Impact of osmotic pressure on the stability of Taylor vortices

2022 ◽  
Vol 933 ◽  
Author(s):  
Rouae Ben Dhia ◽  
Nils Tilton ◽  
Denis Martinand
Keyword(s):  
Osmotic Pressure ◽  
Critical Conditions ◽  
Hydrodynamic Instabilities ◽  
Taylor Vortices ◽  
Dynamic Filtration ◽  
Analytical Criterion ◽  
Permeable Cylinders ◽  
Couette Cell ◽  
Taylor Couette ◽  
The Stability

We use linear stability analysis and direct numerical simulations to investigate the coupling between centrifugal instabilities, solute transport and osmotic pressure in a Taylor–Couette configuration that models rotating dynamic filtration devices. The geometry consists of a Taylor–Couette cell with a superimposed radial throughflow of solvent across two semi-permeable cylinders. Both cylinders totally reject the solute, inducing the build-up of a concentration boundary layer. The solute retroacts on the velocity field via the osmotic pressure associated with the concentration differences across the semi-permeable cylinders. Our results show that the presence of osmotic pressure strongly alters the dynamics of the centrifugal instabilities and substantially reduces the critical conditions above which Taylor vortices are observed. It is also found that this enhancement of the hydrodynamic instabilities eventually plateaus as the osmotic pressure is further increased. We propose a mechanism to explain how osmosis and instabilities cooperate and develop an analytical criterion to bound the parameter range for which osmosis fosters the hydrodynamic instabilities.

The stability of viscous flow between horizontal concentric cylinders

1959 ◽  
Vol 251 (1264) ◽  
pp. 76-91 ◽  
Keyword(s):  
Free Surface ◽  
Experimental Verification ◽  
Theoretical Work ◽  
Critical Conditions ◽  
Dimensionless Number ◽  
Annular Space ◽  
Taylor Vortices ◽  
Concentric Cylinders ◽  
The Stability ◽  
Small Disturbances

The critical conditions for the formation of Taylor vortices between horizontal concentric cylinders are considered in detail. (1) Where the flow is unidirectional round the annular space and is caused entirely by the rotation of the inner cylinder. (2) Where the flow is caused entirely by pumping round the annular space. (3) Where a liquid is caused to reverse its flow at a free surface, the flow being entirely caused by the rotation of the inner cylinder. The last case is analyzed by the method of small disturbances and the conditions under which Taylor vortices will form are found. Results for the first two cases are already available in the literature. From examination of the three criteria a dimensionless number is proposed to correlate the critical values of the various parameters at the onset of these Taylor vortices. The proposed number has the advantage that it is insensitive to the velocity distribution in the annulus. It is subsequently used to predict the critical conditions for the onset of Taylor vortices under conditions that have not been analyzed, i.e. where flow is due to pumping and rotation of the inner cylinder. The criterion is found to predict successfully the results of various experiments carried out. In addition experimental verification of the theoretical work of Dean (1928) and of the additional analysis carried out in this paper is also given.

Experimental studies on the stability of Newtonian Taylor–Couette flow in the presence of viscous heating

2002 ◽  
Vol 462 ◽  
pp. 133-159 ◽  
Author(s):  
JAMES M. WHITE ◽  
SUSAN J. MULLER
Keyword(s):  
Reynolds Number ◽  
Outer Cylinder ◽  
Experimental Studies ◽  
Onset Time ◽  
Critical Conditions ◽  
Viscous Heating ◽  
Steady Temperature ◽  
Taylor Couette ◽  
The Stability ◽  
Visualization Techniques

The dramatic effects of viscous dissipation on the stability of Newtonian Taylor–Couette (TC) flows are studied experimentally using flow visualization techniques. Viscous heating, parameterized by the Nahme–Griffith number Na, drives a transition to a new, oscillatory mode of instability when coupled with the effects of centrifugal destabilization. This instability, consisting of travelling axisymmetric vortices, only occurs when viscous heating and centrifugal destabilization are both present. Step tests in cylinder velocity show that the time following initiation of shearing required for onset of instability scales well with the time for the fluid to reach a steady temperature profile under the action of viscous heating. The onset time can be dramatically reduced at fixed Na by increasing the centrifugal destabilization through the addition of co-rotation of the outer cylinder. The onset time can also be reduced while holding the centrifugal destabilization constant by increasing the amount of viscous heating (i.e. holding Reynolds number Re constant while increasing Na). The effects of viscous heating on the critical conditions of Newtonian TC flows are also quantified using ramp tests in cylinder velocity. These tests reveal the large extent to which viscous heating is destabilizing; at Na ≈ 2, a transition occurs at a critical Re that is less than 5% of the isothermal value.

Influence of the Aspect Ratio on the Stability of Pseudoplastic Fluids Between Rotating Cylinders

2012 ◽  
Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi
Keyword(s):  
Couette Flow ◽  
Gap Effect ◽  
Critical Conditions ◽  
Taylor Vortices ◽  
Circular Couette Flow ◽  
Centrifugal Instability ◽  
Toroidal Vortices ◽  
The Stability ◽  
Pseudoplastic Fluids ◽  
Good Agreement

Pseudoplastic circular Couette flow in annulus is investigated in finite gap. The onset of the Taylor vortices is determined theoretically by solving the conservation equations, constructing the solution path as the inner cylinder speed rises and detecting the critical conditions. The obtained governing equations were solved by the spectral method. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, known as Taylor vortices. A range of parameters is found in which the combination of shear thinning and gap effect leads to destabilizing the vortex structure indicated as the point of Hopf bifurcation. Comparison with existing measurements on pseudoplastic circular Couette flow results in good agreement.

Twist vortices and their instabilities in the Taylor–Couette system

1991 ◽  
Vol 226 ◽  
pp. 549-564 ◽  
Author(s):  
E. Weisshaar ◽  
F. H. Busse ◽  
M. Nagata
Keyword(s):  
Analytical Model ◽  
Parameter Space ◽  
Three Dimensional ◽  
Class Ii ◽  
Numerical Results ◽  
Narrow Gap ◽  
Taylor Vortices ◽  
Taylor Couette ◽  
The Stability

The problem of three-dimensional flows arising from the twist instability of Taylor vortices is investigated numerically in the narrow gap limit of the Taylor–Couette system with nearly corotating cylinders. There are two types of twist vortices: those that do not deform the in– and outflow boundaries of the Taylor vortices and those that do. The latter type are called wavy twist vortices and correspond to class II of Nagata (1986). The stability of the twist vortices with respect to arbitrary infinitesimal disturbances is analysed with the result that the twist solutions are unstable within a large part of the parameter space with respect to Eckhaus and skewed-varicose-type instabilities. An analytical model is described which fits the numerical results on the transition from axisymmetric vortices to unstable twist solutions. The theoretical findings are compared with experimental observations.

Development and Effects of Super-Critical Taylor-Vortex Flow in a Lightly Loaded Journal Bearing

1974 ◽  
Vol 96 (1) ◽  
pp. 28-35 ◽  
Author(s):  
R. C. DiPrima ◽  
J. T. Stuart
Keyword(s):  
Vortex Flow ◽  
Axial Direction ◽  
Basic Flow ◽  
Circular Cylinders ◽  
Taylor Vortex ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Secondary Motion ◽  
The Stability ◽  
Unified Description

At sufficiently high operating speeds in lightly loaded journal bearings the basic laminar flow will be unstable. The instability leads to a new steady secondary motion of ring vortices around the cylinders with a regular periodicity in the axial direction and a strength that depends on the azimuthial position (Taylor vortices). Very recently published work on the basic flow and the stability of the basic flow between eccentric circular cylinders with the inner cylinder rotating is summarized so as to provide a unified description. A procedure for calculating the Taylor-vortex flow is developed, a comparison with observed properties of the flow field is made, and formulas for the load and torque are given.

Adhesion of Partially and Fully Collapsed Nanotubes

2018 ◽  
Vol 86 (1) ◽  
Author(s):  
Ming Li ◽  
Hao Li ◽  
Fengwei Li ◽  
Zhan Kang
Keyword(s):  
Finite Deformation ◽  
Adhesion Energy ◽  
Van Der Waals Interactions ◽  
Critical Conditions ◽  
Nano Composites ◽  
Deformation Model ◽  
Analysis And Design ◽  
Structural Rigidity ◽  
Multiwall Nanotubes ◽  
The Stability

The competition between the structural rigidity and the van der Waals interactions may lead to collapsing of aligned nanotubes, and the resulting changes of both configurations and properties promise the applications of nanotubes in nano-composites and nano-electronics. In this paper, a finite-deformation model is applied to study the adhesion of parallel multiwall nanotubes with both partial and full collapsing, in which the noncontact adhesion energy is analytically determined. The analytical solutions of both configurations and energies of collapsed nanotubes are consistent with the molecular dynamics (MD) results, demonstrating the effectiveness of the finite-deformation model. To study the critical conditions of generating the partially and fully collapsed multiwall nanotubes, our analytical model gives the predictions for both the geometry- and energy-related critical diameters, which are helpful for the stability analysis and design of nanotube-based nano-devices.

scholarly journals Slit Wall Effect on the Stability of Wavy Vortex Flow

2014 ◽  
Vol 6 ◽  
pp. 853069 ◽  
Author(s):  
Dong Liu ◽  
Ying-ze Wang ◽  
Hyoung-Bum Kim ◽  
Fang-neng Zhu ◽  
Chun-lin Wang
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Radial Velocity ◽  
Flow Regime ◽  
Experimental Measurement ◽  
Vortex Flow ◽  
Wall Effect ◽  
Taylor Vortices ◽  
Simulation Results ◽  
The Stability

The wavy vortex flow in the plain model was studied by experimental measurement; the preliminary feature of wavy vortex flow was obtained. This flow field in the plain model was also studied by numerical simulation. The reliability of numerical simulation was verified by comparing with the experimental and numerical simulation results. To study the slit wall effect on the wavy vortex flow regime, another two models with different slit number were considered; the slit number was 6 and 12. By comparing the wavy vortex flow field in different models, the axial fluctuation of Taylor vortices was found to be different, which was increased with the increasing of slit number. The maximum radial velocity from the inner cylinder to the outer one in the 6-slit number was increased by 12.7% compared to that of plain model. From the results of different circumferential position in the same slit model, it can be found that the maximum radial velocity in slit plane is significantly greater than that in other planes. The size of Taylor vortices in different models was also calculated, which was found to be increased in the 6-slit model but was not changed as the slit number increased further.

Laminar Swirling Pipe Flow

1954 ◽  
Vol 21 (1) ◽  
pp. 1-7
Author(s):  
L. Talbot
Keyword(s):  
Swirling Flow ◽  
Nonlinear Effects ◽  
Critical Conditions ◽  
Flow Conditions ◽  
Rotationally Symmetric ◽  
Rate Of Decay ◽  
Linearized Theory ◽  
The Stability ◽  
Experimental Values ◽  
Rates Of Decay

Abstract The problem of the decay of a rotationally symmetric steady swirl superimposed on Poiseuille flow in a round pipe was investigated theoretically and experimentally. The object was to determine the degree to which the rate of decay of the swirl as predicted by a linearized theory agreed with measured rates of decay at flow conditions near the critical conditions for swirl instability. The solution to the linearized equation of motion for the swirl was obtained. Swirling flow was produced experimentally by rotating a section of the test pipe. Swirl velocities were determined from motion-picture studies of colored oil droplets introduced in the flow. The stability of the swirl was investigated through visualization of a dye filament, and a critical curve for swirl instability was determined experimentally relating the angular velocity of the rotating section to the Reynolds number. The theoretical and experimental values for the decay parameter were found to agree closely, even at conditions of flow near the critical conditions for instability. It was concluded that in the problem under consideration the nonlinear effects are not appreciable for stable decay of the swirl.

Ionic strength and polyelectrolyte molecular weight effects on floc formation and growth in Taylor–Couette flows

Soft Matter ◽  
2021 ◽  
Author(s):  
Athena E. Metaxas ◽  
Vishal Panwar ◽  
Ruth L. Olson ◽  
Cari S. Dutcher
Keyword(s):  
Molecular Weight ◽  
Ionic Strength ◽  
Solution Ionic Strength ◽  
Radial Injection ◽  
Couette Cell ◽  
Taylor Couette

A Taylor–Couette cell capable of radial injection was used to study the effects of varying solution ionic strength and polyelectrolyte molecular weight on the polyelectrolyte-driven flocculation of bentonite suspensions.

First-principles study on the stability and magnetoelectric properties of multiferroic materials XTiO3 (X = Mn, Fe, Co, Ni)

2018 ◽  
Vol 32 (09) ◽  
pp. 1850105 ◽  
Author(s):  
Xing-Yuan Chen ◽  
Guo-Xia Lai ◽  
Di Gu ◽  
Wei-Ling Zhu ◽  
Tian-Shu Lai ◽  
...  
Keyword(s):  
Magnetic Property ◽  
First Principles ◽  
Phonon Dispersion ◽  
Critical Conditions ◽  
First Principles Calculations ◽  
Multiferroic Materials ◽  
Equilibrium Conditions ◽  
Magnetoelectric Properties ◽  
Strong Hybridization ◽  
The Stability

The XTiO3 (X = Mn, Fe, Co and Ni) materials with R3c structure could be grown under critical conditions based on first-principles calculations and thermodynamic stability analysis. FeTiO3 and MnTiO3 could be synthesized relatively easily under metal-rich and O-poor conditions, while NiTiO3 could be stable under Ni-rich, O-rich and Ti-poor conditions. The predicted R3c CoTiO3 under thermodynamic equilibrium conditions is suggested to be synthesized under Co-rich, O-rich and Ti-poor conditions, but the calculated phonon dispersion indicates R3c CoTiO3 becomes unstable under the dynamical conditions. The ferroelectric behavior in the XTiO3 (X = Mn, Fe, Co and Ni) system could be dominated by the Ti ion with d0 state and the strong hybridization between Ti and O, while the magnetic property is mainly caused by the contribution of 3d transition metal.

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