Positive Soret Research Articles

Effect of Soret diffusion on the growth of spherical crystals in supercooled alloy melts under oscillatory flow.

The growth of spherical crystals in binary alloy melts with thermal diffusion effects under oscillatory flow is investigated analytically. Using the multiple scale method, we derive approximate analytical solutions for both the crystal interface growth rate and the solute concentration. Our results demonstrate that the Soret effect significantly influences both the solute concentration near the crystal interface and the crystal growth rate. Specifically, with a positive Soret coefficient, the growth rate of spherical crystals in a binary dilute alloy melt decreases as the coefficient increases, while the solute concentration near the interface increases. In contrast, with a negative Soret coefficient, the growth rate of the spherical crystals increases as the coefficient decreases, and the solute concentration near the interface decreases. Additionally, the presence of oscillatory flow markedly promotes the grain refinement induced by the Soret effect.

Instability of Jeffrey Fluid Throughflow in a Porous Layer Induced by Heat Source and Soret Effect

Abstract In this study, we investigated the instability of thermosolutal convection of Jeffrey fluid in a porous layer with internal heating and the Soret effect. The layer is bounded by two fixed permeable parallel plates which are assumed to be isothermal and isosolutal. An existing initial flow in the vertical direction is passing the layer at a constant speed. The flow fields are adequately presented by PDEs and transformed into dimensionless forms. A small perturbation to the basic flow profiles with linear stability analysis results the problem in an eigenvalue problem. The Runge-Kutta method is used to derive the numerical value of the critical thermal Rayleigh number. The convective instability for asymptotic cases for Le = 1 and Pe = 0 are also examined as special cases. The analysis reveals that for a non-positive Soret parameter, the flow is stable for all Lewis numbers and independent of the heat source. But with a positive Soret parameter in the absence of a heat source, the fluid flow is stable for Le = 3 while the influence of a heat source destabilizes the flow for Le > 2. In high and low shear flows with increasing solutal gradient, the solutal Rayleigh number shows a highly destabilizing nature for all Le. Moreover, smaller relaxation and higher retardation time are the most unstable characteristics of the heat source system. In convective longitudinal rolls, the uni-cellular streamline patterns tend to become bi-cellular by the influence of positive Soret parameters and energy sources.

Cross‐diffusion effects on the onset of double‐diffusive convection in a rotating vertical heterogeneous porous cylinder with vertical throughflow

AbstractThe effects of vertical throughflow, rotation, cross‐diffusion, and vertical heterogeneous permeability on the onset of double‐diffusive convection in a finite vertical porous cylinder have been studied. The fluid in the cylinder is warmed and salted from below with its top and lower walls considered to be isothermal, isosolutal, and permeable. In the model, the Brinkman model was adopted, coupled with the Oberbeck–Boussinesq approximation. The normal mode technique is used for linear stability analysis and a single‐term Galerkin method is used to solve the eigenvalue problem. Further, the influence of parameters such as the thermal and solute Rayleigh, Taylor, and the Soret and Dufour numbers on the fluid system instability have been investigated. Among other results, we found that vertical heterogeneity may either stabilize or destabilize a fluid system. The stabilization of the throughflow remains consistent irrespective of the orientation in the absence of a cross‐diffusion effect. The dual effect of throughflow is observed when there are cross‐diffusion effect. We found that increasing the Dufour parameter delays the onset of both stationary and oscillatory convection. The positive Soret number has a stabilizing effect on stationary convection and a destabilizing effect on the oscillatory convection case.

Thermo-Mechanical and Mechano-Thermal Effects in Liquids Explained by Means of the Dual Model of Liquids

We pursue to illustrate the capabilities of the Dual Model of Liquids (DML) showing that it may explain crossed effects notable in Non-Equilibrium Thermodynamics (NET). The aim of the paper is to demonstrate that the DML may correctly model the thermodiffusion, in particular getting formal expressions for positive and negative Soret coefficient, and another “unexpected” mechano-thermal effect recently discovered in liquids submitted to shear strain, for which the first-ever theoretical interpretation is provided. Both applications of the DML are supported by the comparison with experimental data. The phenomenology of liquids, either pure or mixtures, submitted to external force fields is characterized by coupled effects, for instance mechano-thermal and thermo-mechanical effects, depending on whether the application of a mechanical force field generates a coupled thermal effect in the liquid sample or vice-versa. Although these phenomena have been studied since their discoveries, dating back to the XIX century, no firm theoretical interpretation exists yet. Very recently the mesoscopic model of liquids DML has been proposed and its validity and applicability demonstrated in several cases. According to DML, liquids are arranged on a mesoscopic scale by means of aggregates of molecules, or liquid particles. These structures share the liquid world with a population of lattice particles, i.e., elastic waves that interact with the liquid particles by means of an inertial force, allowing the mutual exchange of energy and momentum between the two populations. The hit particle relaxes the acquired energy and momentum due to the interaction, giving them back to the system a step forward and a time-lapse later, alike in a tunnel effect.

Determination of diffusivities in binary fluid mixtures with various Lewis numbers as well as positive and negative Soret coefficients by the shadowgraph method.

The present work demonstrates the accessibility of the Fick diffusion coefficient D11 and/or the thermal diffusivity a of the binary mixtures dicyclohexylmethane/diphenylmethane, n-hexane/carbon dioxide, 1-hexanol/carbon dioxide, and methane/propane by the analysis of the dynamics of non-equilibrium fluctuations using the shadowgraph method. It is evidenced that D11 and a can be simultaneously determined for binary mixtures with Lewis numbers Le = a/D11 ranging over two orders of magnitude down to Le ≈ 5 or in the presence of minor advection for binary mixtures possessing a negative Soret coefficient in the investigated temperature and pressure ranges from (298.15 to 473.15) K and from about (0.5 to 25) MPa. The determined diffusivities are compared with those measured by heterodyne dynamic light scattering or obtained from the literature, with a focus on achievable uncertainties. By this comparison, it is shown that the determination of a by the shadowgraph method was hindered by mode-coupling effects for Le ≈ 5, whereas a determination of D11 was always possible for mixtures with Le ≥ 5. Furthermore, it is demonstrated that even in the presence of solutal advection, the description of the purely diffusive behavior of non-equilibrium fluctuations in concentration remains valid.

Melting of micro/nanoparticles in an alloy melt with the Soret effect

ABSTRACT The melting of micro/nanoparticles considering the Soret effect in an alloy melt is studied in terms of the asymptotic method. The results reveal that the positive Soret coefficient weakens the dynamic disequilibrium near the interface, and then enhances the melting temperature of the particle and decreases the melting speed of the particle. The negative Soret coefficient strengthens the dynamic disequilibrium near the interface, and then reduces the melting temperature of the particle and increases the melting speed of the particle. The positive Soret coefficient weakens the accumulation of the solute flux near the interface and enhances the solute concentration. The negative Soret coefficient strengthens the accumulation of the solute flux near the interface and reduces the solute concentration. The size dependence of the melting temperature considering the Soret coefficient is quantitatively consistent with the experimental data, especially for the micro/nanoparticles with a radius smaller than 5 nm.

Fick diffusion coefficients probed by the shadowgraph method considering confinement and advection.

The present work contributes to the development of the shadowgraph method for its routine application for an accurate determination of the Fick diffusion coefficient D11 of binary fluid mixtures. In this context, measurement and data evaluation strategies for thermodiffusion experiments where confinement and advection are potentially present are elaborated by studying two binary liquid mixtures with positive and negative Soret coefficients, i.e., 1,2,3,4-tetrahydronaphthalene/n-dodecane and acetone/cyclohexane. For obtaining accurate D11 data, the dynamics of non-equilibrium fluctuations in concentration is analyzed considering recent theory by data evaluation procedures that are demonstrated to be suitable for different experimental configurations.

Effect of an excess of surfactant on thermophoresis, mass diffusion and viscosity in an oily surfactant-stabilized ferrofluid.

The effect of an excess of surfactant on the thermophoresis of a sterically stabilized ferrofluid is investigated experimentally by forced Rayleigh scattering (FRS). The experiments are performed with a stable magnetic fluid sample to which controlled amounts of surfactant are added. A decrease in the thermally induced transport of magnetic nanoparticles is observed while increasing the temperature T. The positive Soret coefficient [Formula: see text] decreases by adding 2vol% of surfactant at room temperature. As shown by FRS relaxation, this decreasing is mainly associated with a reduction of the interaction between the carrier fluid and individual nanoparticles. No significant effect of extra surfactant on the sign of [Formula: see text] is observed at higher T's (up to [Formula: see text]C). Dynamic light scattering at room temperature reveals the presence of a small amount of clusters/aggregates in the samples, which are hardly detectable by FRS relaxation. The presence of these small clusters/aggregates is confirmed by a rheological probing of the fluid properties. Whatever T, a small amount of added surfactant first causes a decrease of the ferrofluid viscosity, associated with a 10% decreasing of the flow activation energy. Further on, viscosity and activation energy both recover at higher excess surfactant concentrations. These results are analyzed in terms of saturation of the surfactant layer, concentration of free surfactant chains and heat of transport of the nanoparticles.

Thermodiffusive effect on the local Debye-length in an electroosmotic flow of a viscoelastic fluid in a slit microchannel

This work theoretically studies the influence of the thermodiffusive effect on the local Debye length thickness in a purely electroosmotic flow in a parallel flat plate microchannel. An imposed electric field between the ends of the microchannel interacts with an ionized viscoelastic fluid causing Joule heating, which induces a temperature gradients along the microchannel, affecting the fluid’s physical properties, and in a notable manner, the ionic distribution into the electric double layer (EDL), resulting in thermodiffusion. Consequently, an induced pressure field counterbalances the axial variation of the plug-like electroosmotic velocity to maintain the fluid mass continuity. Also, the ionic distribution and electrical potential based on the non-isothermal Poisson-Boltzmann equation are modified. To estimate the local Debye length thickness, the coupled set of the Poisson-Boltzmann, momentum, and energy equations are solved numerically in the limit of the lubrication approximation theory (LAT). Our results indicate that the thermodiffusion has an important effect on the thickness of the local Debye-length, particularly in the warm zone of the fluid. Besides, the ionic response to thermal fields is given by a positive Soret coefficient, which indicates that the ionic particles move from warm to cold regions in the fluid, giving place to a thinner Debye length and lower ionic concentration around the warming zone; this migration of ions confirms that the dimensionless mass-flow rate is affected with the Soret coefficient compared with the non-thermodiffusion case.

Positive and negative soret and dufour mechanism on unsteady heat and mass transfer flow in the presence of viscous dissipation, thermal and mass buoyancy

ABSTRACT The combined effects of positive and negative Soret and Dufour on unsteady heat and mass transfer flow in the presence of viscous dissipation, thermal and mass buoyancy is considered. The governing boundary layer equations are formulated to be coupled, nonlinear partial differential equations and are non-dimensionalised. A robust, efficient and accurate spectral relaxation method is used to solve the dimensionless, unsteady, nonlinear and coupled partial differential equations. All pertinent flow parameters are analysed and presented graphically. The effect of flow parameters on the physical quantities of engineering interest is also tabulated. It was found out that the negative Soret reversed the concentration profile while negative Dufour reversed the temperature profile. The present results are compared with previous works and were found to be in good agreement.

Determination of thermodynamic and microscopic origins of the Soret effect in sodium silicate melts: Prediction of sign change of the Soret coefficient.

The Soret effect in silicate melts has attracted attention in earth and material sciences, particularly in glass science and engineering, because a compositional change caused by the Soret effect modifies the material properties of silicate melts. We investigated the Soret effect in an Na2O-SiO2 system, which is the most common representative of silicate melts. Our theoretical approach based on the modified Kempers model and non-equilibrium molecular dynamics simulation was validated for 30Na2O-70SiO2(mol. %). The sign and order of the absolute values of the calculated Soret coefficients were consistent with the experimental values. The positive Soret coefficient of SiO2 in the SiO2-poor composition range was accurately predicted. Previous experimental studies have focused on SiO2-rich compositions, and only the negative sign, indicating SiO2 migration to the hot side, has been observed. In the SiO2-poor composition range, the Q0 structure was dominant and had four Si-O-Na bonds around an SiO4 unit. The Si-O-Na bond had high enthalpic stability and contributed to the large negative enthalpy of SiO2 mixing. According to our model, components with a large negative partial molar enthalpy of mixing will concentrate in the cold region. The microscopic and thermodynamic origins of the sign change in the Soret effect were determined.

Stability of Stationary Plane-Parallel Flow of Binary Fluid with the Soret Effect in Vertical Layer with Differentially Heated Boundaries

Stability of stationary plane-parallel flow of binary mixture with the Soret effect in vertical layer with differentially heated boundaries is studied. Main attention is paid to the thermal wave instability mode. The dependence of the threshold value of Prandtl number Pr∗, at which the growing thermal wave appear, on the separation ratio e is obtained. Complex scenario of stability change with respect to thermal waves is discovered for the case of positive Soret effect: it is shown that for e Pr∗, with the increase in separation ratio, additional range of growing thermal waves appears near Pr = 0, for e > 0.2634 the thermal wave instability exists at $$ 0\le \mathit{\Pr}\le {\mathit{\Pr}}_1^{\ast } $$ and at $$ \mathit{\Pr}>{\mathit{\Pr}}_2^{\ast } $$. For e > 0.278 the thermal wave instability is possible at any values of Prandtl number.

Separation under thermogravitational effects in binary mixtures.

In the present work, by using a parallelepipedic thermogravitational microcolumn, the temperature gradient influence on the stability of the flow has been examined, emphasizing mixtures with positive Soret coefficients. Experiments were conducted for DCMIX2 Toluene/Methanol and DCMIX3 Water/Ethanol binary subsystems because of their broad range of positive Soret values for high concentrations of methanol and ethanol, respectively. Two different mixtures have been studied here in order to confirm the thermogravitational stability of the mixtures. Experiments were compared with numerical simulations carried out using the open-source software platform OpenFOAM.

The Soret effect in ternary mixtures of water+ethanol+triethylene glycol of equal mass fractions: Ground and microgravity experiments.

Measurements of the Soret and thermodiffusion coefficients of a symmetric ternary mixture with equal mass fractions of water, ethanol, and triethylene glycol have been performed by two-color optical beam deflection (2-OBD) and the thermogravitational column technique (TGC) in the laboratory and under microgravity conditions in the Selectable Optical Diagnostics Instrument (SODI) aboard the International Space Station. The results from all three experimental techniques agree within the experimental error bars, which result mainly from the inversion of the contrast factor matrices. TGC shows by far the lowest, 2-OBD the highest error amplification. The microgravity measurements are in between. The agreement with the microgravity results shows that thermosolutal convection could be well controlled in the 2-OBD experiments by a proper orientation of the temperature gradient. Despite the different condition numbers, the results are invariant under the choice of the independent compositions. Based on the orientation of the confidence ellipsoid in the ternary composition diagram, not all coefficients are equally affected by experimental errors. Although there are appreciable uncertainties for water and ethanol, the Soret and the thermodiffusion coefficients of triethylene glycol could be obtained with a good accuracy due to the favorable orientation of the confidence ellipsoid. We have found that water behaves thermophobic, corresponding to a positive Soret coefficient, whereas both ethanol and triethylene glycol are thermophilic with negative Soret coefficients. This resembles the behaviour of the binary system ethanol/water above the ethanol concentration of the sign change.

Soret and Dufour effects on double diffusive mixed convection of Newtonian and shear-thinning fluids in a two sided lid-driven cavity

Purpose The thermal-diffusion (Soret) and the diffusion-thermo (Dufour) effects play a crucial role in double diffusive mixed convection in a lid-driven cavity; but they have not been studied properly by researchers. The purpose of this paper is to investigate effects of Soret and Dufour parameters on double diffusive laminar mixed convection of shear-thinning and Newtonian fluids in a two-sided lid-driven cavity. Design/methodology/approach Finite Difference Lattice Boltzmann method (FDLBM) has been applied to solve the complex problem. This study has been conducted for the certain pertinent parameters of Richardson number (Ri=0.00062-1), power-law index (n=0.2-1), Soret parameter (Sr=−5-5) as Dufour number effects have been investigated from Dr=−5 to 5 at Buoyancy ratio of N=1 and Lewis number of Le=5. Findings Results indicate that the augmentation of Richardson number causes heat and mass transfer to decrease. The fall of the power-law index declines heat and mass transfer at Ri=0.00062 and 0.01 in various Dufour and Soret parameters. At Ri=1, the heat and mass transfer rise with the increment of power-law index for Dr=0 and Sr=0. The least effect of power-law index on heat and mass transfer among the studied Richardson numbers was observed at Ri=1. The positive Dufour numbers augment the heat transfer gradually as the positive Soret numbers enhance the mass transfer. The Dr=−5 and Sr=−5 provokes the negative average Nusselt and Sherwood numbers, respectively, to be generated. The least magnitude of the average Nusselt and Sherwood numbers were obtained at Dr=−1 and Sr=−1, respectively. Originality/value Soret and Dufour effects in double diffusive mixed convection has not been studied in a lid-driven cavity. In addition. this study has been conducted also for shear-thinning fluids.

Competition between phase transition and thermophoretic expansion of a transient poly(N-isopropylacrylamide) network.

Aqueous solutions of highly entangled ultra-high molar mass ( 2.4×106 g/mol) poly(N-isopropylacrylamide) (PNIPAM) have been subjected to an inhomogeneous temperature field by selective heating of a single embedded gold nanoparticle (GNP) by means of a focused laser beam. Randomly distributed tracer GNPs are trapped in the meshes of the transient entanglement network and serve as tracers for the monitoring of the network deformation field. Because of the positive Soret coefficient of PNIPAM in water, the viscoelastic polymer network is expanded by thermophoretic forces pointing away from the hot center. Close to the heated GNP the thermoresponsive polymer solution crosses the binodal and the network contracts, which is made visible by an inward motion of tracer GNPs, which are randomly embedded in the polymer network and not illuminated by the laser beam. Within a thin transition zone the network contraction and the competing thermophoretic network expansion cancel out in the steady state. There is, however, no cancellation during the transients due to the different time scales of both mechanisms. The network within the crossover region first undergoes an expansion that is followed by a slower contraction. From the global expansion and contraction, the local strain (stretching and compression) of the transient network can be calculated. Due to the long disentanglement times, corresponding to long lifetimes of the meshes of the network, the whole process is fully reversible.

Soret effect on the double diffusive convection instability due to viscous dissipation in a horizontal porous channel

The effect of the Soret parameter on the convective stability of double diffusive convection solely because of the viscous dissipation in a horizontal porous channel is studied. The lower boundary is adiabatic whereas the upper boundary is considered to be isothermal. The convective stability of the present system is governed by the solutal Rayleigh number (R) and is influenced by the viscous dissipation parameter (ξ), Lewis number (Le) and Soret parameter (Sr). For non positive values of the Soret parameter, the longitudinal rolls happen to be the most unstable ones when ξ takes small values. With positive values of the Soret parameter, the transverse rolls are seen to be the most unstable for relatively smaller values of the viscous dissipation parameter. As the viscous dissipation effect becomes stronger, the longitudinal rolls become the most unstable ones even for positive Soret parameter and the transverse rolls become more unstable for non-positive Soret parameter. It is observed that the Soret parameter has significant effect on convective instability and this is discussed. It has also been noticed that viscous dissipation shows a dual effect in presence of the Soret effect. For fixed values of the viscous dissipation parameter and Lewis number, negative values for the Soret number advances the onset of convection. Though positive values of the Soret parameter stabilizes the flow with smaller values of the Lewis number, but it destabilizes the flow when Lewis number and viscous dissipation parameter take larger values.

Involvement of propionate side chains of the heme in circular dichroism of myoglobin: experimental and theoretical analyses.

Incorporation of the heme into globin induces a prominent circular dichroism (CD) band in the Soret region. The appearance of heme optical activity is widely believed to arise from the interaction between the heme and aromatic residues of the globin. However, hemoglobin (Hb) containing the reversed heme exhibits a CD spectrum obviously different from that of native Hb, indicating that the interactions of heme side chains with globin contribute to the appearance of heme optical activity. We examined this possibility by comparing CD spectra of native myoglobin (Mb) and those of Mb reconstituted with synthetic hemes lacking vinyl and/or propionate. Replacement of 2,4-vinyl groups with methyl induced moderate changes. In contrast, replacement of 6,7-propionate groups with carboxylate resulted in complete disappearance of the positive Soret CD band. To get theoretical basis for the contributions of 6,7-side chains on the band, we investigated the CD spectra at a time-dependent density functional theory level. In the antiparallel conformation of the 6,7-side chains, the rotational strengths were calculated to be positive, on the other hand in the parallel conformation to be negative. We also found that the weak Soret CD band in 2,4-dimethyl-6,7-dicarboxyheme can be explained by canceling between different carboxyl conformers.

Thermodiffusion as a close-to-interface effect that matters in non-isothermal (dis)orderly protein aggregations

Abstract The goal of this discussion letter is to argue how and why an inherent nanoscale thermodiffusion (Soret-type) effect can be relevant in (dis)orderly protein aggregation. We propose a model in which the aggregation of proteins, in the presence of temperature gradient, is described in terms of Smoluchowski dynamics in the phase space of nuclei sizes. The Soret coefficient of the aggregation is proportional to the variations of the aggregation free energy over temperature. The free energy is related to the (interface) boundary condition of the system. When boundary condition is of equilibrium Gibbs–Thomson type, with a well-stated surface tension of the nucleus, to the system can be assigned a negative Soret effect. On the contrary, when a non-equilibrium perturbing (salting-out) term enters the boundary condition, a positive Soret effect may manifest. A zero-value Soret regime is expected to occur in between, yielding very soft (“fragile”) non-Kossel protein-type crystals.

Circular Dichroism of Hemoglobin and Myoglobin

While heme alone does not exhibit circular dichroism (CD) spectrum, it exhibits a prominent positive CD band in the Soret region when incorporated into apoglobin of myoglobin (Mb) and hemoglobin (Hb). The appearance of this optical activity is widely accepted to arise from the interactions between the heme and aromatic residues of the globin. However, the reversed heme orientation in Hb was found to exhibit a CD spectrum obviously different from that of native Hb, indicating that the interactions of side chains of heme with globin also contribute to the appearance of heme optical activity. We examined this possibility by comparing CD spectra of native Mb and those of Mb reconstituted with unnatural heme lacking the vinyl and/or propionate. Replacement of vinyls at the 2,4-positions with methyls induced a 30% decrease in CD intensity of the positive Soret CD band without changes of spectral shape. In contrast, the replacement of the propionate at the 6,7-positions with carboxylic acid groups resulted in almost complete disappearance of the Soret CD band. These results seem to suggest that interactions of heme side chains, especially 2,4-vinyls and 6,7-propionates, with globin, as well as the electronic coupling of the heme bands with those of intrinsic protein chromophores, contribute to the appearance of the prominent positive Soret CD band of Mb and Hb.