Thermoosomosis in microfluidic devices containing a temperature gradient normal to the channel walls

We analyze a microfluidic pump from the literature that utilizes a flat channel with boundary walls at different temperatures and tilted elongated pillars within in order to construct an adequate theory for designing devices in which the temperature gradient between channel walls is transformed into a longitudinal temperature gradient along the channel length. The action of the device is based on thermoosmosis in the secondary longitudinal temperature gradient associated with the specific geometry of the device, which can be described using physicochemical hydrodynamics without invoking the concept of thermophoretic force. We also describe a rotating drive device based on the same principle and design.

Coupled non-equilibrium fluctuations in a polymeric ternary mixture

We investigate by dynamic shadowgraphy the non-equilibrium fluctuations at the steady state of a thermodiffusion experiment in a polymeric ternary mixture of polystyrene-toluene-n-hexane. The structure function of the refractive index reveals the existence of quite different decay times, thus requiring the analysis of a wide range of correlation times. This is related to the simultaneous presence of three distinct decay modes corresponding to (from fastest to slowest) the relaxation of temperature fluctuations, of the concentration fluctuations of the mixed solvent, and of the concentration fluctuations of the polymer in the binary solvent. An investigation of the decay times at the corresponding diffusive regimes provides a measurement of the thermal diffusivity and the two eigenvalues of the mass diffusion matrix of the ternary mixture. Similar experiments were performed in the past but here, to suppress the confinement effect and obtain a more direct comparison with the theory, a thicker sample is studied. Moreover, also a faster camera is used allowing the experimental observation of faster modes, like the propagative ones. The experimental values of the decay times are eventually compared with those predicted by different available theories. Finally, we present a more complete theoretical model to describe the non-equilibrium fluctuations in the bulk of a ternary mixture at the steady state of a thermodiffusion experiment.

Thermodiffusion and hydrolysis of 1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC)

Presently, microfluidic traps are designed mimicking the environment of hydrothermal pores, where a combination of thermophoresis and convection leads to accumulation so that high concentrations of organic matter can be reached. Such a setup is interesting in the context of the origin of life to observe accumulation and possible further synthesis of small organic molecules or prebiotic molecules such as nucleotides or RNA-fragments, but could also be used to replicate DNA-strands. The addition of coupling agents for the activation of carboxyl or phosphate groups such as 1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) and EDC-hydrochloride (EDC-HCl) is necessary in order to speed up the process. This work characterizes the thermophoretic properties of EDC and EDC-HCl needed to optimize the design of the traps. At p H 4-6 spontaneous hydrolysis of EDC is observed, which also leads to a neutralisation of the p H. In order to evaluate the thermodiffusion measurements the rate constants were measured at 23 and [Formula: see text] C and the activation energy of the hydrolysis calculated.

A thermomechanical coupling in cholesteric liquid crystals: Unidirectional rotation of double-twist cylinders driven by heat flux

We made aggregates of cholesteric liquid crystalline Cylinders with Double-Twist orientational structure (DTC) and investigated their rigid-body rotation under a temperature gradient, focusing on how the rotational speed should depend on the cylinder size. The experimental results showed that the angular velocity of the DTC aggregates linearly increased with the height of the cylinders and was inversely proportional to the base area. With a phenomenological equation, we analyzed the torque caused by the heat flux and its balance with the viscous friction, and found that the simple analysis well explained the size-dependence of the rotation of the DTC aggregates. The coupling constant between the heat flux and the torque to drive the rigid-body rotation was in the same order of magnitude as that for the director rotation.

Limiting diffusion coefficients of [Formula: see text],[Formula: see text]-amino acids in water and in sodium chloride aqueous solutions at 298.15 K

Transport properties of model compounds in aqueous solutions such as amino acids can provide valuable information in order to understand the complex interactions in aqueous solutions as well as the protein stability in water and the relevant factors involved. Informations about the diffusion of amino acids in water and in aqueous solutions of sodium chloride are very scarce, especially for the 5-aminopentanoic acid and 6-aminohexanoic acid. In this study, limiting binary mutual diffusion coefficients at 298.15 K of 5-aminopentanoic and 6-aminohexanoic acids in aqueous solutions of NaCl 0.15 mol kg^-1, using the Taylor dispersion technique, were determined and the results compared with the limiting binary mutual diffusion coefficients for 2-aminopentanoic acid, and 2-aminohexanoic acid, obtained in the same experimental conditions. The discussion of the properties of the selected amino acids is centered on the positions of the ionic groups in the hydrocarbon chain and, in addition, we have discussed the effects of NaCl on their structures and properties. The data on diffusion properties are supported by ¹H, ¹³C and ²³Na NMR experiments, which we have obtained for 5-aminopentanoic and 6-aminohexanoic acids, in aqueous solution, also in the presence of NaCl.

Thermal orientation and thermophoresis of anisotropic colloids: The role of the internal composition

The drift motion experienced by colloids immersed in a fluid with an intrinsic temperature gradient is referred to as thermophoresis. An anisotropic mass distribution inside colloidal particles imparts a net orientation with respect to the applied thermal field, and in turn alters the thermophoretic response of the colloids. This rectification of the rotational Brownian motion is called thermal orientation. To explore the sensitivity of the thermal orientation effect with the internal composition of colloids, we investigate the thermophoretic response of rod-like colloids in the dilute regime, targeting different internal mass distributions. We derive phenomenological equations to model the dependence of the Soret coefficient with degree of mass anisotropy and test these equations using non-equilibrium molecular dynamics simulations. Using both theory and simulation, we show that the average orientation and the Soret coefficients of the colloids can depend significantly on the internal mass distribution. This observation suggests an approach to identify internal colloidal compositions using thermal gradients as sensing probes.

Preliminary analysis of Diffusion Coefficient Measurements in ternary mIXtures 4 (DCMIX4) experiment on board the International Space Station

In the frame of the Diffusion Coefficient Measurements in ternary mIXtures 4 (DCMIX4) project the thermodiffusion experiments were conducted on the International Space Station (ISS) in the Selectable Optical Diagnostics Instrument (SODI) which is on orbit since 2009. We describe the results of the preliminary analysis of images downloaded during the execution of DCMIX4 in order to check the quality of the running experiments and, if needed, adjust the experiment parameters for the following runs. The quick analysis of raw data showed that they are meaningful and will allow to obtain the transport coefficients of examined ternary and binary mixtures.

European Space Agency experiments on thermodiffusion of fluid mixtures in space

This paper describes the European Space Agency (ESA) experiments devoted to study thermodiffusion of fluid mixtures in microgravity environment, where sedimentation and convection do not affect the mass flow induced by the Soret effect. First, the experiments performed on binary mixtures in the IVIDIL and GRADFLEX experiments are described. Then, further experiments on ternary mixtures and complex fluids performed in DCMIX and planned to be performed in the context of the NEUF-DIX project are presented. Finally, multi-component mixtures studied in the SCCO project are detailed.

On the thermodiffusion effect in vertical plate heat exchangers

The subject of the transport phenomena has a pivotal role in the performance of aqueous lithium bromide falling film absorbers. Although the thermodiffusion phenomenon appears inside the solution, very little is known about its influence on the mass transport. This study numerically analyses the influence of the thermal mass transfer mechanism on a vertical plate-type heat exchanger for different Reynolds numbers ([Formula: see text]). Results indicate that, in general, the mass transfer caused by the temperature gradient enhances the total absorption because of the negative Soret coefficient of the salt solution. This improvement is found to be higher at higher Reynolds numbers. Furthermore, the concentration and temperature profiles and, therefore, the absorption change significantly along the flow length. Overall, this analysis assists the understanding of the role of the thermal mechanism in this type of absorbers and it demonstrates that it should be considered in future studies.

Configurational contribution to the Soret effect of a protein ligand system : An investigation with density-of-states simulations

Many of the biological functions of proteins are closely associated with their ability to bind ligands and change conformations in response to changing conditions. Since binding state and conformation of a protein affect its response to a temperature gradient, they may be probed with thermophoresis. In recent years, thermophoretic techniques to investigate biomolecular interactions, quantify ligand binding, and probe conformational changes have become established. To develop a better understanding of the mechanisms underlying the thermophoretic behavior of proteins and ligands, we employ a simple, off-lattice model for a protein and ligand in explicit solvent. To investigate the partitioning of the particles in a temperature gradient, we perform Wang-Landau-type simulations in a divided simulation box and construct the density of states over a two-dimensional state space. This method gives us access to the entropy and energy of the divided system and allows us to estimate the configurational contribution to the Soret coefficient. In this work, we focus on dilute solutions of hydrophobic proteins and investigate the effect of ligand binding on their thermophoretic behavior. We find that our simple model captures important aspects of protein-ligand interactions and allows us to relate the binding energy to the change in Soret coefficient upon ligand binding.

Nonlinear regimes of Soret-driven convection of ternary fluid with fixed vertical heat flux at the boundaries

Nonlinear regimes of the Soret-induced convection of a ternary mixture in a rectangular cavity with the vertical heat flux at the boundaries are studied numerically. Linear stability analysis performed earlier for a plane horizontal layer has shown that in a wide range of parameters the longwave instability is dominant. Nonlinear calculations performed in the present work for the parameter ranges where the monotonic longwave instability is dominant according to the linear stability analysis, show that at large supercriticalities the multi-vortex stationary flows could be realized. With the decrease of absolute value of the Rayleigh number Ra the series of flow structure transformations takes place. This transformation is accompanied by the decrease of a number of the vortices such that near the threshold the flow becomes two-vortex, i.e. the flow with maximum possible wavelength (minimum possible wave number) is realized. Thus, the nonlinear calculations confirm the conclusions of the linear stability analysis that the longwave instability is dominant. For the parameter ranges where according to the linear stability analysis the oscillatory longwave instability is dominant, the nonlinear calculations show that at small values of the net separation ratio the oscillatory regimes could be observed just in a narrow range of Ra close to the convection threshold and with the growth of net separation ratio the range of Ra where they can be observed is extended.

Inversion of thermodiffusive properties of ionic colloidal dispersions in water-DMSO mixtures probed by forced Rayleigh scattering

Thermodiffusion properties at room temperature of colloidal dispersions of hydroxyl-coated nanoparticles (NPs) are probed in water, in dimethyl sulfoxide (DMSO) and in mixtures of water and DMSO at various proportions of water, [Formula: see text]. In these polar solvents, the positive NPs superficial charge imparts the systems with a strong electrostatic interparticle repulsion, slightly decreasing from water to DMSO, which is here probed by Small Angle Neutron Scattering and Dynamic Light Scattering. However if submitted to a gradient of temperature, the NPs dispersed in water with ClO₄^- counterions present a thermophilic behavior, the same NPs dispersed in DMSO with the same counterions present a thermophobic behavior. Mass diffusion coefficient [Formula: see text] and Ludwig-Soret coefficient [Formula: see text] are measured as a function of NP volume fraction [Formula: see text] at various [Formula: see text]. The [Formula: see text]-dependence of [Formula: see text] is analyzed in terms of thermoelectric and thermophoretic contributions as a function of [Formula: see text]. Using two different models for evaluating the Eastman entropy of transfer of the co- and counterions in the mixtures, the single-particle thermophoretic contribution (the NP's Eastman entropy of transfer) is deduced. It is found to evolve from negative in water to positive in DMSO. It is close to zero on a large range of [Formula: see text] values, meaning that in this [Formula: see text]-range [Formula: see text] largely depends on the thermoelectric effect of free co- and counterions.

Correlation between thermophoretic behavior and hydrophilicity for various alcohols⋆

Recent experiments for various amides and sugars showed a clear correlation of the temperature dependence of the Soret coefficient with the hydrophilicity, quantitatively described by the logarithm of the 1-octanol/water partition coefficient log P . This coefficient is a measure for the hydrophilicity/hydrophobicity balance of a solute and is often used to model the transport of a compound in the environment or to screen for potential pharmaceutical compounds. In order to validate whether this concept works also for other water soluble molecules we investigated systematically the thermophoresis of mono- and polyhydric alcohols. As experimental method we use a holographic grating technique called infrared Thermal Diffusion Forced Rayleigh Scattering (IR-TDFRS). Experiments showed that the temperature dependence of the Soret coefficient of polyhydric alcohols also correlates with log P and lies on the same master plot as amides and sugars.

Linking up pressure, chemical potential and thermal gradients

Petroleum reservoirs are remarkable illustrations of the impact of a thermal gradient on fluid pressure and composition. This topic has been extensively studied during the last decades to build tools that are required by reservoir engineers to populate their models. However, one can get only a very limited number of representative samples from a given reservoir and assessing connectivity between all sampling points is often a key issue. In some extreme cases, the whole reservoir fluid properties must be derived from a single point to define the field development plan. To do so, available models are usually not satisfactory as they need too many parameters and so cannot be considered as predictive tools. We propose in this work a comprehensive approach based on the irreversible thermodynamics principles to derive the relationships between pressure, chemical potentials and thermal gradients in porous media. It appears that there is no need for additional assumptions, it is just a matter of a making the right choices along theoretical developments. One of the most important steps is to express the full pressure gradient. As a final result, we obtain the chemical potential gradients for all components of the mixtures that can be easily translated in term of compositions through Equation of State modelling. The most important features of the final expressions are: i) the species relative separation in a thermal field is sensitive to the relative diffusion coefficients at stationary state. In porous media, the separation is sensitive to the permeability when the overall mobility is similar to diffusive mobility; ii) the magnitude of the separation depends on the residual entropy of the species; iii) the separation is not simply balanced by the average residual entropy. The balance is modified by the relative diffusion mobility of the components; iv) in low permeability porous media, the thermal gradient induces a pressure gradient proportional to the fluid residual entropy. As a validation, the proposed approach has been applied on a reservoir fluid subjected to a geothermal gradient and compared with non-equilibrium molecular dynamics simulation results at the stationary state.

Species separation of a binary mixture under acoustic streaming

An analytical and numerical study of the action of ultrasonic waves on species separation within a rectangular cavity filled with a binary fluid (water-ethanol mixture) is presented. An ultrasonic wave was emitted on a portion of one of its vertical walls, while the opposite wall was perfectly absorbent. The two horizontal walls were differentially heated. A progressive acoustic wave was used to generate, at a large scale, a stationary flow of the viscous binary fluid (Eckart Streaming) within the cavity. The authors analytically determined the temperature T, mass fraction C and velocity fields under the parallel flow hypothesis used for cells with high aspect ratio [Formula: see text], in the presence of the gravitational field. From the analysis of the velocity fields the authors concluded that the associated flow is either unicellular or consists of three counter-rotating cells superimposed in the horizontal direction of the cavity. They also found the variation domains of the physical parameters leading to one or the other of these two types of flows. The algebraic equation allowing the calculation of the mass fraction gradient and hence the species separation between the vertical walls of the cavity was determined. The variation of the dimensional mass fraction gradient, for the water-ethanol mixture, as a function of the two control parameters of the problem, namely the acoustic parameter A and the temperature difference [Formula: see text] imposed on the two horizontal walls was studied.

Elemental and isotopic fractionation of noble gases in gas and oil under reservoir conditions: Impact of thermodiffusion⋆

Noble gases, and the way they fractionate, is a promising approach to better constrain origin, migration and initial state distributions of fluids in gas and oil reservoirs. Thermodiffusion, is one of the phenomena that may lead to isotope and elemental fractionation of noble gases. However, this effect, assumed to be small, has not been quantified, nor measured, in oil and gas under reservoir conditions. Thus, in this work, molecular dynamics simulations have been performed to compute the thermal diffusion factors of noble gases, in a dense gas (methane) and in an oil (n-hexane) under high pressures. Interestingly, it has been found that thermal diffusion factors, associated to both isotopic (³⁶Ar, ⁴⁰Ar) and elemental fractionations of noble gases (⁴He, ²⁰Ne, ⁴⁰Ar, ⁸⁴Kr and ¹³¹Xe) in gas and oil, could be expressed as linear functions of the reduced masses. Regarding the amplitude of the phenomena, it has been found that, in a stationary 1D oil or gas fluid column, thermodiffusion due to a typical geothermal gradient has an impact on noble gas isotopic and elemental fractionation which is of the same order of magnitude than gravity segregation, but opposite in sign. In addition, the relative impact of thermodiffusion on isotopic and elemental fractionations depends on the fluid type which is another interesting feature. Thus, these first numerical results on isotopic and elemental fractionation of noble gases by thermodiffusion in simple pure gas and oil emphasize their interest as natural tracers that could be used to improve the pre-exploitation description of oil and gas reservoirs.

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 coefficient from the Faxén theorem for a particle moving in a fluid under a temperature gradient

We compute the Soret coefficient for a particle moving through a fluid subjected to a temperature gradient. The viscosity and thermal conductivity of the particle are in general different from those of the solvent and its surface tension may depend on temperature. We find that the Soret coefficient depends linearly on the derivative of the surface tension with respect to temperature and decreases in accordance with the ratios between viscosities and thermal conductivities of particle and solvent. Additionally, the Soret coefficient also depends on a parameter which gives the ratio between Marangoni and shear stresses, a dependence which results from the local stresses inducing a heat flux along the particle surface. Our results are compared to those obtained by using the Stokes value for the mobility in the calculation of the Soret coefficient and in the estimation of the radius of the particle. We show cases in which these differences may be important. The new expression of the Soret coefficient can systematically be used for a more accurate study of thermophoresis.

Definition of frame-invariant thermodiffusion and Soret coefficients for ternary mixtures

The definitions of thermodiffusion and Soret coefficients for a binary mixture include a concentration prefactor x(1 - x), when mole fraction x is used, or w(1 - w), when mass fraction w is used. In this paper the physical reasons behind this choice are reviewed, emphasizing that the use of these prefactors makes the thermodiffusion and the Soret coefficients invariant upon changing in the concentration representation, using either mole fraction or mass faction. Then, it is shown how this invariance property can be extended to ternary mixtures by using appropriate concentration prefactors in matrix form. The paper is completed with some considerations about alternative definitions of thermodiffusion coefficients, binary limits of the concentration triangle, selection of the dependent concentration in a ternary mixture, use of molar concentrations and, finally, extension to multi-component mixtures.

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.

Kinetics of growth of non-equilibrium fluctuations during thermodiffusion in a polymer solution

A thermal diffusion process occurring in a binary liquid mixture is accompanied by long ranged non-equilibrium concentration fluctuations. The amplitude of these fluctuations at large length scales can be orders of magnitude larger than that of equilibrium ones. So far non-equilibrium fluctuations have been mainly investigated under stationary or quasi-stationary conditions, a situation that allows to achieve a detailed statistical characterization of their static and dynamic properties. In this work we investigate the kinetics of growth of non-equilibrium concentration fluctuations during a transient thermodiffusion process, starting from a configuration where the concentration of the sample is uniform. The use of a large molecular weight polymer solution allows to attain a slow dynamics of growth of the macroscopic concentration profile. We focus on the development of fluctuations at small wave vectors, where their amplitude is strongly limited by the presence of gravity. We show that the growth rate of non-equilibrium fluctuations follows a power law [Formula: see text] as a function of time, without any typical time scale and independently of the wave vector. We formulate a phenomenological model that allows to relate the rate of growth of non-equilibrium fluctuations to the growth of the macroscopic concentration profile in the absence of arbitrary parameters.

Determining phoretic mobilities with Onsager's reciprocal relations: Electro- and thermophoresis revisited

We use a hydrodynamic reciprocal approach to phoretic motion to derive general expressions for the electrophoretic and thermophoretic mobility of weakly charged colloids in aqueous electrolyte solutions. Our approach shows that phoretic motion can be understood in terms of the interfacial transport of thermodynamic excess quantities that arises when a colloid is kept stationary inside a bulk fluid flow. The obtained expressions for the mobilities are extensions of previously known results as they can account for different hydrodynamic boundary conditions at the colloidal surface, irrespective of how the colloid-fluid interaction range compares to the colloidal radius.