Effects Of Molecular Diffusion Research Articles

Application of combined physicochemical techniques for the efficient treatment of olive mill wastewaters

Olive Mill Wastewaters (OMW), produced from olive processing for the extraction of olive oil by units scattered in the Mediterranean countries, is a hardly degradable byproduct due to very high concentration of organic load of complex composition. Several treatment methods have been proposed for the efficient treatment of OMW, but because of the high operational cost, the application of these methods seems to be prohibitive, as olive mills are small family units and operate only 3–4 months per year. In the present work, the implementation of a combination of physicochemical treatment methods is proposed for the effective treatment of OMW. Initially, a membrane filtration process was used (ultrafiltration, nanofiltration, and reverse osmosis membranes) for the fractionation of OMW in concentrate and permeate streams. OMW was thus sufficiently treated and as a result the final permeate of the reverse osmosis was a pure water stream appropriate for irrigation purposes or for reuse in the OMW premises. The concentrated fraction from NF and RO membranes was further treated, to separate and isolate carbohydrates and the phenolic compounds, through the implementation of adsorption on specific resins. Alternatively, the enriched in phenolic content concentrated fractions could be investigated for the possibility of their selective recovery from the respective solution by cooling crystallization, applied directly to the concentrated fractions. During this process, it is possible to recover a number of components from their solutions according to the respective freezing points. Two Poly-Phenols (PP) contained in the OMW, namely trans-cinnamic acid (TCA) and ferulic acid (FA) were examined for the possibility of their selective extraction from their aqueous solutions by cooling crystallization, in order an operational model of the process to be developed. Initially, short cooling crystallization experiment cycles were done to test the effect of molecular diffusion and convection phenomena to the total PP recovery. Furthermore, crystallization of FA and TCA was followed during one cooling cycle as a function of time past the immersion of a cold surface in hot homogeneous solutions of the test compounds. It was estimated that in the case of mixtures, a total recovery of 66% FA and 50% TCA was achieved. The combination of membrane filtration and cooling crystallization may be quite promising for the development of more effective and integrated exploitation of OMW abiding to the zero waste targets.

Effect of molecular diffusion on the spin dynamics of a micellized radical pair in low magnetic fields studied by Monte Carlo simulation.

Magnetic field effect is a powerful tool to study dynamics and kinetics of radical pairs (RPs), which are one of the most important intermediates for organic photon-energy conversion reactions. However, quantitative discussion regarding the relationship between the modulation of interelectron interactions and spin dynamics at low magnetic fields (<10 mT) is still an open question. We have studied the spin dynamics of a long-lived RP in a micelle by newly developed Monte Carlo simulation, in which fluctuations of the exchange and magnetic dipolar interactions by in-cage diffusion are directly introduced to the time-domain spin dynamics calculation. State-dependent relaxation/dephasing times of a few to a few tens of nanoseconds are obtained by simulations without hyperfine interactions (HFIs) as a function of the mutual diffusion constant (∼10(-6) cm(2)/s). Simulations with the HFIs exhibit incoherent singlet-triplet (S-T) mixings resulting from interplay between the HFIs and the fluctuating spin-spin interactions. The experimentally observed incoherent S-T mixing of ∼20 ns at 3 mT for a singlet-born RP in a sodium dodecyl sulfate micelle is reproduced by the simulation with reasonable diffusion coefficients. The computational method developed here contributes to quantitative detection of molecular motion that governs the recombination efficiency of RPs.

Regimes of Spray Vaporization and Combustion in Counterflow Configurations

This article addresses the problem of spray vaporization and combustion in axisymmetric opposed-jet configurations involving a stream of hot air counterflowing against a stream of nitrogen carrying a spray of fuel droplets. The Reynolds numbers of the jets are assumed to be large, so that mixing of the two streams is restricted to a thin mixing layer that separates the counterflowing streams. The evolution of the droplets in their feed stream from the injection location is seen to depend fundamentally on the value of the droplet Stokes number, St, defined as the ratio of the droplet acceleration time to the mixing-layer strain time close to the stagnation point. Two different regimes of spray vaporization and combustion can be identified depending on the value of St. For values of St below a critical value, equal to 1/4 for dilute sprays with small values of the spray liquid mass-loading ratio, the droplets decelerate to approach the gas stagnation plane with a vanishing axial velocity. In this case, the droplets located initially near the axis reach the mixing layer, where they can vaporize due to the heat received from the hot air, producing fuel vapor that can burn with the oxygen in a diffusion flame located on the air side of the mixing layer. The character of the spray combustion is different for values of St of order unity, because the droplets cross the stagnation plane and move into the opposing air stream, reaching distances that are much larger than the mixing-layer thickness before they turn around. The vaporization of these crossing droplets, and also the combustion of the fuel vapor generated by them, occur in the hot air stream, without significant effects of molecular diffusion, generating a vaporization-assisted nonpremixed flame that stands on the air side outside the mixing layer. Separate formulations will be given below for these two regimes of combustion, with attention restricted to the near-stagnation-point region, where the solution is self-similar and all variables are only dependent on the distance to the stagnation plane. The resulting formulations display a reduced number of controlling parameters that effectively embody dependences of the structure of the spray flame on spray dilution, droplet inertia, and fuel preferential diffusion. Sample solutions are given for the limiting cases of pure vaporization and of infinitely fast chemistry, with the latter limit formulated in terms of chemistry-free coupling functions that allow for general nonunity Lewis numbers of the fuel vapor.

Competition between water uptake and ice nucleation by glassy organic aerosol particles

Abstract. Organic aerosol particles play a key role in climate by serving as nuclei for clouds and precipitation. Their sources and composition are highly variable, and their phase state ranges from liquid to solid under atmospheric conditions, affecting the pathway of activation to cloud droplets and ice crystals. Due to slow diffusion of water in the particle phase, organic particles may deviate in phase and morphology from their thermodynamic equilibrium state, hampering the prediction of their influence on cloud formation. We overcome this problem by combining a novel semi-empirical method for estimation of water diffusivity with a kinetic flux model that explicitly treats water diffusion. We estimate timescales for particle deliquescence as well as various ice nucleation pathways for a wide variety of organic substances, including secondary organic aerosol (SOA) from the oxidation of isoprene, α-pinene, naphthalene, and dodecane. The simulations show that, in typical atmospheric updrafts, glassy states and solid/liquid core-shell morphologies can persist for long enough that heterogeneous ice nucleation in the deposition and immersion mode can dominate over homogeneous ice nucleation. Such competition depends strongly on ambient temperature and relative humidity as well as humidification rate and particle size. Due to differences in glass transition temperature, hygroscopicity and atomic O / C ratio of the different SOA, naphthalene SOA particles have the highest potential to act as heterogeneous ice nuclei. Our findings demonstrate that kinetic limitations of water diffusion into organic aerosol particles are likely to be encountered under atmospheric conditions and can strongly affect ice nucleation pathways. For the incorporation of ice nucleation by organic aerosol particles into atmospheric models, our results demonstrate a demand for model formalisms that account for the effects of molecular diffusion and not only describe ice nucleation onsets as a function of temperature and relative humidity but also include updraft velocity, particle size and composition.

Assessment of Turbulence-Chemistry Interaction Models in MILD Combustion Regime

The present paper reports on the assessment of different turbulence-chemistry interaction closures for modeling turbulent combustion in the Moderate and Intense Low oxygen Dilution combustion regime. 2D RANS simulations have been carried out to model flames issuing from two burners DJHC burner and Adelaide JHC burner which imitate the MILD combustion. In order to model these flames, two different approaches of turbulence-chemistry interaction models are considered; while in the PDF based modeling, two different variants are invoked to understand the applicability of the PDF based models in the MILD regime: one is based on presumed shape PDF approach and the other one is transported PDF approach. A comprehensive study has been carried out by comparing the results obtained from these different models. For the DJHC burner, the computations are carried out for a jet speed corresponding to Reynolds numbers of Re=4100, whereas the Adelaide JHC burner computations are performed for a jet speed corresponding to Reynolds number of Re=10000. The effects of molecular diffusion on the flame characteristics are also studied by using different micro-mixing models. In the case of DJHC burner, it has been observed that the mean axial velocity and the turbulent kinetic energy profiles are in good agreement with the measurements. However, the temperature profiles are over-predicted in the downstream region by both EDC and the PDF based models. In the context of Adelaide JHC burner, the profiles of the temperature and the mass fraction of major species (CH4, H2, O2, H2O, CO2) obtained using LPDF approach are in better agreement with the measurements compared to those obtained using EDC model; although, both the solution approaches fail to capture CO and OH radical profiles.

Linear Eddy Mixing Model Studies of High Karlovitz Number Turbulent Premixed Flames

Turbulent premixed flames exhibit different structural and propagation characteristics with increasing upstream turbulence intensity starting from thin wrinkled flames in the Corrugated Flamelet regimes to a flame with a thicker preheat zone in the Thin Reaction Zone Regime (TRZ) and finally, becoming more disorganized or broken in the Distributed or Broken Reaction Zone (D/BRZ) regimes under intense turbulence. A single comprehensive predictive model that can span all regimes does not currently exist, and in this study we explore the ability of the stand-alone one-dimensional linear-eddy mixing (LEM) model to simulate the flames in all these regimes. Past applications of this 1DLEM model have demonstrated reasonable predictions in the flamelet and TRZ regimes and here, new experiments in the TRZ regime are specifically addressed to evaluate the predictive capability of this model. Additional simulations in the D/BRZ regimes (where no data is currently available) are performed to determine if the model can be extended to the high turbulence regime. Comparison with the data in the TRZ regime shows satisfactory agreement. Analysis suggests varying levels of preheat zone broadening in all the TRZ and D/BRZ cases. While the average heat release distribution for the TRZ cases is nearly identical to the laminar unstrained baseline, changes to the species and heat release distribution are observed only at a high Karlovitz Number K a > 103. In the D/BRZ regime it is shown that the transition is related to enhanced turbulent diffusion that dominates molecular diffusion effects causing deviations from the laminar baseline.

Dispersion in the large-deviation regime. Part 2. Cellular flow at large Péclet number

AbstractA standard model for the study of scalar dispersion through the combined effect of advection and molecular diffusion is a two-dimensional periodic flow with closed streamlines inside periodic cells. Over long time scales, the dispersion of a scalar released in this flow can be characterized by an effective diffusivity that is a factor$\mathit{Pe}^{1/2}$larger than molecular diffusivity when the Péclet number$\mathit{Pe}$is large. Here we provide a more complete description of dispersion in this regime by applying the large-deviation theory developed in Part 1 of this paper. Specifically, we derive approximations to the rate function governing the scalar concentration at large time$t$by carrying out an asymptotic analysis of the relevant family of eigenvalue problems. We identify two asymptotic regimes and, for each, make predictions for the rate function and spatial structure of the scalar. Regime I applies to distances$|\boldsymbol {x}|$from the scalar release point that satisfy$|\boldsymbol {x}|= O(\mathit{Pe}^{1/4} t)$. The concentration in this regime is isotropic at large scales, is uniform along streamlines within each cell, and varies rapidly in boundary layers surrounding the separatrices between adjacent cells. The results of homogenization theory, yielding the$O(\mathit{Pe}^{1/2})$effective diffusivity, are recovered from our analysis in the limit$|\boldsymbol {x}|\ll \mathit{Pe}^{1/4} t$. Regime II applies when$|\boldsymbol {x}|=O(\mathit{Pe}\, t/{\rm log}\, \mathit{Pe})$and is characterized by an anisotropic concentration distribution that is localized around the separatrices. A novel feature of this regime is the crucial role played by the dynamics near the hyperbolic stagnation points. A consequence is that in part of the regime the dispersion can be interpreted as resulting from a random walk on the lattice of stagnation points. The two regimes overlap so that our asymptotic results describe the scalar concentration over a large range of distances$|\boldsymbol {x}|$. They are verified against numerical solutions of the family of eigenvalue problems yielding the rate function.

Numerical Simulation of Differential Molecular Diffusion Effects in a Hydrogen-rich Turbulent Jet Using LEM3D

The LEM3D stochastic model for numerical simulation of turbulent mixing is used to simulate differential molecular diffusion effects in an isothermal jet of hydrogen and Freon 22 issued into air. The computations are compared with a published experimental study of the flow configuration. Salient features of the measured results are reproduced qualitatively, but the absence of spatial variation of the smallest eddy motion in LEM3D omits the streamwise variation of this length scale in the experimental configuration, resulting in a systematic deviation from the experimental trend. A first-principles basis for incorporating this missing physics into LEM3D is described, indicating the path forward for physically based quantitative prediction of differential diffusion effects, and turbulent combustion phenomenology more generally, using LEM3D.

An Experimental Study of the Matrix-fracture Interaction During Miscible Displacement in Fractured Porous Media: A Micromodel Study

During miscible displacements in fractured porous media, one of the most important factors that plays a significant role in oil production is the matrix-fracture interaction. In this work, a series of hydrocarbon injection experiments have been performed on a fractured glass micromodel that was designed specifically to study matrix-fracture interaction. A high quality image analysis method was used to determine the fluid flow behavior, solvent front movement, and viscous fingering associated with solvent movement in matrix and fractures. Observations showed that in the case of unit viscosity ratio, the injection rate increased the slope of recovery curve and consequently improved the final oil recovery. However, when using a viscosity ratio of 65, the injection rate increased the oil recovery at earlier times due to the breakthrough and fracture drainage. At later times, diffusion and dispersion became dominant and oil recovery decreased. Studying the effect of molecular diffusion revealed that by using an optimum solvent the oil recovery at both early and late times increased. Fingering phenomena appeared in the matrix as fingers and in the matrix as channeling, which drained fracture in early times of the process. In higher viscosity ratios, dispersion dominantly takes place in an upward direction, however, in the lower viscosity ratio the effect of fracture in flooding decreased and dispersion takes place in a left-to-right direction. It can be concluded that during miscible displacement in fractured porous media dispersion in fracture is directly proportional to viscosity ratio while dispersion in matrix is inversely proportional to it. The results of this work are helpful in understanding the matrix-fracture interaction, the effect of injection rate, molecular diffusion, and viscous fingering behavior, which are crucial for accurate prediction of oil recovery in fractured reservoirs during miscible displacements.

An investigation of mixing in a three-stream turbulent jet

Mixing models are required to account for the effects of molecular diffusion in probability density function (PDF) methods for reacting flows, and these models entail one of the greatest sources of modeling uncertainty in PDF calculations. In this work, we perform PDF calculations of a turbulent coaxial jet using both Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) based methods. The configuration of the coaxial jet comes from a recently developed experiment, in which the conditional diffusion and scalar dissipation rate of two conserved scalars are measured. These measurements present the unique opportunity to compare directly the conditional diffusion implied by PDF mixing models to the measured conditional diffusion. In the RANS-PDF calculations, three classic mixing models are evaluated: Interaction by Exchange with the Mean (IEM), Modified Curl (MC), and Euclidean Minimum Spanning Tree (EMST). Though calculations with all three mixing models yield time-averaged mean and RMS statistics of the two scalars in good agreement with the experimental measurements, the joint PDFs of the two scalars show a wide variability from the measurements. The EMST mixing model is unique in that it produces compositions which lie very close to the slow manifold identified in the experimental work. Next, LES calculations of the same flow are performed, and the dissipation rate and conditional diffusion are calculated. The resolved scalar dissipation rate is found to be in good agreement with the experimental data, but depends strongly on the resolution; the total dissipation rate from the RANS-PDF and LES calculations indicates significantly larger scalar dissipation rates than those measured experimentally. Finally, LES-PDF calculations of the same flow yield joint PDFs in very good agreement with the experimental data. The attenuation of variance production model is introduced and tested in this flow: this new model is found to yield calculations of improved accuracy in LES-PDF calculations on coarse grids.

In situ void content measurements during resin transfer molding

In resin transfer molding (RTM), the void content measured after resin curing does not represent the amount of voids at the point of air-trapping. To properly verify a prediction model for the void content based on the occurrence of voids due to the air-trapping mechanism, the void content must be measured immediately at the point of air-trapping. In the present study, we created an in situ method for measuring the void content during resin impregnation by combining image analysis with a technique that visualizes the resin flow and void formation during one-dimensional RTM. Using this proposed method, we measured changes in the distribution of the void content at the air-trapping site and following resin curing. As a result, an inversion phenomenon was observed, in which the void content decreased a short distance from the resin inlet due to the time that elapsed, whereas it increased at a longer distance. This phenomenon can be explained by the ease with which the void moved and by the effect of molecular diffusion. In addition, by measuring the change in void content during the time that elapsed from air-trapping until resin curing, we clarified the behavior of the void change and the factors that affect the void content following void formation.

Collapse of higher‐order solute concentration moments in groundwater transport

In this paper, we use numerical simulations based on a Lagrangian framework to study contaminant transport through highly heterogeneous porous media due to advection and local diffusion (under local diffusion, we assume coupled effect of mechanical dispersion and molecular diffusion). The analysis of the concentration field is done for the case of a two‐dimensional hydraulic conductivity domain representing the aquifer, with three log‐conductivity structures that differ in spatial correlation. In addition to different conductivity structures, we focus our investigation on mild and highly heterogeneous porous media characterized by the values of hydraulic log‐conductivity variance being equal to 1 and 8. In the concentration moment analysis, we show that a linear relationship exists between higher‐order to second‐order normalized concentration moments on a log‐log scale up to the fourth‐order moment. This leads to the important finding that moments of a higher than the second order can be derived based on information about the first two concentration moments only. Such a property has been observed previously for boundary‐layer water channels, wind tunnels, and turbulent diffusion in open terrain and laboratory experiments. Normalized moments are shown to collapse for different types of hydraulic conductivity structures, Peclet (Pe) numbers and values. In the case of local diffusion absence, a linear log‐log relationship is derived analytically and is set as a lower limit. The deviation from the lower limit is explained to be predominantly caused by the local diffusion, which needs time to evolve. In the case of local diffusion presence, we define the moment deriving function (MDF) to describe the linear log‐log relationship between higher‐order concentration moments to the second‐order normalized one. Finally, the comparison between numerical results and those obtained from the Columbus Air Force Base Macrodispersion Experiment (MADE 1) is used to demonstrate the robustness of the moment collapse.

MSE-MRI sequence optimisation for measurement of bi- and tri-exponential T2 relaxation in a phantom and fruit

The transverse relaxation signal from vegetal cells can be described by multi-exponential behaviour, reflecting different water compartments. This multi-exponential relaxation is rarely measured by conventional MRI imaging protocols; mono-exponential relaxation times are measured instead, thus limiting information about of the microstructure and water status in vegetal cells. In this study, an optimised multiple spin echo (MSE) MRI sequence was evaluated for assessment of multi-exponential transverse relaxation in fruit tissues. The sequence was designed for the acquisition of a maximum of 512 echoes. Non-selective refocusing RF pulses were used in combination with balanced crusher gradients for elimination of spurious echoes. The study was performed on a bi-compartmental phantom with known T2 values and on apple and tomato fruit. T2 decays measured in the phantom and fruit were analysed using bi- and tri-exponential fits, respectively. The MRI results were compared with low field non-spatially resolved NMR measurements performed on the same samples.The results demonstrated that the MSE-MRI sequence can be used for up to tri-exponential T2 quantification allowing for estimation of relaxation times from a few tens of milliseconds to over a second. The effects of the crusher moment and the TE value on T2 measurements were studied both on the bi-compartmental phantom and on the fruit tissues. It was demonstrated that the sequence should be optimised with regard to the characteristics of the tissue to be examined by considering the effects of water molecular diffusion in the presence of both imaging gradients and gradients produced by susceptibility inhomogeneities.

Effect of pour point on wax deposition under static cooling conditions

ABSTRACTWith the production of offshore oil and gas, wax deposition in multiphase crude pipelines has become a critical item for flow assurance. The emulsion pour point had a close relationship with the water cut of production liquid and made a significant effect on wax deposition. The investigation of the effects of water cut, pour point, and deposition enduring time on the wax deposition amount and the deposit components was conducted with static cold finger facilities. It was suggested that the effects of molecular diffusion and gelling on deposit thickness in oil–water emulsion are closely related to emulsion pour point. At a constant temperature, the function of molecular diffusion plays a leading role when it is at a low water cut and pour point. Otherwise, the function of gelling plays a leading role. This investigation offered a reference for the development of models for predicting oil–water two‐phase wax deposition in the future. © 2013 Curtin University of Technology and John Wiley &amp; Sons, Ltd.

A222 高圧条件下における予混合気自着火及び火炎伝播の直接数値計算(OS-1:火災安全・燃焼(5))

Direct numerical simulations of autoignition have been conducted to clarify effects of length scale in flow and temperature field and initial temperature fluctuations on turbulent combustion mechanisms in homogeneous charge compression ignition engines. Methane-air mixtures at high pressure with spatial inhomogeneity of temperature are investigated by considering a detailed kinetic mechanism. For the case with lower temperature fluctuations, local autoignition starts later at smaller length scale due to larger effects of turbulent and molecular diffusion before the autoignition, while effects of length scale is relatively weak for high temperature fluctuations. Lagrangian fluid particle tracking method is conducted to identify combustion regimes under the different length-scale conditions.

Direct numerical simulations of high speed reactive mixing layers

The present work is devoted to the analysis of ignition phenomena in high speed turbulent reactive flows. From the computational modelling point of view, this requires to account accurately for the competition between molecular diffusion effects and chemical kinetics as well as complex flowfield structures that may feature shock and expansion waves. Some results of direct numerical simulations of the multicomponent, compressible, reactive Navier-Stokes equations are reported here for the particular case of a two-dimensional mixing layer. Special emphasis is placed on the effects associated with heat release.

Infiltration mechanism of diamond/SiC composites fabricated by Si-vapor vacuum reactive infiltration process

Abstract Dense diamond/SiC composites were fabricated by Si vapor vacuum reactive infiltration of carbon-containing diamond porous preform at 1600 °C for 1 h. The microstructural evolution of the composites was investigated. The infiltration mechanisms during reactive infiltration were discussed. The composite consists of diamond, β-SiC and a small amount of Si. Epitaxial growth of nano-sized SiC on diamond and graphite surfaces occurred due to the diffusion-reaction mechanism in the initial stage of infiltration. Growth of micron-sized SiC with no preferential orientation was controlled by solution-precipitation mechanism in the final stage. The infiltration process was determined both by molecular diffusion and capillary effects. Explosive evaporation of molten Si, volume expansion of the solids and heat release during the reaction were the key factors contributing to the rapid densification of diamond/SiC composites. High thermal conductivity (580 W m −1 K −1 ) and low density (3.33 g cm −3 ) of the composites were beneficial to thermal management applications.

Limitation of Diffusion Effects in Ultrafast 2D Nuclear Magnetic Resonance by Encapsulation of Analytes in Phospholipidic Vesicles

Increased sensitivity: A new sample-preparation procedure is described to limit molecular diffusion effects in NMR experiments. It is based on analyte encapsulation in liposomes and is particularly useful for ultrafast multidimensional NMR experiments.

Spectral analysis of mixing in chaotic flows via the mapping matrix formalism: Inclusion of molecular diffusion and quantitative eigenvalue estimate in the purely convective limit

This paper extends the mapping matrix formalism to include the effects of molecular diffusion in the analysis of mixing processes in chaotic flows. The approach followed is Lagrangian, by considering the stochastic formulation of advection-diffusion processes via the Langevin equation for passive fluid particle motion. In addition, the inclusion of diffusional effects in the mapping matrix formalism permits to frame the spectral properties of mapping matrices in the purely convective limit in a quantitative way. Specifically, the effects of coarse graining can be quantified by means of an effective Péclet number that scales as the second power of the linear lattice size. This simple result is sufficient to predict the scaling exponents characterizing the behavior of the eigenvalue spectrum of the advection-diffusion operator in chaotic flows as a function of the Péclet number, exclusively from purely kinematic data, by varying the grid resolution. Simple but representative model systems and realistic physically realizable flows are considered under a wealth of different kinematic conditions–from the presence of large quasi-periodic islands intertwined by chaotic regions, to almost globally chaotic conditions, to flows possessing “sticky islands”–providing a fairly comprehensive characterization of the different numerical phenomenologies that may occur in the quantitative analysis of mapping matrices, and ultimately of chaotic mixing processes.

Direction of scalar transport in turbulent channel flow

The concept of reverse diffusion, introduced by Corrsin to describe the motion of particles as they move towards a location in the flow field, is fundamental to the understanding of mixing. In this work, direct numerical simulations in conjunction with the tracking of scalar markers are utilized in infinitely long channels to study the principal direction of transport of heat (or mass) for both forwards and backwards single particle dispersion. The viscous sub-layer, the transition region (between the viscous sub-layer and the logarithmic region), and the logarithmic region of a Poiseuille flow and a plane Couette flow channel are studied. Fluctuating velocities of scalar markers captured in these regions are used to obtain the full autocorrelation coefficient tensor forwards and backwards with time. The highest eigenvalue of the velocity correlation coefficient tensor quantifies the highest amount of turbulent heat transport, while the corresponding eigenvector points to the main direction of transport. Different Prandtl number, Pr, fluids are simulated for the two types of flow. It is found that the highest eigenvalues are higher in the case of backwards dispersion compared to the case of forwards dispersion for any Pr, in both flow cases. The principal direction for backwards and forwards dispersion is different than for forwards dispersion, for all Pr, and in all flow regions for both flows. Fluids with lower Pr behave different than the higher Pr fluids because of increased molecular diffusion effects. The current study also establishes an interesting analogy of turbulent dispersion to optics defining the turbulent dispersive ratio, a parameter that can be used to identify the differences in the direction of turbulent heat transport between forwards and backwards dispersion. A spectral analysis of the auto-correlation coefficient for both forwards and backwards dispersion shows a universal behavior with slope of −1 at intermediate frequencies.