Molecular Transport Coefficients Research Articles

Normal-to-Supercooled Liquid Transition in Molecular Glass-Formers: A Hidden Structural Transformation Fuelled by Conformational Interconversion.

Molecular dynamics and transport coefficients change significantly around the so-called Arrhenius crossover in glass-forming systems. In this article, we revisit the dynamic processes occurring in a glass-forming macrocyclic crown thiaether MeBzS2O above its glass transition, revealing two crossover temperatures: TB at 309 and TA at 333 K. We identify the second one as the Arrhenius crossover that is closely related to the normal-to-supercooled liquid transition in this compound. We show that the transformation occurring at this point goes far beyond molecular dynamics (where the temperature dependence of structural relaxation times changes its character from activation-like to super-Arrhenius), being reflected also in the internal structure and diffraction pattern. In this respect, we found a twofold local organization of the nearest-neighbor molecules via weak van der Waals forces, without the formation of any medium-range order or mesophases. The nearest surrounding of each molecule evolves structurally in time due to the ongoing fast conformational changes. We identify several conformers of MeBzS2O, demonstrating that its lowest-energy conformation is preferred mainly at lower temperatures, i.e., in the supercooled liquid state. Its increased prevalence modifies locally the short-range intermolecular order and promotes vitrification. Consequently, we indicate that the Arrhenius transition is fuelled rather by conformational changes in this glass-forming macrocyclic crown thiaether, which is a different scenario from the so-far existing concepts. Our studies combine broadband dielectric spectroscopy (BDS), X-ray diffraction, Fourier transform infrared (FTIR) spectroscopy, molecular dynamics (MD) simulations, and density functional theory (DFT) calculations.

An experimental study of the influence of Lewis number on turbulent flame speed at different pressures

To explore effects of pressure on the magnitude of the influence of differences in molecular transport coefficients on turbulent flame speed ST, experiments with statistically spherical flame kernels expanding in homogeneous isotropic turbulence in a fan-stirred bomb were performed. Flame speeds were evaluated by analyzing flame images obtained using a high-speed Schlieren technique. To reach the study goals, the measurements were done at three different pressures (P = 1, 3, and 5 atm) with three different mixtures: (i) lean (the equivalence ratio ϕ=0.45) H2/air mixture, (ii) lean (ϕ=0.45) H2/O2/He mixture, and (iii) the stoichiometric CH4/air mixture. Mixtures (i) and (iii) are characterized by significantly different Lewis numbers (Le=0.35 and Le≈1, respectively), approximately equal thermal laminar flame thicknesses δL, and close values of the laminar flame speed SL at the three pressures. Combustion chemistry is expected to be weakly affected by substitution of N2 in mixture (i) with He in mixture (ii), with this substitution increasing Le to 0.91, but the two mixtures are characterized by significantly different δL at the three pressures and different SL at P = 3 and 5 atm. Comparison of the normalized turbulent flame speeds ST/SL obtained from the lean H2/air flames and stoichiometric CH4/air flames shows that ST/SL is significantly higher in the former flames, with the difference being significantly increased by P. These experimental data indicate a substantial increase in the magnitude of the influence of differential diffusion effects on ST with pressure. An analysis of data obtained from the lean H2/O2/He flames further supports this conclusion. Based on results of numerical simulations of complex-chemistry laminar premixed flames, the pressure-dependence of the magnitude of the influence of differential diffusion effects on ST/SL is attributed to an increase in the Zel'dovich number by pressure, with the latter effect being most pronounced for the lean H2/O2/He mixture.

Lewis number and preferential diffusion effects in lean hydrogen–air highly turbulent flames

Unsteady three-dimensional direct numerical simulations of highly turbulent, complex-chemistry, lean hydrogen-air flames were performed by changing the equivalence ratio ϕ, root mean square velocity u′, and turbulence length scale L. For each set of ϕ,u′,L, to explore the influence of molecular transport coefficients on the turbulent burning velocity UT, four cases were designed: (i) mixture-averaged diffusivities; (ii) diffusivities equal to the heat diffusivity κ of the mixture for all species; (iii) mixture-averaged diffusivities for all species with the exception of O2, whose diffusivity was equal to the diffusivity DH2 of H2 to suppress preferential diffusion effects; and (iv) mixture-averaged diffusivities multiplied with κ/DH2 to suppress Lewis number effects but retain preferential diffusion effects. The computed results show a significant increase in UT due to differences in molecular transport coefficients even at Karlovitz number Ka as large as 565. The increase is documented in cases (i) and (iii) but is not observed in case (iv)—indicating that this phenomenon is controlled by Lewis number effects, whereas preferential diffusion effects play a minor role. The phenomenon is more pronounced in leaner flames, with all other things being equal. While the temperature profiles TcFcF conditionally averaged at the local value of the combustion progress variable cF and sampled from the entire flame brushes are not sensitive to variations in molecular transport coefficients at high Ka, the TcFcF-profiles sampled from the leading edges of the same flame brushes show significant increase in the local temperature in cases (i) and (iii) characterized by a low Lewis number.

Comprehensive Studies of the Processes of the Molecular Transfer of the Momentum, Thermal Energy and Mass in the Nutrient Media of Biotechnological Industries.

This article puts forward arguments in favor of the necessity of conducting complex measurements of molecular transport coefficients that quantitatively determine the coefficients of dynamic viscosity, thermal diffusivity and molecular diffusion. The rheological studies have been carried out on the viscometers of two types: those with a rolling ball (HÖPPLER® KF 3.2.), and those with a rotary one (Rheotest RN 4.1.). The thermophysical studies have been performed using the analyzer Hot Disk TPS 2500S. The measurements have been taken in the temperature range of 283 to 363 K. The concentration of dry substances has varied from 16.2 to 77.7% dry wt. An empirical equation for calculating the density of aqueous solutions of beet molasses has been obtained. The diagrams of the dependence of the dynamic viscosity on the shear rate in the range of 1 s−1 to 500 s−1 at different temperatures have been provided. The diagrams of the dependence of the coefficients of thermal conductivity and thermal diffusivity on the temperature and the concentration of dry substances have been presented, and empirical equations for their calculation have been obtained. The findings can be used for engineering calculations of hydrodynamic and heat-exchange processes in biotechnological equipment.

Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model

Abstract. This paper presents a novel methodology to use direct numerical simulation (DNS) to study the impact of isotropic homogeneous turbulence on the condensational growth of cloud droplets. As shown by previous DNS studies, the impact of turbulence increases with the computational domain size, that is, with the Reynolds number, because larger eddies generate higher and longer-lasting supersaturation fluctuations that affect growth of individual cloud droplets. The traditional DNS can only simulate a limited range of scales because of the excessive computational cost that comes from resolving all scales involved, that is, from large scales at which the turbulent kinetic energy (TKE) is introduced down to the Kolmogorov microscale, and from following every single droplet. The novel approach is referred to as the “scaled-up DNS”. The scaling up is done in two parts, first by increasing both the computational domain and the Kolmogorov microscale and second by using super-droplets instead of real droplets. To ensure proper dissipation of TKE and scalar variance at small scales, molecular transport coefficients are appropriately scaled up with the grid length. For the scaled-up domains, say, meters and tens of meters, one needs to follow billions of real droplets. This is not computationally feasible, and so-called super-droplets are applied in scaled-up DNS simulations. Each super-droplet represents an ensemble of identical real droplets, and the number of real droplets represented by a super-droplet is referred to as the multiplicity attribute. After simple tests showing the validity of the methodology, scaled-up DNS simulations are conducted for five domains, the largest of 643 m3 volume using a DNS of 2563 grid points and various multiplicities. All simulations are carried out with vanishing mean vertical velocity and with no mean supersaturation, similarly to past DNS studies. As expected, the supersaturation fluctuations as well as the spread in droplet size distribution increase with the domain size, with the droplet radius variance increasing in time t as t1∕2 as identified in previous DNS studies. Scaled-up simulations with different multiplicities document numerical convergence of the scaled-up solutions. Finally, we compare the scaled-up DNS results with a simple stochastic model that calculates supersaturation fluctuations based on the vertical velocity fluctuations updated using the Langevin equation. Overall, the results document similar scaling to previous small-domain DNS simulations and support the notion that the stochastic subgrid-scale model is a valuable tool for the multi-scale simulation of droplet spectral evolution applying a large-eddy simulation model.

Mesoscale elements description of turbulent flow

• Description of turbulent flow as an ensemble of finite size, or mesoscale , Lagrangian elements is formulated. • Mesoscale element has no deterministic position but a probability of presence and a region of influence growing with time. • Consideration of finite size elements allows explicit account of molecular transport described through pairwise interactions. • The method applied to a mixing layer in grid turbulence yielded scalar statistics in quantitative agreement with experiments. This work proposes to describe a turbulent flow using a set of mesoscale elements, that is fluid elements of small, but finite, size the properties of which are representative of larger region surrounding them. Consideration of fluid elements of finite dimensions allows one to formulate a small scale mixing model with an explicit dependency on the molecular transport coefficients. The dimensions of a mesoscale element are determined from an evolution equation accounting for the molecular diffusion and the strain rate induced by small-scale turbulence while its position is determined by convection by large-scale velocity components. In addition to consideration of the fluid elements of a finite size, the second key new concept is the notion of radius of influence over which such an element contributes to the statistics of the flow; this radius grows with time. It is shown that the proposed method satisfies the mass conservation and normalisation of the probability density functions of scalar quantities . The proposed method is illustrated with simulations of thermal mixing layer in grid turbulence.

Photo- and Thermophoresis of Heated Medium-Size Spherical Aerosol Particles

A theory of photo- and thermophoresis of a heated medium-size spherical aerosol particle is proposed in the quasi-stationary Stokes approximation at relatively small Reynolds and Peclet numbers. Gas-dynamic equations are solved with allowance for power dependences of the molecular transport (viscosity and thermal conductivity) coefficients and density of the gas medium on temperature. Boundary conditions take into account effects that are linear with respect to the Knudsen number. Expressions for the total force and velocity are derived. It is shown than the above effects may substantially affect the motion of a heated particle.

Фото- и термофорез нагретых умеренно крупных аэрозольных частиц сферической формы

AbstractA theory of photo- and thermophoresis of a heated medium-size spherical aerosol particle is proposed in the quasi-stationary Stokes approximation at relatively small Reynolds and Peclet numbers. Gas-dynamic equations are solved with allowance for power dependences of the molecular transport (viscosity and thermal conductivity) coefficients and density of the gas medium on temperature. Boundary conditions take into account effects that are linear with respect to the Knudsen number. Expressions for the total force and velocity are derived. It is shown than the above effects may substantially affect the motion of a heated particle.

Thermophoretic motion of large heated aerosol spherical particles

The stationary motion of a large spherical aerosol particle in the external field of a temperature gradient in zero gravity is theoretically described using the Stokes approximation and the assumption that the average temperature of the particle surface differs considerably from the temperature of the surrounding gaseous medium. The gas dynamics equations are solved taking into account the power-law temperature dependence of the molecular transport coefficients (viscosity, thermal conductivity) and the density of the gaseous medium. Numerical estimates show that the dependence of the thermophoretic force and velocity on the average temperature of the particle surface is nonlinear.

Solution of a boundary value problem for the Navier–Stokes equations linearized with respect to velocity: Nonisothermal flow of a gaseous medium past a uniformly heated sphere

For the problem on a plane-parallel gas flow with velocity U∞ past a fixed uniformly heated spherical particle, we obtain a solution of the Navier–Stokes equations linearized with respect to velocity in the spherical coordinate system with regard to the power-law dependence of the molecular transport coefficients (viscosity and thermal conductivity) and the gas medium density on the temperature. The uniqueness of this solution is proved.

A viscous instability in axially symmetric laminar shear flows

A viscous instability in shearing laminar axisymmetric hydrodynamic flows around a gravitating center is described. In the linearized hydrodynamic equations written in the Boussinesq approximation with microscopic molecular transport coefficients, the instability arises when the viscous dissipation is taken into account in the energy equation. Using the local WKB approximation, we derive a third-order algebraic dispersion equation with two modes representing the modified Rayleigh modes R+ and R-, and the third X-mode. We show that in thin accretion flows the viscosity destabilizes one of the Rayleigh modes in a wide range of wavenumbers, while the X-mode always remains stable. In Keplerian flows, the instability increment is found to be a few Keplerian rotational periods at wavelengths with $kr\sim 10-50$. This instability may cause turbulence in astrophysical accretion discs even in the absence of magnetic field.

Measuring ligand–receptor binding kinetics and dynamics using k-space image correlation spectroscopy

Accurate measurements of kinetic rate constants for interacting biomolecules are crucial for understanding the mechanisms underlying intracellular signalling pathways. The magnitude of binding rates plays a very important molecular regulatory role which can lead to very different cellular physiological responses under different conditions. Here, we extend the k-space image correlation spectroscopy (kICS) technique to study the kinetic binding rates of systems wherein: (a) fluorescently labelled, free ligands in solution interact with unlabelled, diffusing receptors in the plasma membrane and (b) systems where labelled, diffusing receptors are allowed to bind/unbind and interconvert between two different diffusing states on the plasma membrane. We develop the necessary mathematical framework for the kICS analysis and demonstrate how to extract the relevant kinetic binding parameters of the underlying molecular system from fluorescence video-microscopy image time-series. Finally, by examining real data for two model experimental systems, we demonstrate how kICS can be a powerful tool to measure molecular transport coefficients and binding kinetics.

Dispersion-Relation Fluorescence Spectroscopy

Because of its ability to study specifically labeled structures, fluorescence microscopy is the most widely used technique for investigating live cell dynamics and function. Fluorescence correlation spectroscopy is an established method for studying molecular transport and diffusion coefficients at a fixed spatial scale. We propose a new approach, dispersion-relation fluorescence spectroscopy (DFS), to study the transport dynamics over a broad range of spatial and temporal scales. The molecules of interest are labeled with a fluorophore whose motion gives rise to spontaneous fluorescence intensity fluctuations that are analyzed to quantify the governing mass transport dynamics. These data are characterized by the effective dispersion relation. We report on experiments demonstrating that DFS can distinguish diffusive from advection motion in a model system, where we obtain quantitatively accurate values of both diffusivities and advection velocities. Because of its spatially resolved information, DFS can distinguish between directed and diffusive transport in living cells. Our data indicate that the fluorescently labeled actin cytoskeleton exhibits active transport motion along a direction parallel to the fibers and diffusive in the perpendicular direction.

Effects of radiative heat transfer on the structure of turbulent supersonic channel flow

The interaction between turbulence in a minimal supersonic channel and radiative heat transfer is studied using large-eddy simulation. The working fluid is pure water vapour with temperature-dependent specific heats and molecular transport coefficients. Its line spectra properties are represented with a statistical narrow-band correlated-k model. A grey gas model is also tested. The parallel no-slip channel walls are treated as black surfaces concerning thermal radiation and are kept at a constant temperature of 1000 K. Simulations have been performed for different optical thicknesses (based on the Planck mean absorption coefficient) and different Mach numbers. Results for the mean flow variables, Reynolds stresses and certain terms of their transport equations indicate that thermal radiation effects counteract compressibility (Mach number) effects. An analysis of the total energy balance reveals the importance of radiative heat transfer, compared to the turbulent and mean molecular heat transport.

Effects of radiative heat transfer on the structure of turbulent supersonic channel flow

The interaction between turbulence in a minimal supersonic channel and radiative heat transfer is studied using large-eddy simulation. The working fluid is pure water vapour with temperature-dependent specific heats and molecular transport coefficients. Its line spectra properties are represented with a statistical narrow-band correlated-k model. A grey gas model is also tested. The parallel no-slip channel walls are treated as black surfaces concerning thermal radiation and are kept at a constant temperature of 1000 K. Simulations have been performed for different optical thicknesses (based on the Planck mean absorption coefficient) and different Mach numbers. Results for the mean flow variables, Reynolds stresses and certain terms of their transport equations indicate that thermal radiation effects counteract compressibility (Mach number) effects. An analysis of the total energy balance reveals the importance of radiative heat transfer, compared to the turbulent and mean molecular heat transport.

気液共存線近傍におけるメタノール中の１価イオンの並進運動に対する密度効果

For a better understanding of the molecular transport mechanism in fluids, it is important to study the density dependence in the intermediate region between liquid and gas. The hydrodynamic theory is considered to explain the molecular transport coefficients at high liquid densities, while the binary collision theory is valid in dilute gases. In this article, we report the density dependence of the electrolyte conductivities of alkali-metal halides in liquid methanol near the liquid-vapor coexistence curve up to the critical temperature (240°C) and those of tetraalkylammonium bromides up to about 180°C, and discuss the application limit of the hydrodynamic theory (Hubbard-Onsager’s dielectric friction theory) for the ionic transport process in liquids.

Raison d'être and general formulation of two-point statistical description of turbulent premixed combustion

This work undertakes an analysis of parameters defining the rate of chemical reactions in turbulent premixed combustion with particular emphasis on the strong turbulence case. Experimental data show that not only the laminar flame speed and rms turbulent velocity but also both the details of chemical kinetics and the molecular transport coefficients are important in this case. Determination of the molecular transport rates inside a turbulent flame requires a two-point statistical description. In order to construct such a description the transport equation for the two-point joint velocity and scalars probability density function is considered. It proved possible to achieve a closure of the unclosed terms in this equation, including the micromixing terms, following Ievlev's method. To cite this article: A.A. Burluka, C. R. Mecanique 334 (2006).

Turbulence in circumstellar disks

We investigate the analogy between circumstellar disks and the Taylor-Couette flow. Using the Reynolds similarity principle, the analogy results in a number of parameter-free predictions about stability of the disks, and their turbulent transport properties, provided the disk structure is available. We discuss how the latter can be deduced from interferometric observations of circumstellar material. We use the resulting disk structure to compute the molecular transport coefficients, including the effect of ionization by the central object. The resulting control parameter indicates that the disk is well into the turbulent regime. The analogy is also used to compute the effective accretion rate, as a function of the disk characteristic parameters (orbiting velocity, temperature and density). These values are in very good agreement with experimental, parameter-free predictions derived from the analogy. The turbulent viscosity is also computed and found to correspond to an $\alpha$-parameter $2\times 10^{-4}<\alpha<2\times 10^{-2}$. Predictions regarding fluctuations are also checked: luminosity fluctuations in disks do obey the same universal distribution as energy fluctuations observed in a laboratory turbulent flow. Radial velocity dispersion in the outer part of the disk is predicted to be of the order of 0.1 km/s, in agreement with available observations. All these issues provide a proof of the turbulent character of the circumstellar disks, as well as a parameter-free theoretical estimate of effective accretion rates.

Heterogeneous combustion of a pair of interacting particles with an arbitrarily shaped surface

The heterogeneous combustion of two immobile interacting particles with arbitrarily shaped surfaces is theoretically described under conditions of rapid chemical reaction, where the concentration of oxidizer molecules on the surface of the particles can be considered to be zero. The problem is solved for an arbitrary temperature dependence of molecular transport coefficients when molecular transport in the vicinity of the particles takes place by diffusion. Analytical formulas found allow for the direct characterization of the combustion of individual spheroidal particles and interacting spherical particles in several particular cases. At the same volumes, heavily elongated and oblate particles are shown to burn significantly faster. The approach of the particles significantly influences the time of burning the finer particle if its size is far less than that of the coarser one.

Characteristics of chemically reacting compressible homogeneous turbulence

Direct numerical simulations (DNS) are conducted to study the turbulence-chemical reaction interactions in homogeneous decaying compressible fluid flows. The reaction is of a single-step irreversible Arrhenius type. The results indicate that the heat of reaction has a noticeable influence on the solenoidal and the dilatational turbulent motions. The effect of reaction on the solenoidal velocity field is primarily due to variation of the molecular diffusivity coefficients with temperature and appears at small scales. However, the dilatational motions are affected more than the solenoidal motions and are intensified at all length scales. The decay rate of the turbulent kinetic energy is dependent on the molecular dissipation and the pressure-dilation correlation. In isothermal reacting cases, the net contribution of the pressure-dilatation is small and the turbulent energy decays continuously due to viscous dissipation. In the exothermic reacting cases, the pressure-dilatation tends to increase the turbulent kinetic energy when the reaction is significant. Analysis of the flow structure indicates that the flow is dominated by strain in the reaction zones. Also, consistent with previous studies, the scalar gradient tends to align with the most compressive strain eigenvector and the vorticity vector tends to align with the intermediate strain eigenvector. The heat of reaction weakens this preferential alignment, primarily due to variation in molecular transport coefficients. The spatial and the compositional structure of the flame are also affected by the modification of the turbulence and the molecular coefficients.