Abstract
The flow instabilities of solutions of high molecular weight DNA in the entangled semi-dilute concentration regime were investigated using optical coherence tomography velocimetry, a technique that provides high spatial (probe volumes of 3.4 pL) and temporal resolution (sub μs) information on the flow behaviour of complex fluids in a rheometer. The velocity profiles of the opaque DNA solutions (high and low salt) were measured as a function of the distance across the gap of a parallel plate rheometer, and their evolution over time was measured. At lower DNA concentrations and low shear rates, the velocity fluctuations were well described by Gaussian functions and the velocity gradient was uniform across the rheometer gap, which is expected for Newtonian flows. As the DNA concentration and shear rate were increased there was a stable wall slip regime followed by an evolving wall slip regime, which is finally followed by the onset of elastic turbulence. Strain localization (shear banding) is observed on the boundaries of the flows at intermediate shear rates, but decreases in the high shear elastic turbulence regime, where bulk strain localization occurs. A dynamic phase diagram for non-linear flow was created to describe the different behaviours.
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Affiliation(s)
- A V Malm
- Biological Physics, School of Physics and Astronomy, University of Manchester, Oxford Rd., Manchester, M13 9PL, UK.,Photon Science Institute, University of Manchester, Oxford Rd., Manchester, M13 9PL, UK
| | - T A Waigh
- Biological Physics, School of Physics and Astronomy, University of Manchester, Oxford Rd., Manchester, M13 9PL, UK. .,Photon Science Institute, University of Manchester, Oxford Rd., Manchester, M13 9PL, UK.
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Sturman R, Springham J. Rate of chaotic mixing and boundary behavior. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012906. [PMID: 23410403 DOI: 10.1103/physreve.87.012906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2011] [Revised: 06/27/2012] [Indexed: 06/01/2023]
Abstract
We discuss rigorous results on the rate of mixing for an idealized model of a class of fluid mixing device. These show that the decay of correlations of a scalar field is governed by the presence of boundaries in the domain, and in particular by the behavior of the modeled fluid at such boundaries.
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Affiliation(s)
- Rob Sturman
- Department of Applied Mathematics, University of Leeds, Leeds, United Kingdom.
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Fardin MA, Lerouge S. Instabilities in wormlike micelle systems. From shear-banding to elastic turbulence. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2012; 35:91. [PMID: 23001785 DOI: 10.1140/epje/i2012-12091-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2012] [Revised: 08/01/2012] [Accepted: 08/02/2012] [Indexed: 06/01/2023]
Abstract
Shear-banding is ubiquitous in complex fluids. It is related to the organization of the flow into macroscopic bands bearing different viscosities and local shear rates and stacked along the velocity gradient direction. This flow-induced transition towards a heterogeneous flow state has been reported in a variety of systems, including wormlike micellar solutions, telechelic polymers, emulsions, clay suspensions, colloidal gels, star polymers, granular materials, or foams. In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In wormlike micelle solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Different candidates have been identified, the main ones being wall slip, interfacial instability between bands or bulk instability of one of the bands. In this review, we present experimental evidence for a purely elastic instability of the high shear rate band as the main origin for fluctuating shear-banding flows.
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Affiliation(s)
- M-A Fardin
- Laboratoire Matière et Systèmes Complexes, CNRS UMR 7057-Université Paris Diderot, Paris, France
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Jun Y, Steinberg V. Elastic turbulence in a curvilinear channel flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:056325. [PMID: 22181516 DOI: 10.1103/physreve.84.056325] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2011] [Indexed: 05/31/2023]
Abstract
We report detailed quantitative studies of elastic turbulence in a curvilinear channel flow in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent. Detailed studies of the average and rms velocity and velocity gradients profiles reveal the emergence of a boundary layer associated with the nonuniform distribution of the elastic stresses across the channel. The characteristic boundary width is independent of the Weissenberg number Wi and proportional to the channel width, which is consistent with the findings our early investigations of the boundary layer in elastic turbulence in different flow geometries. The nonuniform distribution of the elastic stresses across the channel and appearance of the characteristic spatial scales of the order of the boundary layer width of both velocity and velocity gradient in the correlation functions of the velocity and velocity gradient fields in a bulk flow may suggest that excessive elastic stresses, concentrated in the boundary layer, are ejected into the bulk flow similar to jets observed in passive scalar mixing in elastic turbulence observed recently. Finally, the experimental results show that one of the main predictions of the theory of elastic turbulence, namely, the saturation of the normalized rms velocity gradient in the bulk flow of elastic turbulence contradicts the experimental observations both qualitatively and quantitatively in spite of the fact that the theory explains well the observed sharp power-law decay of the velocity power spectrum. The experimental findings call for further development of theory of elastic turbulence in a bounded container, similar to what was done for a passive scalar problem.
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Affiliation(s)
- Yonggun Jun
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel
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Majumdar S, Sood AK. Universality and scaling behavior of injected power in elastic turbulence in wormlike micellar gel. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:015302. [PMID: 21867248 DOI: 10.1103/physreve.84.015302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2011] [Revised: 06/17/2011] [Indexed: 05/31/2023]
Abstract
We study the statistical properties of spatially averaged global injected power fluctuations for Taylor-Couette flow of a wormlike micellar gel formed by surfactant cetyltrimethylammonium tosylate. At sufficiently high Weissenberg numbers the shear rate, and hence the injected power p(t), at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian PDFs can be well described by a universal, large deviation functional form given by the generalized Gumbel distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence.
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Affiliation(s)
- Sayantan Majumdar
- Department of Physics, Indian Institute of Science, Bangalore, India
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Watanabe T, Gotoh T. Coil-stretch transition in an ensemble of polymers in isotropic turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:066301. [PMID: 20866516 DOI: 10.1103/physreve.81.066301] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2010] [Indexed: 05/29/2023]
Abstract
We study the statistical properties of ensembles of polymers in isotropic turbulence numerically in the one-way coupling regime. A linear polymer chain passively convected by turbulence is modeled by a line of beads, each of which is connected by a finitely extensible nonlinear elastic force and subject to Brownian motion. We find that when the Weissenberg number Wi(η)<1, the polymer chain has a coiled configuration, while for Wi(η)>10, it remains stretched for a much longer time than the typical time scale of the fluctuating turbulent velocity gradient. Various statistical quantities characterizing the ensemble of polymers, such as the mean, variance, autocorrelation time, and probability density function of the end-to-end vector distance, indicate that the coil-stretch transition occurs at Wi(η)=3-4. We also find that this trend is insensitive to the number of beads N(b) ( N(b)=20 or N(b)=2), provided that the parameters in the model with a small number of beads are properly generated from the one with a large number of beads (i.e., using the formula of Jin and Collins). Finally, the Wi(η) effects on the alignment of the end-to-end vector versus the principal axis of the rate of strain tensor and on the polymer elongation are examined from the viewpoint of local flow topology.
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Affiliation(s)
- Takeshi Watanabe
- Graduate School of Engineering, Department of Scientific and Engineering Simulation, Nagoya Institute of Technology, Gokiso, Showa-ku, Nagoya 466-8555, Japan.
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Goddard C, Hess O, Hess S. Low Reynolds number turbulence in nonlinear Maxwell-model fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:036310. [PMID: 20365857 DOI: 10.1103/physreve.81.036310] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2008] [Revised: 11/11/2009] [Indexed: 05/29/2023]
Abstract
A generalized nonlinear Maxwell model which had previously been analyzed for plane Couette geometry is here applied to a lid-driven cavity flow. The full three-dimensional hydrodynamical problem is treated numerically. Depending on the relevant model parameters, both smooth laminar and low Reynolds number turbulent flows are found, strikingly similar to the experimentally observed elastic turbulence phenomena in polymer solutions. Representative results of the calculated flow patterns, as well as measures for the turbulent nature of the flow are presented graphically.
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Affiliation(s)
- Chris Goddard
- Department of Physics, Faculty of Engineering and Physical Sciences, University of Surrey, Advanced Technology Institute, Guildford GU2 7XH, United Kingdom.
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Jun Y, Steinberg V. Power and pressure fluctuations in elastic turbulence over a wide range of polymer concentrations. PHYSICAL REVIEW LETTERS 2009; 102:124503. [PMID: 19392285 DOI: 10.1103/physrevlett.102.124503] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2008] [Indexed: 05/27/2023]
Abstract
Injected power P and pressure p fluctuations in a swirling flow of polymer solutions in a wide range of polymer concentrations c in elastic turbulence regime show non-Gaussian statistics that strongly resemble statistical behavior of P and p in hydrodynamic turbulence. Together with this fact, weak dependence of the statistics of rescaled variables on c may suggest that there are universal mechanisms determining the intermittent statistics of P and p. We also show that the study of the statistics of p provides a way to study statistics of the elastic stresses in elastic turbulence otherwise currently unattainable.
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Affiliation(s)
- Yonggun Jun
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100 Israel
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