A Model of Flow in a Closed-Loop Thermosyphon Including the Soret Effect

1985 ◽  
Vol 107 (4) ◽  
pp. 840-849 ◽  
Author(s):  
J. E. Hart
Keyword(s):  
Rayleigh Number ◽  
Soret Effect ◽  
Vertical Plane ◽  
Soret Coefficient ◽  
Chaotic Motions ◽  
Thermohaline Convection ◽  
Existence And Stability ◽  
Convective Motions ◽  
Steady Solutions ◽  
Set Up

This theoretical study addresses the nature of convective motions in a toroidal loop of binary fluid oriented in the vertical plane and heated from below. The boundaries of the loop are impermeable, but gradients of the solute can be set up by Soret diffusion in the direction around the loop. The existence and stability of steady solutions are discussed over the Rayleigh number-Soret coefficient parameter plane. When the Soret coefficient is negative, periodic and chaotic oscillations analogous to those of thermohaline convection are predicted. When the Soret coefficient is positive, relaxation oscillations and low Rayleigh number chaotic motions are found. Both sets of phenomena are predicted to occur for realistic thermosyphon parameters.

scholarly journals Experimental Investigation of Thermal Diffusion in Binary and Ternary Hydrocarbon Mixtures

2021 ◽  
Author(s):  
Seyyed Arash Mousavi
Keyword(s):  
Thermal Diffusion ◽  
Soret Effect ◽  
Measurement Instrument ◽  
Optical Interferometry ◽  
Temperature Fields ◽  
Soret Coefficient ◽  
Hydrocarbon Mixtures ◽  
Space Experiments ◽  
Convective Motions ◽  
Laser Sources

In a multi-component liquid mixture, the process of disassociation of the components induced by thermal gradient is called thermal diffusion or Soret effect. This effect plays a crucial role in separation of the components in hydrocarbon mixtures of oil. Accordingly, the main goal of this study is to experimentally investigate the Soret effect in binary and ternary hydrocarbon mixtures. Optical interferometry technique with Mach-Zehnder scheme was used to conduct the experiments. The interferometry techniques are not intrusive and the separation of the components in the mixture is not affected by the measurement instrument. A Soret cell is defined as a cubic cavity where the sample mixture is placed in it and, the separation of the components takes place in the cell by heating it from the above. Soret cells are used in convectionless experiments and natural convections are undesirable. The Soret cell used in space experiments was re-designed and optimized for ground-based experiments to avoid the natural convections. Computational studies were made on the both cells to obtain the temperature and velocity fields. Then a set of thermal diffusion experiments conducted in order to compare the performance of the cells. The results shows that the induced convective motions in the second cell are significantly weaker than those in the previous cell which is desirable. In the next step, the effect of the inclination of the cell on the thermal diffusion was studied. First numerical analysis was made to find the velocity and temperature fields in different inclinations and then a set of experiments was performed and the concentration distribution of the components in a binary mixture in different inclinations of the cell was found. Finally, ground based experiments were performed to study the thermal diffusion in five ternary hydrocarbon mixtures. Optical interferometry with Mach-Zehnder scheme using two laser sources with different wavelengths was used. The Soret information of one of the mixtures is available in the literature and this mixture was studied here to validate the present experimental setup. The temperature and concentration of the mixtures were measured successfully in the Soret cell and a table of the measured Soret coefficient were provided.

A Model of Bioconvection of a Dilute Suspension of Gravitactic Microorganisms in an Isotropic Porous Medium

2001 ◽  
Author(s):  
A. V. Kuznetsov ◽  
N. Jiang
Keyword(s):  
Porous Medium ◽  
Conservation Equation ◽  
Darcy Law ◽  
Existence And Stability ◽  
Conservative Finite Difference Scheme ◽  
Convective Motions ◽  
Dilute Suspension ◽  
Swimming Microorganisms ◽  
Pattern Forming ◽  
Set Up

Abstract A new continuum model is formulated for bioconvection in a dilute suspension of swimming, gravitactic microorganisms in a porous medium. ‘Bioconvection’ is the name given to pattern-forming convective motions set up in suspensions of swimming microorganisms. ‘Gravitaxis’ describes the way of the swimming and means that microorganisms tend to swim against the gravity. The aim of this paper is to analyze collective behaviour and pattern formation in populations of swimming microorganisms. The existence and stability of a two-dimensional plume in a tall, narrow chamber with stress-free sidewalls is investigated. Governing equations include the Darcy law and the microorganism conservation equation. A conservative finite-difference scheme is used to solve these equations numerically.

scholarly journals Experimental Investigation of Thermal Diffusion in Binary and Ternary Hydrocarbon Mixtures

2021 ◽  
Author(s):  
Seyyed Arash Mousavi
Keyword(s):  
Thermal Diffusion ◽  
Soret Effect ◽  
Measurement Instrument ◽  
Optical Interferometry ◽  
Temperature Fields ◽  
Soret Coefficient ◽  
Hydrocarbon Mixtures ◽  
Space Experiments ◽  
Convective Motions ◽  
Laser Sources

In a multi-component liquid mixture, the process of disassociation of the components induced by thermal gradient is called thermal diffusion or Soret effect. This effect plays a crucial role in separation of the components in hydrocarbon mixtures of oil. Accordingly, the main goal of this study is to experimentally investigate the Soret effect in binary and ternary hydrocarbon mixtures. Optical interferometry technique with Mach-Zehnder scheme was used to conduct the experiments. The interferometry techniques are not intrusive and the separation of the components in the mixture is not affected by the measurement instrument. A Soret cell is defined as a cubic cavity where the sample mixture is placed in it and, the separation of the components takes place in the cell by heating it from the above. Soret cells are used in convectionless experiments and natural convections are undesirable. The Soret cell used in space experiments was re-designed and optimized for ground-based experiments to avoid the natural convections. Computational studies were made on the both cells to obtain the temperature and velocity fields. Then a set of thermal diffusion experiments conducted in order to compare the performance of the cells. The results shows that the induced convective motions in the second cell are significantly weaker than those in the previous cell which is desirable. In the next step, the effect of the inclination of the cell on the thermal diffusion was studied. First numerical analysis was made to find the velocity and temperature fields in different inclinations and then a set of experiments was performed and the concentration distribution of the components in a binary mixture in different inclinations of the cell was found. Finally, ground based experiments were performed to study the thermal diffusion in five ternary hydrocarbon mixtures. Optical interferometry with Mach-Zehnder scheme using two laser sources with different wavelengths was used. The Soret information of one of the mixtures is available in the literature and this mixture was studied here to validate the present experimental setup. The temperature and concentration of the mixtures were measured successfully in the Soret cell and a table of the measured Soret coefficient were provided.

scholarly journals The convection of a Bingham fluid in a differentially-heated porous cavity

2016 ◽  
Vol 26 (3/4) ◽  
pp. 879-896 ◽  
Author(s):  
D. Andrew S. Rees
Keyword(s):  
Rayleigh Number ◽  
Yield Stress ◽  
Piecewise Linear ◽  
Rectangular Cavity ◽  
Content Type ◽  
Multigrid Algorithm ◽  
Bingham Number ◽  
Steady Solutions ◽  
Darcy Flux ◽  
Darcy Rayleigh Number

Purpose – The purpose of this paper is to determine the manner in which a yield stress fluid begins convecting when it saturates a porous medium. A sidewall-heated rectangular cavity is selected as the testbed for this pioneering work. Design/methodology/approach – Steady solutions are obtained using a second order accurate finite difference method, line relaxation based on the Gauss-Seidel smoother, a Full Approximation Scheme multigrid algorithm with V-cycling and a regularization of the Darcy-Bingham model to smooth the piecewise linear relation between the Darcy flux and the applied body forces. Findings – While Newtonian fluids always convect whenever the Darcy-Rayleigh number is nonzero, Bingham fluids are found to convect only when the Darcy-Rayleigh number exceeds a value which is linearly dependent on both the Rees-Bingham number and the overall perimeter of the rectangular cavity. Stagnation is always found in the centre of the cavity and in regions close to the four corners. Care must be taken over the selection of the regularization constant. Research limitations/implications – The Darcy-Rayleigh number is restricted to values which are at or below 200. Originality/value – This is the first investigation of the effect of yield stress on nonlinear convection in porous media.

Numerical Analysis of Thermal-Solutal Convection in Heterogeneous Porous Media

2005 ◽  
Vol 73 (1) ◽  
pp. 21-25 ◽  
Author(s):  
Charles-Guobing Jiang ◽  
M. Ziad Saghir ◽  
M. Kawaji
Keyword(s):  
Porous Media ◽  
Thermal Diffusion ◽  
Soret Effect ◽  
Heterogeneous Porous Media ◽  
Soret Coefficient ◽  
Solutal Convection ◽  
Coefficient Distribution ◽  
Separation Ratio ◽  
Diffusion In Porous Media ◽  
Vertical Cavity

Thermal diffusion, or Soret effect, in porous media is mathematically modeled with the Firoozabadi model based on non-equilibrium thermodynamics. The Soret effect in a binary mixture is investigated in a vertical cavity with heterogeneous permeability, where natural convection can occur. The thermo solutal convection with heterogeneous permeability was studied in terms of flow pattern, concentration distribution, component separation ratio, and Soret coefficient distribution. A consistent analysis was conducted and it is concluded that the Soret coefficient of thermal diffusion in porous media strongly depends on the heterogeneity of permeability.

scholarly journals Bifurcations of a Controlled Two-Bar Linkage Motion with Considering Viscous Frictions

2011 ◽  
Vol 18 (1-2) ◽  
pp. 365-375 ◽  
Author(s):  
Qingkai Han ◽  
Xueyan Zhao ◽  
Xingxiu Li ◽  
Bangchun Wen
Keyword(s):  
Phase Space ◽  
Lyapunov Exponents ◽  
Time Domain ◽  
Shooting Method ◽  
Viscous Friction ◽  
Dynamical Model ◽  
Chaotic Motions ◽  
Amplitude Spectra ◽  
Set Up ◽  
Joint Motions

In this paper, we investigate the joint viscous friction effects on the motions of a two-bar linkage under controlling of OPCL. The dynamical model of the two-bar linkage with an OPCL controller is firstly set up with considering the two joints' viscous frictions. Thereafter, the motion bifurcations of the two-bar linkage along the values of joint viscous frictions are obtained using shooting method. Then, single-periodic, multiple-periodic, quasi-periodic and chaotic motions of link rotating angles are simulated with given different viscous friction values, and they are illustrated in time domain waveforms, phase space portraits, amplitude spectra and Poincare mapping graphs, respectively. Additionally, for the chaotic case, Lyapunov exponents and hypothesis possibilities of the two joint motions are also estimated.

scholarly journals Thermophoresis: The Case of Streptavidin and Biotin

Polymers ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 376 ◽  
Author(s):  
Doreen Niether ◽  
Mona Sarter ◽  
Bernd W. Koenig ◽  
Jörg Fitter ◽  
Andreas M. Stadler ◽  
...  
Keyword(s):  
Heavy Water ◽  
Rayleigh Scattering ◽  
Soret Effect ◽  
Binding Constants ◽  
Soret Coefficient ◽  
Protein Solutions ◽  
Elastic Neutron ◽  
Solvent Interactions ◽  
Free Protein ◽  
Promising Tool

Thermophoretic behavior of a free protein changes upon ligand binding and gives access to information on the binding constants. The Soret effect has also been proven to be a promising tool to gain information on the hydration layer, as the temperature dependence of the thermodiffusion behavior is sensitive to solute–solvent interactions. In this work, we perform systematic thermophoretic measurements of the protein streptavidin (STV) and of the complex STV with biotin (B) using thermal diffusion forced Rayleigh scattering (TDFRS). Our experiments show that the temperature sensitivity of the Soret coefficient is reduced for the complex compared to the free protein. We discuss our data in comparison with recent quasi-elastic neutron scattering (QENS) measurements. As the QENS measurement has been performed in heavy water, we perform additional measurements in water/heavy water mixtures. Finally, we also elucidate the challenges arising from the quantiative thermophoretic study of complex multicomponent systems such as protein solutions.

scholarly journals Traveling-Wave Convection with Periodic Source Defects in Binary Fluid Mixtures with Strong Soret Effect

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 283
Author(s):  
Laiyun Zheng ◽  
Bingxin Zhao ◽  
Jianqing Yang ◽  
Zhenfu Tian ◽  
Ming Ye
Keyword(s):  
Rayleigh Number ◽  
Traveling Wave ◽  
Soret Effect ◽  
Binary Fluid ◽  
Fluid Mixtures ◽  
Bénard Convection ◽  
Benard Convection ◽  
Binary Fluid Mixtures ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper studied the Rayleigh–Bénard convection in binary fluid mixtures with a strong Soret effect (separation ratio ψ = − 0.6 ) in a rectangular container heated uniformly from below. We used a high-accuracy compact finite difference method to solve the hydrodynamic equations used to describe the Rayleigh–Bénard convection. A stable traveling-wave convective state with periodic source defects (PSD-TW) is obtained and its properties are discussed in detail. Our numerical results show that the novel PSD-TW state is maintained by the Eckhaus instability and the difference between the creation and annihilation frequencies of convective rolls at the left and right boundaries of the container. In the range of Rayleigh number in which the PSD-TW state is stable, the period of defect occurrence increases first and then decreases with increasing Rayleigh number. At the upper bound of this range, the system transitions from PSD-TW state to another type of traveling-wave state with aperiodic and more dislocated defects. Moreover, we consider the problem with the Prandtl number P r ranging from 0.1 to 20 and the Lewis number L e from 0.001 to 1, and discuss the stabilities of the PSD-TW states and present the results as phase diagrams.

The Soret Effect: A Review of Recent Experimental Results

2005 ◽  
Vol 73 (1) ◽  
pp. 5-15 ◽  
Author(s):  
Jean K. Platten
Keyword(s):  
Rayleigh Scattering ◽  
Soret Effect ◽  
Organic Liquid ◽  
Oil Industry ◽  
Liquid Mixtures ◽  
Beam Deflection ◽  
Soret Coefficient ◽  
Onset Of Convection ◽  
New Techniques ◽  
Scattering Technique

In the first part of the paper, we recall what the Soret effect is, together with its applications in science and industry. We emphasize the need to have a reliable data base for the Soret coefficient. Next we review the different techniques to measure the Soret coefficient (elementary Soret cell, beam deflection technique, thermal diffusion forced Rayleigh scattering technique, convective coupling and, in particular, the onset of convection in horizontal layers and the thermogravitational method). Results are provided for several systems, with both negative and positive Soret coefficients, and comparison between several laboratories are made for the same systems. We end with “benchmark” values of the Soret coefficient for some organic liquid mixtures of interest in the oil industry and to which all future new techniques should refer before gaining confidence. We conclude that correct values of the Soret coefficient can be obtained in earth conditions and we deny the need to go to microgravity.

scholarly journals Magneto Convection in a Layer of Nanofluid With Soret Effect

2015 ◽  
Vol 9 (2) ◽  
pp. 63-69 ◽  
Author(s):  
Ramesh Chand ◽  
Gian Chand Rana
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Fluid Layer ◽  
Soret Effect ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Diffusive Convection ◽  
Mode Method ◽  
Double Diffusive

AbstractDouble diffusive convection in a horizontal layer of nanofluid in the presence of uniform vertical magnetic field with Soret effect is investigated for more realistic boundary conditions. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries. The normal mode method is used to find linear stability analysis for the fluid layer. Oscillatory convection is ruled out because of the absence of the two opposing buoyancy forces. Graphs have been plotted to find the effects of various parameters on the stationary convection and it is found that magnetic field, solutal Rayleigh number and nanofluid Lewis number stabilizes fluid layer, while Soret effect, Lewis number, modified diffusivity ratio and nanoparticle Rayleigh number destabilize the fluid layer.

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