Thermodiffusion of rigid particles in pure liquids

Thermodiffusion of particles suspended in a pure liquid is a thorny problem which has not yet received a solution admitted by all the different communities interested in. We approach the subject with macroscopic tools exclusively, hydrodynamics and irreversible thermodynamics. These tools have proved their relevance for molecular mixtures and the Soret effect, and we here extend them to suspensions of particles with supra-molecular size. In particular, we obtain the momentum balance of the particulate phase from which are deduced all the physical phenomena inducing a migration of the particles relative to the carrier fluid. Focussing on thermodiffusion, we show that the osmotic pressure is irrelevant and that thermodiffusion cannot have but two distinct origins : the temperature dependence of the stress associated with the distorted particle microstructure and a fluid-particle interaction force involving the temperature gradient. For deformable particles, it is well known that the origin of the fluid-particle temperature gradient force is the temperature dependence of the surface tension. For rigid particles, we suggest it stems from the temperature dependence of the small density jump, the carrier liquid displays close to the particle’s surface.     

Driving forces and polymer hydrodynamics in the Soret effect

A temperature gradient induces different driving forces on the components of a mixture which translates into their segregation. We show that these driving forces constitute the physical picture behind the thermodiffusion effect, and provide an alternative expression of the Soret coefficient which can be applied to both colloidal suspensions and molecular mixtures. To verify the validity of the formalism, we quantify the related forces in an Eulerian reference frame by non-equilibrium molecular simulations. Furthermore, we present an analytical argument to show that the hydrodynamic interactions need to be accounted for to obtain the proper scaling of the thermophoretic force. This result combined with the presented expression satisfactorily explains the experimentally known size dependence of the thermodiffusion coefficient in dilute polymer solutions.     

Scaling theory of polymer thermodiffusion

The motion of a linear polymer chain in a good solvent under a temperature gradient is examined theoretically by breaking up the flexible chain into Brownian rigid rods, and writing down an equation of motion for each rod. The motion is driven by two forces. The first one is Waldmann’s thermophoretic force (stemming from the departure of the solvent’s molecular-velocity distribution from Maxwell’s equilibrium distribution) which here is extrapolated to a dense medium. The second force is due to the fact that the viscous friction varies with position owing to the temperature gradient, which brings an important correction to the Stokes law of friction. We use scaling considerations relying upon disparate length scales and omitting non-universal numerical prefactors. The present scaling theory is compared with recent experiments on the thermodiffusion of polymers and is shown to account for (i) the existence of both signs of the thermodiffusion coefficient of long chains, (ii) the order of magnitude of the coefficient, (iii) its independence of the chain length in the high-polymer limit and (iv) its dependence on the solvent viscosity.     

Role of the velocity frame of reference in thermodiffusion in liquid mixtures

The role and significance of the velocity frame of reference in the interpretation, modeling and formulation of thermodiffusion in multicomponent liquid mixtures were investigated, focused on the nonequilibrium thermodynamics modeling approach. The effect of the velocity frame of reference on the phenomenological equations and thermodiffusion coefficients and expressions is explored. Theoretically and also by the aid of representative calculations, it is shown that while in binary mixtures transformation from one frame to another does not affect the sign and magnitude of the thermodiffusion coefficients, in multicomponent mixtures (ternary and higher), even the sign of the thermodiffusion coefficients may change when an alternative frame is used. This implies that in multicomponent mixtures for either experimental data or model estimations, the employed velocity frame for the thermodiffusion coefficients plays an important role in calculations. The Soret coefficients and the thermodiffusion factors are independent of the frame of reference.     

Connection between thermophoresis and thermodiffusion in a liquid binary mixture

In a liquid suspension, thermophoresis is the motion of a suspended particle under a temperature gradient. In a liquid binary mixture, thermodiffusion is the generation of a composition gradient upon application of a temperature gradient. A quantitative connection is established between the two phenomena without making assumptions about their mechanisms. It is shown that Galilean invariance and the choice of a Galilean reference frame play a key role in that connection. The results are not restricted to very dilute suspensions or mixtures.     

Kinetic theory of inhomogeneous diffusion

This paper theoretically investigates particle diffusion in a medium where the diffusivity depends on position. We exclusively consider continuous-time, continuous-space transport and our working tool is the linear kinetic theory pertinent to guest particles in a passive host medium (Lorentz’s picture of transport). The host medium may or may not thermalize the guest particles. It may be inhomogeneous in two ways: either particle scattering features depend on position in an explicit way (geometric inhomogeneity), or they depend on position through the medium’s local temperature (thermal inhomogeneity). When the inhomogeneity is geometric, it is found that Fick’s law is valid and the particle-current equation exhibits drift without current. When the inhomogeneity is thermal, current without drift is possible, but there is no generally valid pattern for the current equation. The consistency of our results with non-equilibrium thermodynamics is brought out. The results shed light on thermodiffusion (the Ludwig-Soret effect), which often combines inhomogeneities of both kinds. Finally, a limitation of the Lorentz picture of transport in accounting for thermodiffusion is outlined.     

Reduction of sound radiation by using force radiation modes

The location of a vibration source within a machine is sometimes found to have a significant effect upon its radiated acoustic power. It is known that a simple reduction of vibration cannot always reduce the radiated acoustic power, so that treatments based on analysis of a structure’s vibration modes are not always effective. At the same time, radiation mode analysis is known to be a powerful tool for interpreting sound radiation since those modes are independent of a structure’s surface vibration. However, knowledge of the radiation modes alone cannot be used directly to understand the relationship between vibration source location and acoustic power radiation. In this paper, it is shown that the radiation mode concept can be extended to understand the relationship between acoustic power and driving force distribution by considering the product of the structure’s mobility matrix and the radiation modes: the resulting functions are here defined to be force radiation modes (f_rad-modes). An example is presented in which the acoustic power radiated by a simply-supported, baffled beam is reduced by using guidance provided by the structure’s force radiation modes. The results demonstrate that the force radiation modes can be used to guide the reduction of radiated acoustic power by changing the driving force location without the need to perform additional calculations or experiments.     

Formation of Ring-Banded Spherulites of Poly (L-lactide) in its Miscible Mixture with an Ionic Liquid

Incorporation of an ionic liquid, nonvolatile and thermally stable, promoted formation of ring-banded spherulites in poly (l-lactide) (PLLA) during its sol–gel transition. Their formation is correlated with low viscosity and insignificant chain entanglements in the mixtures induced by the ionic liquid. In addition to a driving force for lamellar twisting that depended on the crystallization temperatures, it is believed that reduced lamellar twisting resistance caused by the ionic liquid plays a vital role in the formation of the ring-banded spherulites of PLLA from the mixtures. This study gives further insights into the structural formation of PLLA during a sol–gel transition, which could open new opportunities to tailor the properties of ion gels based on PLLA.     

Joule–Thomson cooling with binary mixtures

The possibility of achieving temperatures below that of liquid nitrogen for applications in miniature one-shot Joule–Thomson (J–T) coolers using a mixture of nitrogen and neon gases is discussed. An expression for the maximum inversion temperature of binary mixtures is derived. It is shown that it is possible to achieve temperatures near the triple point of nitrogen (63 K) with a mixture of neon and nitrogen.     

Electro-optic and dielectric behavior of a FLC material having doped with a non-mesogenic polar molecules

Liquid crystal mixtures of non-mesogenic polar molecule with a commercial ferroelectric liquid crystal (FLC) mixture were prepared. Two mixtures were prepared by mixing 0.5% (w/w) and 1% (w/w) of polar molecules with commercial FLC mixture. Comprehensive studies of dielectric and electro-optic properties of the commercial FLC mixture and the polar molecules doped FLC mixtures have been made as a function of temperatures. Our studies reveal a higher tilt angle in lower concentration (0.5%) mixture but in case of 1% mixture tilt angle is decreased in comparison to 0.5% mixture. The spontaneous polarization of the commercial FLC mixture and other two mixtures is almost equal in magnitude at all temperatures. At the lower temperature region of SmC¹ phase, Goldstone mode (GM) dielectric strength of the commercial FLC mixture and low concentration (0.5%) mixture is found almost equal but it is slightly higher in case of high concentration (1%) mixture. With the increase of temperature GM dielectric strength of both the doped mixtures rapidly converges at different temperatures which are much lower than the temperature of transition (T_C) from SmC¹ – SmA phase. The results have been discussed.     

非平衡热力学中传热过程熵产表达式的修正

熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.     

The performance of non-polarizable and polarizable force-field parameter sets for ethylene glycol in molecular dynamics simulations of the pure liquid and its aqueous mixtures

Non-polarizable and polarizable force-field parameter sets for liquid ethylene glycol (EG) were developed for use in biomolecular simulation. In the polarizable models, electronic polarization effects were explicitly taken into account using the charge-on-spring method. The quality of the new force fields and two non-polarizable EG models taken from the literature was investigated by calculating relevant properties of the pure liquid and its aqueous mixtures, and comparing simulation results with experimental data. The performance of the EG models as a co-solvent in aqueous mixtures was additionally evaluated in a hydrophobic hydration study. The question was whether the experimentally known maximum in the solvation free enthalpy of argon at intermediate mixture compositions could be reproduced in the simulations. Values for the dielectric properties and excess free energy were found to be more off from experiment for the polarizable models than for the non-polarizable ones. However, a Kirkwood–Buff analysis of the aqueous mixtures and the hydrophobic hydration results exemplified that electronic polarization plays an important role in correctly describing attractive interactions between the EG and water co-solvent molecules. The trans/gauche ratio for ethylene glycol's O–C–C–O torsional angle was not found to systematically affect the properties of the pure liquid and aqueous mixtures.     

The effect of volatility on the thermophoretic motion of a high-viscosity sphere in a binary gaseous mixture with regard for thermodiffusion and Stefan effects

The effect of the evaporation coefficient of a large aerosol particle on the velocity of its thermophoretic motion in a binary gaseous mixture is studied. The thermodiffusion of the mixture components and Stefan phenomena are taken into consideration. The results of this study are more general than those obtained previously. The conventional theories of thermophoresis, as applied to a volatile high-viscosity liquid drop, are extended for the cases of weak and moderately intense diffusive evaporation.     

Spinodal decomposition of two-dimensional fluid mixtures: A spectral analysis of droplet growth

The spinodal decomposition of two-dimensional fluid mixture is studied by numerical simulation. For the high viscous fluid mixture it has not been evident whether the interfacial tension is relevant to the droplet growth or not. A length scale R defined by the structure function extracting the effect of the long wavelength mode justifies a rapid growth close to R approximately t, but the length scale energetically defined reveals a much slower growth R approximately t(0.5), where t is time. This discrepancy represents the violation of the dynamical scaling with single length scale. The slow gowth of the length scale is attributed to the accumulation of the number of isolated droplets in phase separating state, whereas the rapid growth represents the relevance of the surface tension as the driving force in two dimensions. For a low viscous fluid mixture the dynamical scaling is a good assumption with the growth law R approximately t(2/3) up to a very large Reynolds number Re approximately 1500, which is the limit in the present simulation.     

Ultrasonic velocity, density, viscosity and their excess parameters of the binary mixtures of tetrahydrofuran with methanol and o-cresol at varying temperatures

The ultrasonic velocity, density and viscosity of binary mixtures of tetrahydrofuran (THF) with methanol and o-cresol were measured at 293, 303 and 313 K over the entire range of composition. Using these experimental data, various thermo-acoustic parameters such as deviation in isentropic compressibility Δκ_s, excess molar volume , viscosity deviation Δη and excess Gibb’s free energy of activation for viscous flow ΔG^∗E have been calculated and fitted to Redlich-Kister polynomial equation. The deviation/excess parameter were plotted against the mole fraction of THF over the whole composition range. The observed negative and positive values of deviation/excess thermo-acoustic parameters were explained on the basis of the intermolecular interactions present in these mixtures. Since methanol is less acidic than o-cresol, the removal of proton from methanol is less likely than the removal of proton from o-cresol which is more acidic than methanol. Hence the intermolecular interaction in the mixture of THF with o-cresol is found to be stronger than mixture of THF with methanol, which is reflected from the observed positive and negative values of excess thermo-acoustic parameters. Thus it may be concluded that THF + o-cresol mixture exhibits strong intermolecular interaction. However, dispersive forces are responsible for THF + methanol mixture due to weak interaction. Further, Nomoto, Junjie, CFT and Flory’s theory were applied for evaluating the ultrasonic velocity theoretically. The theoretical evaluation of ultrasonic velocity based on molecular models in liquid mixtures has been used to correlate with the experimental findings and to know the thermodynamics of the mixtures. The comparison of theoretical and experimental results provides better understanding about the validity of the various thermodynamic, empirical, semi empirical and statistical theories.     

Current Inversion in a Temperature Ratchet with Asymmetric Unbiased External Forces

Transport of a Brownian particle moving in a symmetric potential is investigated in the presence of an asymmetric unbiased external force. The viscous medium is alternately in contact with the two heat reservoirs. We present the analytical expression of the net current at the quasi-steady state limit. It is found that the competition of the temporal asymmetric parameter of the driving force with the temperature difference leads to current reversals. The competition between the two opposite driving factors is a necessary but not a sufficient condition for current reversals.     

Volumetric and viscometric study of molecular interactions in the mixtures of some secondary alcohols with equimolar mixture of ethanol and N,N-dimethylacetamide at 308.15 K

Densities and viscosities of mixtures of isopropanol, isobutanol and isoamylalcohol with equimolar mixture of ethanol and N,N-dimethylacetamide have been measured at 308.15 K over the entire composition range. Deviations in viscosity, excess molar volume and excess Gibb’s free energy of activation of viscous flow have been calculated from the experimental values of densities and viscosities. Excess properties have been fitted to the Redlich-Kister type polynomial equation and the corresponding standard deviations have been calculated. The experimental data of viscosity have been used to test the applicability of empirical relations of Grunberg-Nissan, Hind-McLaughlin, Katti-Chaudhary and Heric-Brewer for the systems studied. Molecular interactions in the liquid mixtures have been investigated in the light of variation of deviation and of excess values in evaluated properties.     

Theoretical calculation of acoustic non-linearity parameter B/A of binary mixtures

Acoustic non-linearity parameter B/A is calculated for five binary liquid mixtures using Tong and Dong equation along with the Flory’s statistical theory. Similar to other excess thermodynamical quantities an excess non-linearity parameter (B/A)^E is defined for binary liquid mixtures. The interactions in the liquid mixtures are explained on the basis of the excess non-linearity parameter.