Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session A12: Non-Newtonian Flows: Simulation and Stability |
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Chair: Christian Wagner, Saarland University Room: 200 |
Sunday, November 22, 2015 8:00AM - 8:13AM |
A12.00001: The primary instability of viscoelastic flow through a curvilinear square--duct channel is a Hopf bifurcation Christian Wagner Curvilinear channels are of specific interest, because they might open the way for mixing application in microfluidic devices and most of the existing studies on curvilinear channels have investigated the large Weissenber number Wi regime where the flow is rather turbulent. Less is known on the type of the primary instability. Recently it was shown both experimentally and numerically that the Pakdel-McKinley-criterion is indeed fulfilled in curvilinear channels, i.e. that the onset of linear instability scales with the square root of the radius of curvature. Recent numerical work predict that the primary instability of the flow should be an oscillatory one. It is one goal of our current work to supply experimental evidences for this prediction. We characterize the bifurcation scenario of the primary instability of viscoleastic flow in a curvilinear channel. We find that the instability sets in first at the end of the channel and the primary instability of the laminar flow is oscillatory, i.e. a Hopf bifurcation. With increasing flow velocity the characteristic period of the instability starts to change slowly in time in an irregular manner but it is always comparable to the polymer relaxation. At higher Weissenberg numbers the flow becomes finally featureless and viscoelastic turbulence sets in. [Preview Abstract] |
Sunday, November 22, 2015 8:13AM - 8:26AM |
A12.00002: Lopsided coatings of a visco-elastic fluid on a vertical fibre Edward Hinch, Claire McIlroy It has been observed by Boulogne, Pauchard and Giorgiutti-Dauphine that, when a visco-elastic coating drains on a vertical fibre, the coating becomes lopsided. A theory is proposed in which the non-axisymmetry develops through an instability driven by second normal stresses, i.e.\ tension in the vortex lines. At long times the coating dewets one side of the fibre. [Preview Abstract] |
Sunday, November 22, 2015 8:26AM - 8:39AM |
A12.00003: Synchronized Molecular-Dynamics simulation for thermal lubrication of a polymeric liquid between parallel plates Shugo Yasuda, Ryoichi Yamamoto The Synchronized Molecular-Dynamics simulation which was recently proposed by authors [Phys. Rev. X {\bf 4}, 041011 (2014)] is applied to the analysis of polymer lubrication between parallel plates. In the SMD method, the MD simulations are assigned to small fluid elements to calculate the local stresses and temperatures and are synchronized at certain time intervals to satisfy the macroscopic heat- and momentum-transport equations.The rheological properties and conformation of the polymer chains coupled with local viscous heating are investigated with a non-dimensional parameter, the Nahme-Griffith number, which is defined as the ratio of the viscous heating to the thermal conduction at the characteristic temperature required to sufficiently change the viscosity. The present simulation demonstrates that strong shear thinning and a transitional behavior of the conformation of the polymer chains are exhibited with a rapid temperature rise when the Nahme-Griffith number exceeds unity.The results also clarify that the reentrant transition of the linear stress-optical relation occurs for large shear stresses due to the coupling of the conformation of polymer chains with heat generation under shear flows. [Preview Abstract] |
Sunday, November 22, 2015 8:39AM - 8:52AM |
A12.00004: Origin and nature of the high Weissenberg number singularity and its removal via a new Boltzmann-type molecular non-Hookean model Rho Shin Myong The Maxwell-Oldroyd model in viscoelastic fluids is known to break down at frustratingly low values of the Weissenberg number. In this work, the origin of the mathematical singularity was shown to be the unbalanced treatment between two open kinematic and interacting terms in the Maxwell-Oldroyd model. Under severe extension, the stress-strain coupling term of quadratic nature will grow far faster than the strain rate term, resulting in a blow-up singularity from an imbalance with the first-order linear interacting term and eventually numerical instability associated with unstable saddle topology. On the other hand, the singularity arising from unbalanced treatment does not occur in the case of velocity shear and contracting flows, since the second-order interaction effects are cancelled under the constraint of asymptotic behavior. In order to remove the singularity, a new theoretical non-Hookean spring force model from the Boltzmann-type molecular-level description based on the concept of gain and loss was proposed. The new second-order implicit model with a hyperbolic sine factor was then shown to be well-posed for all regimes, completely removing the high Weissenberg number singularity. [Preview Abstract] |
Sunday, November 22, 2015 8:52AM - 9:05AM |
A12.00005: Compressible Viscoelastic Flows Generated by Vibrating Nanoscale Structures in Simple Liquids John Sader, Debadi Chakraborty, Matthew Pelton, Edward Malachosky, Philippe Guyot-Sionnest, Kuai Yu, Todd Major, Mary Sajini Devadas, Gregory Hartland Recent measurements show that the natural viscoelastic response of simple nominally Newtonian liquids, like water and glycerol, can be interrogated directly using the high frequency (20 GHz) vibration of nanomaterials. The extensional mode vibrations of bipyramidal gold nanoparticles were used, generating a predominantly incompressible shear flow. Here, we study the complementary and general case of compressible viscoelastic nanoscale flows. We show that all available constitutive models for these flows, with the exception of a very recent proposal, do not reproduce the required response at high frequency. We demonstrate the utility of this recent model through measurements of the breathing mode vibrations of single gold nanowires immersed in glycerol, over the 40-70 GHz frequency range. [Preview Abstract] |
Sunday, November 22, 2015 9:05AM - 9:18AM |
A12.00006: Shear alignment of lamellar mesophase systems Jaju S.J., Kumaran V. Mixtures of oil, water and surfactants form different microphases. Some of these phases, e.g. lamellar, hexagonal phases, lead to complex rheological behaviour at macroscale due to inherent anisotropy and irregularities in the microstructures. We present a comprehensive simulation study to examine the structure-rheology relationship in lamellar phase flow. At mesoscale, Reynolds number (Re), Schmidt number (Sc), Ericksen number (Er), extent of segregation between hydrophilic and hydrophobic components ($r$), ratio of viscosity of the two components ($\Delta\mu/\mu_0$), and system size to layer width ratio ($L/\lambda$) complete the lamellar phase description. We have used lattice Boltzmann simulations to study a two dimensional lamellar phase system of moderate size. The domains and grain boundaries seen at low Sc are replaced by isolated edge dislocations at high Sc. The alignment mechanism does not change with changes in layer bending moduli (Er), viscosity contrast or $r$. Increasing segregation, increases disorder; this however does not lead to higher resistance to flow. At high Er, the shear tries homogenise the concentration field and disrupt layer formation. We see significantly higher peak viscosity at low Er at high viscosity contrast and due to defect pinning. [Preview Abstract] |
Sunday, November 22, 2015 9:18AM - 9:31AM |
A12.00007: An immersed boundary method for fluid-structure interactions in a nematic liquid crystal Saverio Spagnolie The nematic phase of a liquid crystal is characterized by a spontaneous local molecular alignment leading to an anisotropic (direction-dependent) response to deformations. A body moving through such a phase can induce complex viscous and elastic structures in the flow, and the fluid's anisotropic response can generate surprising forces on the immersed body. Bacteria swimming in a liquid crystal, for instance, have been observed to align with the orientation of the underlying director field. The complexity of such problems generally makes mathematical analysis intractable, and the computation of solutions can still be very challenging. In this talk an immersed boundary method for computing fluid-structure interactions in a nematic liquid crystal will be discussed. The Ericksen-Leslie equations, or a more general Landau-de Gennes model, are solved on a fixed, regular grid. Immersed boundaries communicate forces onto the fluid as in Peskin's original method, but now also torques on the nematic director field through molecular anchoring boundary conditions. Sample applications will also be discussed, including the locomotion of undulatory bodies in anisotropic fluids. [Preview Abstract] |
Sunday, November 22, 2015 9:31AM - 9:44AM |
A12.00008: Viscoelastic Flow Modelling for Polymer Flooding Shauvik De, Johan Padding, Frank Peters, Hans Kuipers Polymer liquids are used in the oil industry to improve the volumetric sweep and displacement efficiency of oil from a reservoir. Surprisingly, it is not only the viscosity but also the elasticity of the displacing fluid that determine the displacement efficiency. The main aim of our work is to obtain a fundamental understanding of the effect of fluid elasticity, by developing an advanced computer simulation methodology for the flow of non-Newtonian fluids through porous media. We simulate a 3D unsteady viscoelastic flow through a converging diverging geometry of realistic pore dimension using computational fluid dynamics (CFD).The primitive variables velocity, pressure and extra stresses are used in the formulation of models. The viscoelastic stress part is formulated using a FENE-P type of constitutive equation, which can predict both shear and elongational stress properties during this flow. A Direct Numerical Simulation (DNS) approach using Finite volume method (FVM) with staggered grid has been applied. A novel second order Immersed boundary method (IBM) has been incorporated to mimic porous media. The effect of rheological parameters on flow characteristics has also been studied. The simulations provide an insight into 3D flow asymmetry at higher Deborah numbers. Micro-Particle Image Velocimetry experiments are carried out to obtain further insights. These simulations present, for the first time, a detailed computational study of the effects of fluid elasticity on the imbibition of an oil phase. [Preview Abstract] |
Sunday, November 22, 2015 9:44AM - 9:57AM |
A12.00009: A computational study of two-phase viscoelastic systems in a capillary tube with a sudden contraction/expansion Metin Muradoglu, Daulet Izbassarov Two-phase viscoelastic systems are computationally studied in a pressure-driven tube with a sudden contraction and expansion using a finite-difference/front-tracking method. The effects of viscoelasticity in drop and bulk fluids are investigated including high Weissenberg and Reynolds number cases up to $Wi = 100$ and $Re = 100$. The FENE-CR model is used to account for the fluid viscoelasticity. Extensive computations are performed to examine drop dynamics for a wide range of parameters. It is found that viscoelasticity interacts with drop interface in a non-monotonic and complicated way, and the two-phase viscoelastic systems exhibit very rich dynamics especially in the expansion region. At high $Re$, the drop undergoes large deformation in the contraction region followed by shape oscillations in the downstream of the expansion. For a highly viscous drop, a re-entrant cavity develops in the contraction region at the trailing edge which, in certain cases, grows and eventually causes encapsulation of ambient fluid. The re-entrant cavity formation is initiated at the entrance of the contraction and is highly influenced by the viscoelasticity. The effects of viscoelasticity are reversed in the constricted channel: Viscoelasticity in drop/continuous phase hinders/enhances format [Preview Abstract] |
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