Mixing of a viscoelastic fluid in a time-periodic flow

1993 ◽  
Vol 256 ◽  
pp. 243-268 ◽  
Author(s):  
T. C. Niederkorn ◽  
J. M. Ottino
Keyword(s):  
Viscoelastic Fluid ◽  
Three Dimensional ◽  
Deborah Number ◽  
Weissenberg Number ◽  
Periodic Flow ◽  
Dimensionless Numbers ◽  
Fluid Elasticity ◽  
Exponential Stretching ◽  
The Impact ◽  
Time Periodic

We present an experimental and computational investigation of mixing of a viscoelastic fluid in two-dimensional time-periodic flows generated in an eccentric cylindrical geometry. The objective of the study is to investigate the impact of fluid elasticity on the morphological structures produced by the advection of passive tracers in chaotic flows. The relevant dimensionless numbers that quantify the rheological differences with respect to the Newtonian fluid are the Deborah number (De), defined as the ratio of the fluid timescale to the flow timescale, and the Weissenberg number (We), defined as the product of the fluid timescale and the mean shear rate. The effects of elasticity are investigated in the limit of slow flows, De ≈ 0 and We < 0.1. The experimental window of We is limited to Newtonian behaviour on the low end and the transition to three-dimensional flow on the high end; experiments show that this window is small, 0.02 < We < 0.1. Typical values of the Reynolds number and the Strouhal number are O(0.001) and O(0.1), respectively.Results from experiments with a constant-viscosity elastic fluid and computations using the upper-convected Maxwell constitutive equation are presented. Even though the streamlines for the elastic flow are nearly indistinguishable from the Newtonian flow, small deviations in the velocity field produce large effects on chaotically advected patterns. Elasticity affects both the asymptotic coverage of a dyed passive tracer and the rate at which the tracer is stretched. In all cases the tracer undergoes exponential stretching, but on a longer timescale as the elasticity increases. According to flow conditions, elasticity might increase or decrease the degree of regularity; however, island symmetry does not seem to be affected. Similar phenomena are observed in both the experiments and computations; therefore, an analysis of the chaotic dynamics of the periodic flow using numerical techniques is possible.

scholarly journals Coherent structures and chaotic advection in three dimensions

2010 ◽  
Vol 654 ◽  
pp. 1-4 ◽  
Author(s):  
STEPHEN WIGGINS
Keyword(s):  
Dynamical Systems ◽  
Fluid Mechanics ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Point Of View ◽  
Three Dimensions ◽  
Chaotic Advection ◽  
Periodic Flow ◽  
Two Dimensional ◽  
Time Periodic

In the 1980s the incorporation of ideas from dynamical systems theory into theoretical fluid mechanics, reinforced by elegant experiments, fundamentally changed the way in which we view and analyse Lagrangian transport. The majority of work along these lines was restricted to two-dimensional flows and the generalization of the dynamical systems point of view to fully three-dimensional flows has seen less progress. This situation may now change with the work of Pouransari et al. (J. Fluid Mech., this issue, vol. 654, 2010, pp. 5–34) who study transport in a three-dimensional time-periodic flow and show that completely new types of dynamical systems structures and consequently, coherent structures, form a geometrical template governing transport.

A three-dimensional computation of the force and torque on an ellipsoid settling slowly through a viscoelastic fluid

1995 ◽  
Vol 283 ◽  
pp. 1-16 ◽  
Author(s):  
J. Feng Feng ◽  
D. D. Joseph ◽  
R. Glowinski ◽  
T. W. Pan
Keyword(s):  
Reynolds Number ◽  
Viscoelastic Fluid ◽  
Tilt Angle ◽  
Three Dimensional ◽  
Major Axis ◽  
Weissenberg Number ◽  
Second Order ◽  
The Body ◽  
Fall Velocity ◽  
Elasticity Number

The orientation of an ellipsoid falling in a viscoelastic fluid is studied by methods of perturbation theory. For small fall velocity, the fluid's rheology is described by a second-order fluid model. The solution of the problem can be expressed by a dual expansion in two small parameters: the Reynolds number representing the inertial effect and the Weissenberg number representing the effect of the non-Newtonian stress. Then the original problem is split into three canonical problems: the zeroth-order Stokes problem for a translating ellipsoid and two first-order problems, one for inertia and one for second-order rheology. A Stokes operator is inverted in each of the three cases. The problems are solved numerically on a three-dimensional domain by a finite element method with fictitious domains, and the force and torque on the body are evaluated. The results show that the signs of the perturbation pressure and velocity around the particle for inertia are reversed by viscoelasticity. The torques are also of opposite sign: inertia turns the major axis of the ellipsoid perpendicular to the fall direction; normal stresses turn the major axis parallel to the fall. The competition of these two effects gives rise to an equilibrium tilt angle between 0° and 90° which the settling ellipsoid would eventually assume. The equilibrium tilt angle is a function of the elasticity number, which is the ratio of the Weissenberg number and the Reynolds number. Since this ratio is independent of the fall velocity, the perturbation results do not explain the sudden turning of a long body which occurs when a critical fall velocity is exceeded. This is not surprising because the theory is valid only for slow sedimentation. However, the results do seem to agree qualitatively with ‘shape tilting’ observed at low fall velocities.

scholarly journals Energy and Temperature-Dependent Viscosity Analysis on Magnetized Eyring-Powell Fluid Oscillatory Flow in a Porous Channel

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7829
Author(s):  
Meng Yang ◽  
Munawwar Ali Abbas ◽  
Wissam Sadiq Khudair
Keyword(s):  
Thermal Radiation ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Engineering Sciences ◽  
Dependent Viscosity ◽  
The Impact

In this research, we studied the impact of temperature dependent viscosity and thermal radiation on Eyring Powell fluid with porous channels. The dimensionless equations were solved using the perturbation technique using the Weissenberg number (ε ≪ 1) to obtain clear formulas for the velocity field. All of the solutions for the physical parameters of the Reynolds number (Re), magnetic parameter (M), Darcy parameter (Da) and Prandtl number (Pr) were discussed through their different values. As shown in the plots the two-dimensional and three-dimensional graphical results of the velocity profile against various pertinent parameters have been illustrated with physical reasons. The results revealed that the temperature distribution increases for higher Prandtl and thermal radiation values. Such findings are beneficial in the field of engineering sciences.

Dynamics of capsules enclosing viscoelastic fluid in simple shear flow

2018 ◽  
Vol 840 ◽  
pp. 656-687 ◽  
Author(s):  
Zheng Yuan Luo ◽  
Bo Feng Bai
Keyword(s):  
Shear Flow ◽  
Viscoelastic Fluid ◽  
Simple Shear ◽  
Deformation Behaviour ◽  
Three Dimensional ◽  
High Viscosity ◽  
Deborah Number ◽  
Simple Shear Flow ◽  
Capsule Deformation ◽  
Internal Fluid

Previous studies on capsule dynamics in shear flow have dealt with Newtonian fluids, while the effect of fluid viscoelasticity remains an unresolved fundamental question. In this paper, we report a numerical investigation of the dynamics of capsules enclosing a viscoelastic fluid and which are freely suspended in a Newtonian fluid under simple shear. Systematic simulations are performed at small but non-zero Reynolds numbers (i.e. $Re=0.1$) using a three-dimensional front-tracking finite-difference model, in which the fluid viscoelasticity is introduced via the Oldroyd-B constitutive equation. We demonstrate that the internal fluid viscoelasticity presents significant effects on the deformation behaviour of initially spherical capsules, including transient evolution and equilibrium values of their deformation and orientation. Particularly, the capsule deformation decreases slightly with the Deborah number De increasing from 0 to $O(1)$. In contrast, with De increasing within high levels, i.e. $O(1{-}100)$, the capsule deformation increases continuously and eventually approaches the Newtonian limit having a viscosity the same as the Newtonian part of the viscoelastic capsule. By analysing the viscous stress, pressure and viscoelastic stress acting on the capsule membrane, we reveal that the mechanism underlying the effects of the internal fluid viscoelasticity on the capsule deformation is the alterations in the distribution of the viscoelastic stress at low De and its magnitude at high De, respectively. Furthermore, we find some new features in the dynamics of initially non-spherical capsules induced by the internal fluid viscoelasticity. Particularly, the transition from tumbling to swinging of oblate capsules can be triggered at very high viscosity ratios by increasing De alone. Besides, the critical viscosity ratio for the tumbling-to-swinging transition is remarkably enlarged with De increasing at relatively high levels, i.e. $O(1{-}100)$, while it shows little change at low De, i.e. below $O(1)$.

Three-Dimensional Rotating Flow of an Oldroyd-B Nanofluid with Relaxation-Retardation Viscous Dissipation

2021 ◽  
Vol 10 (3) ◽  
pp. 408-419
Author(s):  
Manoj K. Nayak ◽  
Ibukun S. Oyelakin ◽  
Ali J. Chamkha ◽  
Sabyasachi Mondal ◽  
Precious Sibanda
Keyword(s):  
Viscous Dissipation ◽  
Three Dimensional ◽  
Linearization Method ◽  
Time Parameter ◽  
Rotating Flow ◽  
Nonlinear Thermal Radiation ◽  
Transfer Coefficients ◽  
Exponential Stretching ◽  
Exponential Stretching Sheet ◽  
The Impact

The principal aim of this study is to explore the impact of relaxation-retardation viscous dissipation, nonlinear convection, variable chemical reaction, and nonlinear thermal radiation on the three-dimensional rotating flow of an Oldroyd-B nanofluid over an exponentially extended surface. The Buongiorno model that takes into account the Brownian movement and thermophoresis responsible for nanoparticle motion. Exponentially varying temperature and concentration associated with convective heat transfer coefficients are assumed in the boundary conditions. The system of dimensionless ODEs is solved by the spectral quasi-linearization method. The results of the analysis show, among other results that the relaxation time parameter opposes the momentum transport while assisting heat transportation. The retardation time parameter acts to support momentum growth while reducing and resists heat transport. The present study focused on the investigation the effect of relaxation and retardation viscous dissipation on rotating flow of a non-Newtonian fluid (Oldroyd B fluid) past an exponential stretching sheet.

scholarly journals Low Reynolds Number Pulsatile Flow of a Viscoelastic Fluid Through a Channel: Effects of Fluid Rheology and Pulsation Parameters

2021 ◽  
Author(s):  
Subhasisa Rath ◽  
Bimalendu Mahapatra
Keyword(s):  
Reynolds Number ◽  
Viscoelastic Fluid ◽  
Pulsatile Flow ◽  
Low Reynolds Number ◽  
Flow Characteristics ◽  
Deborah Number ◽  
Pulsation Frequency ◽  
Process Industries ◽  
Fluid Elasticity ◽  
Low Reynolds

Abstract As the first endeavour, we have analyzed the pulsatile flow of Oldroyd-B viscoelastic fluid where the combined effects of fluid elasticity and pulsation parameters on the flow characteristics are numerically studied at a low Reynolds number. Computations are performed using a finite-volume based open-source solver OpenFOAM\textsuperscript{\textregistered} by appending the log-conformation tensor approach to stabilize the numerical solution at high Deborah number. Significant flow velocity enhancement is achieved by increasing the viscoelastic behaviour of the fluid. High-velocity gradient zones and high polymeric stress regions are observed near the channel wall. The magnitude of axial velocity attenuates with increasing pulsation amplitude or pulsation frequency, and the extent of this attenuation is highly dependent on the Deborah number or the retardation ratio. This work finds application in the transport of polymeric solutions, extrusion, and injection moulding of polymer melts in several process industries.

The First Instability Mechanism in Differentially Heated Cavities With Conducting Horizontal Walls

1995 ◽  
Vol 117 (3) ◽  
pp. 626-633 ◽  
Author(s):  
R. J. A. Janssen ◽  
R. A. W. M. Henkes
Keyword(s):  
Thermal Instability ◽  
Three Dimensional ◽  
Thermal Engineering ◽  
Periodic Flow ◽  
Instability Mechanism ◽  
Horizontal Cavity ◽  
Vertical Walls ◽  
Cold Walls ◽  
Time Periodic ◽  
Good Agreement

A classical configuration in thermal engineering is the rectangular cavity that is differentially heated over two opposing vertical walls. In this paper, the instability mechanism responsible for the transition from steady to time-periodic flow in both two and three-dimensional cavities with perfectly conducting horizontal walls is studied. For both air (Pr = 0.71) and water (Pr = 7.0), the instability is a thermal instability resulting from an unstable stratification in the boundary layers along the horizontal cavity walls. The frequency is in good agreement with the frequency predicted using Howard’s model (1966). For air, the perturbations arise at fixed depths in the cavity whereas for water they travel along the hot and cold walls of the cavity.

Analyzing the Impact of X-Ray Tomography on the Reliability of Integrated Circuits

2015 ◽  
Author(s):  
Halit Dogan ◽  
Md Mahbub Alam ◽  
Navid Asadizanjani ◽  
Sina Shahbazmohamadi ◽  
Domenic Forte ◽  
...  
Keyword(s):  
Integrated Circuits ◽  
Integrated Circuit ◽  
3D Imaging ◽  
Three Dimensional ◽  
Serial Sectioning ◽  
Promising Technique ◽  
Flash Memories ◽  
X Ray ◽  
3D Information ◽  
The Impact

Abstract X-ray tomography is a promising technique that can provide micron level, internal structure, and three dimensional (3D) information of an integrated circuit (IC) component without the need for serial sectioning or decapsulation. This is especially useful for counterfeit IC detection as demonstrated by recent work. Although the components remain physically intact during tomography, the effect of radiation on the electrical functionality is not yet fully investigated. In this paper we analyze the impact of X-ray tomography on the reliability of ICs with different fabrication technologies. We perform a 3D imaging using an advanced X-ray machine on Intel flash memories, Macronix flash memories, Xilinx Spartan 3 and Spartan 6 FPGAs. Electrical functionalities are then tested in a systematic procedure after each round of tomography to estimate the impact of X-ray on Flash erase time, read margin, and program operation, and the frequencies of ring oscillators in the FPGAs. A major finding is that erase times for flash memories of older technology are significantly degraded when exposed to tomography, eventually resulting in failure. However, the flash and Xilinx FPGAs of newer technologies seem less sensitive to tomography, as only minor degradations are observed. Further, we did not identify permanent failures for any chips in the time needed to perform tomography for counterfeit detection (approximately 2 hours).

scholarly journals Numerical simulation of the impact of an integrated renovation project on the Maowei Sea hydrodynamic environment

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Cui Wang ◽  
Ling Cai ◽  
Yaojian Wu ◽  
Yurong Ouyang
Keyword(s):  
Water Exchange ◽  
Land Reclamation ◽  
Three Dimensional ◽  
Exchange Capacity ◽  
Reclamation Project ◽  
Hydrodynamic Environment ◽  
Sea Area ◽  
Water Quality Models ◽  
The Impact ◽  
Main Factor

AbstractIntegrated renovation projects are important for marine ecological environment protection. Three-dimensional hydrodynamics and water quality models are developed for the Maowei Sea to assess the hydrodynamic environment base on the MIKE3 software with high resolution meshes. The results showed that the flow velocity changed minimally after the project, decreasing by approximately 0.12 m/s in the east of the Maowei Sea area and increasing by approximately 0.01 m/s in the northeast of the Shajing Port. The decrease in tidal prism (~ 2.66 × 106 m3) was attributed to land reclamation, and accounted for just 0.86% of the pre-project level. The water exchange half-life increased by approximately 1 day, implying a slightly reduced water exchange capacity. Siltation occurred mainly in the reclamation and dredging areas, amounting to back-silting of approximately 2 cm/year. Reclamation project is the main factor causing the decrease of tidal volume and weakening the hydrodynamics in Maowei Sea. Adaptive management is necessary for such a comprehensive regulation project. According to the result, we suggest that reclamation works should strictly prohibit and dredging schemes should optimize in the subsequent regulation works.

scholarly journals Mechanical Behavior of Hydroxyapatite-Chitosan Composite: Effect of Processing Parameters

Minerals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 213
Author(s):  
Hamid Ait Said ◽  
Hassan Noukrati ◽  
Hicham Ben Youcef ◽  
Ayoub Bayoussef ◽  
Hassane Oudadesse ◽  
...  
Keyword(s):  
Molecular Weight ◽  
Compressive Strength ◽  
Mechanical Strength ◽  
Bone Repair ◽  
Mechanical Stability ◽  
Three Dimensional ◽  
Processing Parameters ◽  
Composite Effect ◽  
Solid Liquid ◽  
The Impact

Three-dimensional hydroxyapatite-chitosan (HA-CS) composites were formulated via solid-liquid technic and freeze-drying. The prepared composites had an apatitic nature, which was demonstrated by X-ray diffraction and Infrared spectroscopy analyses. The impact of the solid/liquid (S/L) ratio and the content and the molecular weight of the polymer on the composite mechanical strength was investigated. An increase in the S/L ratio from 0.5 to 1 resulted in an increase in the compressive strength for HA-CSL (CS low molecular weight: CSL) from 0.08 ± 0.02 to 1.95 ± 0.39 MPa and from 0.3 ± 0.06 to 2.40 ± 0.51 MPa for the HA-CSM (CS medium molecular weight: CSM). Moreover, the increase in the amount (1 to 5 wt%) and the molecular weight of the polymer increased the mechanical strength of the composite. The highest compressive strength value (up to 2.40 ± 0.51 MPa) was obtained for HA-CSM (5 wt% of CS) formulated at an S/L of 1. The dissolution tests of the HA-CS composites confirmed their cohesion and mechanical stability in an aqueous solution. Both polymer and apatite are assumed to work together, giving the synergism needed to make effective cylindrical composites, and could serve as a promising candidate for bone repair in the orthopedic field.

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