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Gaikwad SN, Surwase DM. Chemically Driven Convective Instabilities in Binary Nanofluids with Thermodiffusions. JOURNAL OF NANOFLUIDS 2023. [DOI: 10.1166/jon.2023.1966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
An investigation of the onset of chemically driven convective instabilities in binary nanofluids has been carried out under the influence of thermodiffusion and nanoparticles. In order to investigate the convective instabilities, the Tiwari-Das nanofluid model is used and the thermal
Rayleigh number is derived using linear stability analysis. The effect of nondimensional parameters involved in the study is illustrated graphically. It is found that volume fraction of nanoparticles, Soret effects of nanoparticles and solute destabilize the system and Lewis number stabilizes
the system. The heat of chemical reaction parameter performs a dual consequence on the stability. It has stabilizing effect for its negative values and destabilizing effect for its non-negative values. The strength of chemical reaction is also discussed. It is reported that the chemical reaction
is fast when the system is heated from below and it is slow when the system is heated from above. Water-ethylene glycol based silver and cupric oxide pseudoplastic non-Newtonian binary nanofluids are considered and the impact of nanoparticles is analyzed through addition factors. The binary
nanofluids convection driven by chemical reaction has a great importance in absorption based industrial applications such as refrigeration, air conditioning, automobiles, biomedical engineering, solar collectors and falling film.
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Hegseth JJ, Oprisan A, Garrabos Y, Beysens D. Imaging critical fluctuations of pure fluids and binary mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022127. [PMID: 25215709 DOI: 10.1103/physreve.90.022127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2014] [Indexed: 06/03/2023]
Abstract
We use optical microscopy techniques to directly visualize the structures that emerge in binary mixtures and pure fluids near their respective critical points. We attempt to understand these structures by studying the image formation using both a phase contrast and a dark field filter to our microscope. We found that images of critical fluctuations for both liquid-liquid and liquid-gas critical systems have gray level intensity histograms with Gaussian shape. For all fluids investigated, the temperature-dependent standard deviation of the Gaussian histogram follows a power law with the same exponent. Since the image intensity fluctuations are determined by order parameter fluctuations, this direct imaging method allowed us to estimate the critical exponent of compressibility with very good accuracy.
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Affiliation(s)
- John J Hegseth
- Department of Physics, University of New Orleans, New Orleans, Louisiana 70148, USA
| | - Ana Oprisan
- Department of Physics and Astronomy, College of Charleston, Charleston, South Carolina 29424, USA
| | - Yves Garrabos
- ESEME, Institut de Chimie de la Matière Condensée de Bordeaux, UPR 9048, CNRS, Université de Bordeaux I, Avenue du Dr. Schweitzer, F-33608 Pessac Cedex, France
| | - Daniel Beysens
- Physique et Mécanique des Milieux Hétérogènes, UMR 7636 CNRS - ESPCI - Université Pierre et Marie Curie - Université Paris Diderot, 10 rue Vauquelin, 75005 Paris, France and Service des Basses Températures, CEA-Grenoble & Université Joseph Fourier, Grenoble, France
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Umla R, Augustin M, Huke B, Lücke M. Three-dimensional convection of binary mixtures in porous media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:056326. [PMID: 22181517 DOI: 10.1103/physreve.84.056326] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2011] [Revised: 10/28/2011] [Indexed: 05/31/2023]
Abstract
We investigate convection patterns of binary mixtures with a positive separation ratio in porous media. As setup, we choose the Rayleigh-Bénard system of a fluid layer heated from below. Results are obtained by a multimode Galerkin method. Using this method, we compute square and crossroll patterns, and we analyze their structural, bifurcation, and stability properties. Evidence is provided that, for a strong enough Soret effect, both structures exist as stable forms of convection. Some of their properties are found to be similar to square and crossroll convection in the system without porous medium. However, there are also qualitative differences. For example, squares can be destabilized by oscillatory perturbations with square symmetry in porous media, and their velocity isolines are deformed in the so-called Soret regime.
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Affiliation(s)
- R Umla
- Institut für Theoretische Physik, Universität des Saarlandes, Saarbrücken, Germany.
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Weggler S, Huke B, Lücke M. Roll and square convection in binary liquids: a few-mode Galerkin model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:016309. [PMID: 20365462 DOI: 10.1103/physreve.81.016309] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2009] [Indexed: 05/29/2023]
Abstract
We present a few-mode Galerkin model for convection in binary fluid layers subject to an approximation to realistic horizontal boundary conditions at positive separation ratios. The model exhibits convection patterns in form of rolls and squares. The stable squares at onset develop into stable rolls at higher thermal driving. In between, a regime of a so-called cross roll structure is found. The results of our few-mode model are in good agreement with both experiments and numerical multimode simulations.
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Affiliation(s)
- S Weggler
- Institut für Theoretische Physik, Universität des Saarlandes, Saarbrücken, Germany
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Huke B, Pleiner H, Lücke M. Thermal convection in mixtures with an inversion of the separation ratio. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:046315. [PMID: 18999534 DOI: 10.1103/physreve.78.046315] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2007] [Revised: 09/05/2008] [Indexed: 05/27/2023]
Abstract
We have numerically investigated Rayleigh-Bénard convection in binary mixtures assuming a thermal diffusion ratio that depends on the local temperature and changes its sign within the cell. The stationary instability has been found to precede the oscillatory one for a wide range of negative mean psi values. The bifurcation diagram for stationary rolls turns out to be qualitatively different from that for constant Soret effect. Nevertheless, it can be mapped onto this special case by using a scaling argument, taking into account the fact that for small convection amplitudes the rolls are restricted to parts of the cell where the sign of the Soret coefficient favors instability.
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Affiliation(s)
- B Huke
- Institut für Theoretische Physik, Universität des Saarlandes, D-66041 Saarbrücken, Germany
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Huke B, Pleiner H, Lücke M. Convection patterns in colloidal solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:036203. [PMID: 17500765 DOI: 10.1103/physreve.75.036203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2006] [Indexed: 05/15/2023]
Abstract
We investigate the bifurcation properties and pattern selection in Rayleigh-Bénard convecting binary mixtures for parameter combinations that are typical for colloidal fluids using the Galerkin method. In such fluids the typical Lewis numbers and separation ratios differ by orders of magnitude from the values found in molecular mixtures like alcohol/water. We study stationary rolls, square and crossroll patterns for positive separation ratios, and traveling waves for negative separation ratios. Results are compared to those for molecular mixtures.
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Affiliation(s)
- B Huke
- Institut für Theoretische Physik, Universität des Saarlandes, D-66041 Saarbrücken, Germany
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Rogers JL, Pesch W, Brausch O, Schatz MF. Complex-ordered patterns in shaken convection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:066214. [PMID: 16089856 DOI: 10.1103/physreve.71.066214] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2005] [Indexed: 05/03/2023]
Abstract
We report and analyze complex patterns observed in a combination of two standard pattern forming experiments. These exotic states are composed of two distinct spatial scales, each displaying a different temporal dependence. The system is a fluid layer experiencing forcing from both a vertical temperature difference and vertical time-periodic oscillations. Depending on the parameters these forcing mechanisms produce fluid motion with either a harmonic or a subharmonic temporal response. Over a parameter range where these mechanisms have comparable influence the spatial scales associated with both responses are found to coexist, resulting in complex, yet highly ordered patterns. Phase diagrams of this region are reported and criteria to define the patterns as quasiperiodic crystals or superlattices are presented. These complex patterns are found to satisfy four-mode (resonant tetrad) conditions. The qualitative difference between the present formation mechanism and the resonant triads ubiquitously used to explain complex-ordered patterns in other nonequilibrium systems is discussed. The only exception to quantitative agreement between our analysis based on Boussinesq equations and laboratory investigations is found to be the result of breaking spatial symmetry in a small parameter region near onset.
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Funfschilling D, Ahlers G. Plume motion and large-scale circulation in a cylindrical Rayleigh-Bénard cell. PHYSICAL REVIEW LETTERS 2004; 92:194502. [PMID: 15169408 DOI: 10.1103/physrevlett.92.194502] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2003] [Indexed: 05/24/2023]
Abstract
We used the time correlation of shadowgraph images to determine the angle Theta of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-Bénard cell of aspect ratio Gamma identical with D/L=1 (D is the diameter and L approximately 87 mm is the height) in the Rayleigh-number range 7 x 10(7)</=R</=3 x 10(9) for a Prandtl number sigma=6. We expect that Theta gives the direction of the large-scale circulation. It oscillates time periodically. Near the top and bottom plates Theta(t) has the same frequency but is anticorrelated.
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Affiliation(s)
- Denis Funfschilling
- Department of Physics and iQUEST, University of California, Santa Barbara, California 93106, USA
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Daya ZA, Ecke RE. Prandtl-number dependence of interior temperature and velocity fluctuations in turbulent convection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:045301. [PMID: 12443249 DOI: 10.1103/physreve.66.045301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2002] [Indexed: 05/24/2023]
Abstract
Temperature and vertical velocity fluctuations are measured in turbulent Rayleigh-Bénard convection at the center of an approximately unit aspect ratio container of cylindrical cross section. Our measurements show that the Rayleigh-number scaling exponent gamma of the interior temperature fluctuations (i.e., sigma(T)/deltaT approximately Ragamma) is a strong and nontrivial function of the Prandtl number in the range 2.9<Pr<12.4. Other measurements at constant Ra=2.0 x 10(9) show that the interior turbulent fluctuations decrease significantly with increasing Pr; the temperature and velocity fluctuations decrease by about approximately 45% and approximately 68% over our range in Pr.
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Affiliation(s)
- Z A Daya
- Center for Nonlinear Studies and Condensed Matter & Thermal Physics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Xu X, Bajaj KM, Ahlers G. Heat transport in turbulent rayleigh-Benard convection. PHYSICAL REVIEW LETTERS 2000; 84:4357-4360. [PMID: 10990685 DOI: 10.1103/physrevlett.84.4357] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2000] [Indexed: 05/23/2023]
Abstract
We present measurements of the Nusselt number N as a function of the Rayleigh number R in cylindrical cells with aspect ratios 0. 5</=gamma identical withD/d</=12.8 ( D is the diameter and d is the height). We used acetone with a Prandtl number sigma = 4.0 for 10(5) less, similarR less, similar4x10(10). A fit of a power law N = N(0)R(gamma(eff)) over limited ranges of R yielded values of gamma(eff) from 0.275 near R = 10(7) to 0.300 near R = 10(10). The data are inconsistent with a single power law for N(R). For R>10(7) they are consistent with N = asigma-1/12R1/4+bsigma-1/7R3/7 as proposed by Grossmann and Lohse for sigma greater, similar2.
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Affiliation(s)
- X Xu
- Department of Physics and Quantum Institute, University of California, Santa Barbara, California 93106, USA
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Tokaruk WA, Molteno TC, Morris SW. Benard-Marangoni convection in two-layered liquids. PHYSICAL REVIEW LETTERS 2000; 84:3590-3593. [PMID: 11019153 DOI: 10.1103/physrevlett.84.3590] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/1998] [Indexed: 05/23/2023]
Abstract
We describe experiments on Benard-Marangoni convection in horizontal layers of two immiscible liquids. Unlike previous experiments, which used gases as the upper fluid, we find a square planform close to onset which undergoes a secondary bifurcation to rolls at higher temperature differences. The scale of the convection pattern is that of the thinner lower fluid layer for which buoyancy and surface tension forces are comparable. The wave number of the pattern near onset agrees with the linear stability prediction for the full two-layer problem. The square planform is in qualitative agreement with recent two-layer weakly nonlinear theories, which fail however to predict the transition to rolls.
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Affiliation(s)
- WA Tokaruk
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7
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Liu J, Ahlers G. Spiral-Defect Chaos in Rayleigh-Bénard Convection with Small Prandtl Numbers. PHYSICAL REVIEW LETTERS 1996; 77:3126-3129. [PMID: 10062140 DOI: 10.1103/physrevlett.77.3126] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Jung C, Lücke M, Büchel P. Influence of through-flow on linear pattern formation properties in binary mixture convection. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:1510-1529. [PMID: 9965223 DOI: 10.1103/physreve.54.1510] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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