Diffusion of polarizable colloids in electromagnetic fields

Magnetic field line diffusion coefficient and Kolmogorov entropy in the percolation regime

A free-diffusion method has been developed for the determination of the intradiffusion coefficient ('self-diffusion coefficient') of a polymer in highly concentrated solutions. A fraction of the polymer is labelled with a small amount of light-absorbing substituent. The diffusion of this labelled species, present in low concentration, is followed in the presence of a high concentration of unlabelled material with the aid of absorption optics in the analytical ultracentrifuge. The diffusion proceeds over a boundary at which the difference in concentration of unlabelled material is varied. The average concentration of total polymer and the concentration of the labelled material are, however, constant. From theoretical considerations it is shown that by extrapolation of the diffusion coefficient so obtained to zero concentration difference of total material, the intradiffusion coefficient of the polymer at that concentration is obtained. The procedure also permits the ordinary translational diffusion coefficient to be estimated. The method has been applied to two dextran fractions with weight-average molecular weights of 19000 and 150000, which were labelled with fluorescein groups. As expected, the intradiffusion coefficient decreases with increasing polymer concentration, the decrease being more pronounced for the high-molecular-weight material. This decrease in the diffusion rate of dextran is, however, less than the corresponding decrease in the sedimentation rate which proteins with similar hydrodynamic parameters experience in dextran solutions. This agrees with the hypothesis that flexible linear polymers move through a network as chains rather than as hydrodynamic spheres. By combining measurements of the ordinary diffusion coefficient and the intradiffusion coefficient, it is possible to calculate the thermodynamic properties (as expressed by the virial expansion) of the system. This method is of particular importance in studies on concentrated solutions of high-molecular-weight polymers.

The energy flux carried by energetic electrons at the edge of the RFP experiment ETA BETA II has been derived by comparing the total heat collected by calorimetric probes oriented parallel and antiparallel to the magnetic field. Assuming that the energetic electrons flow along the stochastic magnetic field lines without undergoing collisions, the magnetic diffusion coefficient has been inferred from the radial behaviour of the energy flux. The diffusion coefficient is then compared with the magnetic fluctuation amplitude measured at the edge for different reversal of the toroidal field at the wall. It is found that the magnetic diffusion coefficient increases with magnetic fluctuations and the energy flux carried by energetic electrons decreases with Theta .

The inverse gas chromatography (IGC) method has been evaluated as a method to determine diffusion coefficients in polymer–solvent systems near the glass transition temperature. The poly(vinyl acetate)–toluene system was used for this purpose. Diffusion and partition coefficients were measured over a wide range of temperature. At temperatures significantly above the glass transition of the polymer, the capillary column model developed by Pawlisch and co-workers1,2 was used. At temperatures near the glass transition temperature, the modification of the capillary column model, proposed by Vrentas et al.3 was used. A sensitivity analysis of the capillary column model was made to delineate the range of applicability of the model. The diffusion coefficients obtained from IGC were compared with those extrapolated from the gravimetric sorption technique. The values agree within the expected range of error. Finally, free-volume theory was evaluated for its ability to predict the temperature and concentration dependencies of diffusion coefficients at temperatures near the glass transition from high temperature IGC data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1233–1240, 1997

The magnetic field line diffusion coefficients Dx and D(y) are obtained by numerical simulations in the case that all the magnetic turbulence correlation lengths l(x), l(y), and l(z) are different. We find that the variety of numerical results can be organized in terms of the Kubo number, the definition of which is extended from R=(deltaB/B(0))(l(parallel)/l(perpendicular)) to R=(deltaB/B(0))(l(z)/l(x)), for l(x) > or = l(y). Here, l(parallel) (l(perpendicular)) is the correlation length along (perpendicular to) the average field B(0)=B(0)ê(z). We have anomalous, non-Gaussian transport for R less, similar 0.1, in which case the mean square deviation scales nonlinearly with time. For R greater, similar 1 we have several Gaussian regimes: an almost quasilinear regime for 0.1 less, similar R less, similar 1, an intermediate, transition regime for 1 less, similar R less, similar 10, and a percolative regime for R greater, similar 10. An analytical form of the diffusion coefficient is proposed, D(i)=D(deltaBl(z)/B(0)l(x))(mu)(l(i)/l(x))(nu)l(2)(x)/l(z), which well describes the numerical simulation results in the quasilinear, intermediate, and percolative regimes.

The 17–18 March 2015 storm is the largest geomagnetic storm in the Van Allen Probes era to date. The Lyon‐Fedder‐Mobarry global MHD model has been run for this event using ARTEMIS data as solar wind input. The ULF wave power spectral density of the azimuthal electric field and compressional magnetic field is analyzed in the 0.5–8.3 mHz range. The lowest three azimuthal modes account for 70% of the total power during quiet times. However, during high activity, they are not exclusively dominant. The calculation of the radial diffusion coefficient is presented. We conclude that the electric field radial diffusion coefficient is dominant over the magnetic field coefficient by one to two orders of magnitude. This result contrasts with the dominant magnetic field diffusion coefficient used in most 3‐D diffusion models.

Waves which couple to energetic electrons are particularly important in space weather, as they drive rapid changes in the topology and intensity of Earth's outer radiation belt during geomagnetic storms. This includes Ultra Low Frequency (ULF) waves that interact with electrons via radial diffusion which can lead to electron dropouts via outward transport and rapid electron acceleration via inward transport. In radiation belt simulations, the strength of this interaction is specified by ULF wave radial diffusion coefficients. In this paper we detail the development of new models of electric and magnetic radial diffusion coefficients derived from in‐situ observations of the azimuthal electric field and compressional magnetic field. The new models use as it accounts for adiabatic changes due to the dynamic magnetic field coupled with an optimized set of four components of solar wind and geomagnetic activity, , , , and , as independent variables (inputs). These independent variables are known drivers of ULF waves and offer the ability to calculate diffusion coefficients at a higher cadence then existing models based on Kp. We investigate the performance of the new models by characterizing the model residuals as a function of each independent variable and by comparing to existing radial diffusion models during a quiet geomagnetic period and through a geomagnetic storm. We find that the models developed here perform well under varying levels of activity and have a larger slope or steeper gradient as a function of as compared to existing models (higher diffusion at higher values).

Ray tracing method is used to study the propagation of collimated beams in a liquid–core cylindrical lens (LCL), which has dual functions of diffusion cell and image formation. The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations, the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution. Guided by the calculation conditions, the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper. The spatial and temporal concentration profile Ce(z, t) of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL; Then, the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C) = D0 × (1 + α1C + α2C2 + α3C3 + ⋅). The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cn(z, t). The D(C)of triethylene glycol aqueous solution is obtained by comparing the Cn(z, t) with Ce(z,t). Finally, the obtained polynomial D(C) is used to calculate the refractive index profiles nn(z,t)s of diffusion solution in the used LCL. Based on the ray propagation law in inhomogeneous media and the calculated n(z,t), the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C). The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.

Solute diffusion is an important process that determines the dendrite growth during solidification. The theoretical model generally simplifies the solute diffusion coefficient in liquid phase into a constant. Nevertheless, the composition of the boundary layer changes greatly in the solidification process, the diffusion coefficient will no longer be a constant and is dependent on concentration. In this paper, the quantitative phase field model is used to simulate the effect of concentration-dependent diffusion coefficient on dendrite growth in directional solidification. In the model, the concentration-dependent diffusion process is investigated by coupling the concentration-dependent diffusion coefficient in the liquid solute diffusion equation. A series of simulation results confirms that the concentration-dependent diffusion process has a significant effect on the dendrite growth. The results show that the increase of the coupling intensity of solute concentration will enhance the diffusion of solute in the mushy zone between primary dendrites to the dendrite tip, resulting in the increase of solute enrichment at the dendrite tip, thereby increasing the tip undercooling. The variation of diffusion coefficient in liquid phase has little effect on the tip radius of dendrite, and the simulation results are in good agreement with those from the theoretical model. Moreover, the amplitude of dendritic side branches decreases with the increase of solute diffusion coefficient. In the study of dendrite arrays, it is found that the concentration-dependent diffusion coefficient increases the primary spacing and reduce the tip position. The results of this study indicate that for a system with a concentration-dependent coefficient significantly, the effect of concentration-dependent diffusion on tip undercooling and side branches should be considered in the quantitative and experimental verification of the existing model.

Uniform regularity and vanishing dissipation limit for the 3D magnetic Bénard equations in half space

In this paper, we consider a non-equilibrium diffusion approximation model in thermally radiative magnetohydrodynamics (MHD) which describe the compressible viscous, heat-conducting fluid coupled with the Maxwell equations governing the behavior of the magnetic field with taking into account the radiation effect under the non-local thermal equilibrium case. The system consists of the radiative transfer equation coupled with the compressible MHD equations, and the magnetic diffusion coefficient, viscosity coefficient, heat-conducting coefficient are all allowed to be positive constants. We prove existence, uniqueness and regularity of global-in-time classical solutions to one-dimensional case of this model. Based on the fundamental local existence results and global-in-time a priori estimates, we can establish the global existence of a unique classical solutions with large initial data to the initial-boundary value problems.

Diffusion coefficients in molten metals were measured for Sn-Pb, Bi-Pb, Sb-Pb, Cd-Pb, Sn-Bi, and Sb-Sn from 450° to 600°C. Since the observed activation energies of these metals in the liquid state were found to be of the same order as those for nonmetallic solutions, the diffusing substance may be small particles such as metal ions. For Pb-Sn, Pb-Bi, and Sn-Bi, the concentration dependences of diffusion coefficients were determined at about 500°C. The results show that the relations between diffusion coefficients and atomic fractions obey the thermodynamic formulas of irreversible processes. For a ternary system, Pb-Sn-Bi, the diffusion coefficient of tin decreases as bismuth is added. This effect has been explained in thermodynamic terms.

Correlation of diffusion coefficients for naphthalene and dimethylnaphthalene isomers in supercritical carbon dioxide

Microfluidics to determine the diffusive mass transfer of a low viscosity solvent into a high viscosity hydrocarbon

The well-known size exclusion chromatography (SEC) universal calibration allows the characterization of a polymer sample using a set of polymer standards of a different polymer family. This is a polymer-transferable calibration method. A more “universal” calibration method has been proposed for thermal field-flow fractionation (ThFFF) where the calibration constants closely describe the ratio of ordinary (molecular) diffusion coefficient D to thermal diffusion coefficient (or, more correctly, thermophoretic mobility) DT. The universal calibration for ThFFF is therefore instrument or system transferable. Systematic experiments have previously been carried out to verify this calibration method for a wide range of conditions. Results showed that the method holds well provided experimental conditions such as sample size and cold wall temperature Tc are the same for each system. This paper quantifies the effect of cold wall temperature on polymer retention in ThFFF and on the universal calibration constants for the polystyrene−tetrahydrofuran, poly(methyl methacrylate)−tetrahydrofuran, and polyisoprene−tetrahydrofuran systems, respectively. The universal calibration for ThFFF is thereby extended to account for variation of cold wall temperature. The extended calibration will allow for accurate data retrieval from analyses obtained at any cold wall temperature. It will even allow for accurate information retrieval when cold wall temperature is not held constant during sample elution, such as may occur with a change in coolant flow rate or with a programmed decay of ΔT.