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Journal articles on the topic 'Double diffusion'

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Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2023

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1

Khair, Abul, Nilay Kumar Dey, Mohammad Harun-Ur-Rashid, Mohammad Abdul Alim, Newas Mohammad Bahadur, Sultan Mahamud, and Syekat Ahmed. "Diffusimetry Renounces Graham’s Law, Achieves Diffusive Convection, Concentration Gradient Induced Diffusion, Heat and Mass Transfer." Defect and Diffusion Forum 407 (March 2021): 173–84. http://dx.doi.org/10.4028/www.scientific.net/ddf.407.173.

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Absolute diffusion rates of KMnO4 in vertical and flattened diffusimeters show the concentration gradient force as being stronger than the gravitational force. Hot water molecules move downward on self-diffusion against buoyancy. Diffusive convection (DC) in warm water and double-diffusive convection (DDC) in warm, saline water take place inside the diffusimeter with DDC transferring more heat than DC. In the diffusing medium the original reagents change or retain their compositions to give the diffusate molecules to diffuse. In water, the change is mostly hydration. The syngener BaCl2.2H2O separately with congeners 3CdSO4.8H2O, ZnSO4.7H2O, and ZnSO4.H2O presents two distinct pairs of overlapping concentration versus rate curves, first for having very close MWs of BaCl2 and CdSO4 and second for having ZnSO4.H2O as the common congener for both the zinc sulfates. Chlorides of Li, Na, and K diffusing at hindered rates in glucose solution show the least rate for LiCl inevitably on grounds of low mass and high Li+ hydration radius. Diffusion blocking occurs at higher glucose concentration. Diffusion of 0.6M AgNO3-0.6M NH4Cl standardizes this diffusimeter. Mass transfer of HCl, H2SO4, and H2C2O4 show oxalic acid diffusing as hydrate and 88 percentage transfer of sulfuric acid in 5 minutes. The Superdiffusive Anti Graham’s Law, Vd , is further consolidated by Ca (NO3)2-M2CO3(M = Na, K, NH4+) and Ca (NO3)2-Na2HPO4 diffusions. Odd and even diffusions are illustrated by AgNO3-NH4Cl and AgNO3-BaCl2 diffusions.

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2

Cox, Stephen M., Sidney Leibovich, Irene M. Moroz, and Amit Tandon. "Nonlinear dynamics in Langmuir circulations with O(2) symmetry." Journal of Fluid Mechanics 241 (August 1992): 669–704. http://dx.doi.org/10.1017/s0022112092002192.

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A direct comparison is made between the dynamics obtained by weakly nonlinear theory and full numerical simulations for Langmuir circulations in a density-stratified layer having finite depth and infinite horizontal extent. In one limit, the mathematical formulation employed is analogous to that of double-diffusion phenonema with the flux of one diffusing quantity fixed at the boundaries of the layer. These problems have multiple bifurcation points, but their amplitude equations have no intrinsic (nonlinear) degeneracies, in contrast to ‘standard’ double-diffusion problems. The symmetry of the physical problem implies invariance with respect to translations and reflections in the horizontal direction normal to the applied wind stress (so-called O(2) symmetry). A multiple bifurcation at a double-zero point serves as an organizing centre for dynamics over a wide range of parameter values. This double zero, or Takens–Bogdanov, bifurcation leads to doubly periodic motions manifested as modulated travelling waves. Other multiple bifurcation points appear as double-Hopf bifurcations. It is believed that this paper gives the first quantitative comparison of dynamics of double-diffusive type predicted by rationally derived amplitude equations and by full nonlinear partial differential equations. The implications for physically observable natural phenomena are discussed. This problem has been treated previously, but the earlier numerical treatment is in error, and is corrected here. When the Stokes drift gradient due to surface waves is not constant, the analogy with the common formulations of double-diffusion problems is compromised. Our bifurcation analyses are extended here to include the case of exponentially decaying Stokes drift gradient.

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3

Schmitt, R. W. "Double Diffusion in Oceanography." Annual Review of Fluid Mechanics 26, no. 1 (January 1994): 255–85. http://dx.doi.org/10.1146/annurev.fl.26.010194.001351.

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4

Carpenter, J. R., T. Sommer, and A. Wüest. "Stability of a Double-Diffusive Interface in the Diffusive Convection Regime." Journal of Physical Oceanography 42, no. 5 (May 1, 2012): 840–54. http://dx.doi.org/10.1175/jpo-d-11-0118.1.

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Abstract In this paper, the authors explore the conditions under which a double-diffusive interface may become unstable. Focus is placed on the case of a cold, freshwater layer above a warm, salty layer [i.e., the diffusive convection (DC) regime]. The “diffusive interface” between these layers will develop gravitationally unstable boundary layers due to the more rapid diffusion of heat (the destabilizing component) relative to salt. Previous studies have assumed that a purely convective-type instability of these boundary layers is what drives convection in this system and that this may be parameterized by a boundary layer Rayleigh number. The authors test this theory by conducting both a linear stability analysis and direct numerical simulations of a diffusive interface. Their linear stability analysis reveals that the transition to instability always occurs as an oscillating diffusive convection mode and at boundary layer Rayleigh numbers much smaller than previously thought. However, these findings are based on making a quasi-steady assumption for the growth of the interfaces by molecular diffusion. When diffusing interfaces are modeled (using direct numerical simulations), the authors observe that the time dependence is significant in determining the instability of the boundary layers and that the breakdown is due to a purely convective-type instability. Their findings therefore demonstrate that the relevant instability in a DC staircase is purely convective.

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5

Oshchepkov, V. O., Е. А. Mosheva, and А. I. Mizev. "Double diffusive instability during codirectional diffusion of dissolved components." Вестник Пермского университета. Физика, no. 4 (2019): 60–65. http://dx.doi.org/10.17072/1994-3598-2019-4-60-65.

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6

Gudbjartsson, Hákon, Stephan E. Maier, and Ferenc A. Jolesz. "Double line scan diffusion imaging." Magnetic Resonance in Medicine 38, no. 1 (July 1997): 101–9. http://dx.doi.org/10.1002/mrm.1910380115.

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7

Milhazes, Jorge, and Pedro J. Coelho. "Adaptive Finite Element Simulation of Double-Diffusive Convection." Energies 16, no. 4 (February 17, 2023): 2010. http://dx.doi.org/10.3390/en16042010.

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Double-diffusive convection plays an important role in many physical phenomena of practical importance. However, the numerical simulation of these phenomena is challenging since fine meshes are often required to capture the flow physics. Hence, several different numerical methods have been employed in the past. This work reports the development and application of an adaptive finite element method for the simulation of these phenomena, thereby avoiding the need for the use of very fine meshes over the whole domain. The weak formulation of the conservation equations for mass, momentum, energy and species concentration is used. The Boussinesq approximation relates the density of the fluid to the temperature and/or the species concentration. A second-order backward difference method is used for time discretization and the Galerkin method is employed for spatial discretization. Both adaptive time step and grid refinement techniques are employed, and the code is parallelized using MPI. Three different stabilization methods of the convective-diffusion equations are compared; namely, the streamline upwind Petrov–Galerkin (SUPG) method, and two modified methods aimed at diminishing spurious oscillations that include an artificial diffusion term. This diffusion term may be either isotropic or orthogonal to the streamlines. The addition of artificial isotropic diffusion to the SUPG method provides enhanced stability. The method is applied to double-diffusive finger convection in a sucrose-salt aqueous mixture and a stratified salt solution heated from below. The method accurately reproduces the experimentally observed temporal evolution of the salt fingers in the former case and the location of the interfaces between convective and non-convective zones in the latter.

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8

Radko, Timour, and Melvin E. Stern. "Finescale Instabilities of the Double-Diffusive Shear Flow*." Journal of Physical Oceanography 41, no. 3 (March 1, 2011): 571–85. http://dx.doi.org/10.1175/2010jpo4459.1.

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Abstract This study examines dynamics of finescale instabilities in thermohaline–shear flows. It is shown that the presence of the background diapycnal temperature and salinity fluxes due to double diffusion has a destabilizing effect on the basic current. Using linear stability analysis based on the Floquet theory for the sinusoidal basic velocity profile, the authors demonstrate that the well-known Richardson number criterion (Ri < ¼) cannot be directly applied to doubly diffusive fluids. Rigorous instabilities are predicted to occur for Richardson numbers as high as—or even exceeding—unity. The inferences from the linear theory are supported by the fully nonlinear numerical simulations. Since the Richardson number in the main thermocline rarely drops below ¼, whereas the observations of turbulent patches are common, the authors hypothesize that some turbulent mixing events can be attributed to the finescale instabilities associated with double-diffusive processes.

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9

Bratsun, D. A., V. O. Oschepkov, E. A. Mosheva, and R. R. Siraev. "The effect of concentration-dependent diffusion on double-diffusive instability." Physics of Fluids 34, no. 3 (March 2022): 034112. http://dx.doi.org/10.1063/5.0079850.

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The article studies the stability of a two-layer miscible system to the double-diffusive instability. The system is placed in a vertical Hele–Shaw cell and is composed of two homogeneous aqueous solutions initially separated by a narrow transient zone. We have restricted our consideration to the initially stable density stratification that precludes the Rayleigh–Taylor instability. The main objective of the study is to elucidate the effect of a concentration-dependent diffusion coefficient, which has been commonly ignored by researchers. Assuming linear dependence of the diffusion coefficient of each solute and using Picard's iteration scheme, we have derived a closed-form analytical expression for the time-dependent density profile. This permits the stability boundary to be established for a two-layer system with respect to the double-diffusive instability by taking into account the effect of a concentration-dependent diffusion coefficient. The obtained analytical result has been substantiated by the results of direct numerical simulation. The experiments have shown that a successive increase in the concentrations of both solutes, with their ratio remaining unchanged, can lead to opposite results. In the case of a NaNO3-H2SO4 pair, the two-layer system, being stable at low concentrations, becomes unstable as the concentrations proportionally increase, giving rise to convective motion in the form of salt fingers. On the contrary, a two-layer system consisting of LiCl and NaNO3 solutions is stabilized with increasing concentrations of dissolved substances. A further increase in the concentrations of these substances causes mechanical equilibrium breaking and subsequent formation of the so-called diffusive-layer convection. The experimental results are in good agreement with the theoretical predictions.

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10

Pulicani, J. P. "Modélisation isotherme d'une interface diffusive en convection de double-diffusion." International Journal of Heat and Mass Transfer 37, no. 18 (December 1994): 2835–58. http://dx.doi.org/10.1016/0017-9310(94)90339-5.

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11

Ahmad, Muhammad, Dalal Alrowaili, Rifaqat Ali, Zohaib Zahid, and Imran Siddique. "Double Metric Resolvability in Convex Polytopes." Journal of Mathematics 2022 (July 31, 2022): 1–10. http://dx.doi.org/10.1155/2022/5884924.

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Nowadays, the study of source localization in complex networks is a critical issue. Localization of the source has been investigated using a variety of feasible models. To identify the source of a network’s diffusion, it is necessary to find a vertex from which the observed diffusion spreads. Detecting the source of a virus in a network is equivalent to finding the minimal doubly resolving set (MDRS) in a network. This paper calculates the doubly resolving sets (DRSs) for certain convex polytope structures to calculate their double metric dimension (DMD). It is concluded that the cardinality of MDRSs for these convex polytopes is finite and constant.

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12

Aliakbarzadeh Kashani, Davood, Saeed Dinarvand, Ioan Pop, and Tasawar Hayat. "Effects of dissolved solute on unsteady double-diffusive mixed convective flow of a Buongiorno’s two-component nonhomogeneous nanofluid." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 1 (January 7, 2019): 448–66. http://dx.doi.org/10.1108/hff-04-2018-0168.

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Purpose The purpose of this paper is to numerically study the unsteady double-diffusive mixed convective stagnation-point flow of a water-based nanofluid accompanied with one salt past a vertical flat plate. The effects of Brownian motion and thermophoresis parameters are also introduced through Buongiorno’s two-component nonhomogeneous equilibrium model in the governing equations. Design/methodology/approach In the present explanation of double-diffusive mixed convective model, there are four boundary layers entitled: velocity, thermal, solutal concentration and nanoparticle concentration. The resulting basic equations are solved numerically via an efficient Runge–Kutta fourth-order method with shooting technique after the governing nonlinear partial differential equations are converted into a system of nonlinear ordinary differential equations by the use of similarity transformations. Findings To avail the physical insight of problem, the effects of the mixed convection parameter, unsteadiness parameter and salt/nanoparticle parameters on the boundary layers behavior are investigated. Moreover, four possible types of diffusion problems entitled: double-diffusive nanofluid (DDNF), double-diffusive regular fluid (DDRF), mono-diffusive nanofluid (MDNF) and mono-diffusive regular fluid (MDRF) are considered to analyze and compare them in concepts of heat and mass transfer. Originality/value The results demonstrate that, for a regular fluid, without nanoparticle and salt (MDRF), the dimensionless heat transfer rate is smaller than other diffusion cases. As we include nanoparticle and salt (DDNF), the rate of heat transfer increases due to an increase in thermal conductivity and rate of diffusion of salt. Moreover, it is observed that the highest heat transfer rate is obtained for the situation that the thermophoretic effect of nanoparticles is negligible. Besides, the heat transfer rate enhances with the increase in the regular double-diffusive buoyancy parameter of salt.

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13

Jungnickel, Christian, David Smith, and Stephen Fityus. "Coupled multi-ion electrodiffusion analysis for clay soils." Canadian Geotechnical Journal 41, no. 2 (April 1, 2004): 287–98. http://dx.doi.org/10.1139/t03-092.

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For a well-engineered compacted clay landfill liner, diffusive transport through the liner is the main mass transport mechanism from the landfill. Therefore, accurate estimates of diffusion coefficients for clay liners are essential for the engineering design of liner systems. A long-standing problem has been the effect of ion pairing on the estimation of diffusion coefficients for multicomponent ionic solutions migrating through clay liners. This paper considers the solution of a fully coupled set of transport equations describing the simultaneous diffusion of several ion species through a clayey soil. The analysis takes into account the diffusion coefficient for each ion species, ion pairing (as required by electroneutrality of the solution), and time-dependent first-order ion and (or) ligand exchange reactions with the clay particles. The behaviour of a double-reservoir diffusion cell, often employed for the estimation of diffusion coefficients in the laboratory, is analyzed using the coupled transport model. A detailed theoretical analysis is made of sodium fluoride transport through saturated kaolinitic clay.Key words: multi-ion diffusion, finite element analysis, reactive transport, kaolinite, double-reservoir diffusion cell.

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14

von Rohden, C., B. Boehrer, and J. Ilmberger. "Evidence for double diffusion in temperate meromictic lakes." Hydrology and Earth System Sciences 14, no. 4 (April 13, 2010): 667–74. http://dx.doi.org/10.5194/hess-14-667-2010.

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Abstract. We present CTD-measurements from two shallow meromictic mining lakes. The lakes, which differ in size and depth, show completely different seasonal mixing patterns in their mixolimnia. However, the measurements document the occurrence of similar seasonal convective mixing in discrete layers within their monimolimnia. This mixing is induced by double diffusion and can be identified by the characteristic step-like structure of the temperature and electrical conductivity profiles. The steps develop in the upper part of the monimolimnion, when in autumn cooling mixolimnion temperatures have dropped below temperatures of the underlying monimolimnion. The density gradient across the chemocline due to solutes overcompensates the destabilizing temperature gradient, and moreover, keeps the vertical transport close to molecular level. In conclusion, preconditions for double diffusive effects are given on a seasonal basis. At in general high local stabilities N2 in the monimolimnia of 10−4–10−2s−2, the stability ratio Rρ was in the range of 1–20. This quantitatively indicates that double diffusion can become visible. Between 1 and 6 sequent steps, with sizes between 1 dm and 1 m, were visually identified in the CTD-profiles. In the lower monimolimnion of the deeper lake, the steps systematically emerge at a time delay of more than half a year, which matches with the progression of the mixolimnetic temperature changes into the monimolimnion. In none of the lakes, the chemocline interface is degraded by these processes. However, double diffusive convection is essential for the redistribution of solutes in the inner parts of the monimolimnion at longer time scales, which is crucial for the assessment of the ecologic development of such lakes.

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15

EFTEKHARI, ALI. "LIMITATIONS OF ELECTROCHEMICAL METHODS FOR SURFACE ANALYSIS AT SMALL FRACTALITY SCALES." Surface Review and Letters 13, no. 06 (December 2006): 809–14. http://dx.doi.org/10.1142/s0218625x0600889x.

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Based on solid arguments, it was demonstrated that: (i) the fractality scale detected during electrochemical measurements depends only on the yardstick length, i.e., the diffusion layer width, and not on the size of the diffusing electroactive species; (ii) Fractal analysis cannot be performed by electrochemical methods at scales smaller than 100 nm, since the thickness of Helmholtz double layer is comparable with the diffusion layer width, and the diffusion layer width cannot be assumed to act as yardstick length. Indeed, it should be taken into account that the yardstick length is equal to "diffusion layer width + Helmholtz double layer." On the other hand, thin diffusion layers on rough surfaces lead to 3D diffusion; thus, the fundamental electrochemistry is no longer valid. In general, fractal analyses by electrochemical methods has severe limitations, which should be taken into account before applying it for different cases. In other words, surface analysis by this approach just senses microscale roughness, and ignores nanostructure.

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16

Sohn, Y. H., and M. A. Dayananda. "A double-serpentine diffusion path for a ternary diffusion couple." Acta Materialia 48, no. 7 (April 2000): 1427–33. http://dx.doi.org/10.1016/s1359-6454(99)00454-1.

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17

Rudraiah, N., and M. S. Malashetty. "The Influence of Coupled Molecular Diffusion on Double-Diffusive Convection in a Porous Medium." Journal of Heat Transfer 108, no. 4 (November 1, 1986): 872–76. http://dx.doi.org/10.1115/1.3247026.

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The effect of coupled molecular diffusion on double-diffusive convection in a horizontal porous medium is studied using linear and nonlinear stability analyses. In the case of linear theory, normal mode analysis is employed incorporating two cross diffusion terms. It is found that salt fingers can form by taking cross-diffusion terms of appropriate sign and magnitude even when both concentrations are stably stratified. The conditions for the diffusive instability are compared with those for the formation of fingers. It is shown that these two types of instability will never occur together. The finite amplitude analysis is used to derive the condition for the maintenance of fingers. The stability boundaries are drawn for three different combinations of stratification and the effect of permeability is depicted.

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18

Wichman, Indrek S., and Michael Yang. "Double-spray counterflow diffusion flame model." Combustion Theory and Modelling 2, no. 4 (December 1998): 373–98. http://dx.doi.org/10.1088/1364-7830/2/4/002.

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19

Raupp, S. M., P. G. Kitz, D. Siebel, L. Merklein, P. Scharfer, and W. Schabel. "Modeling Diffusion in Polymer Double Layers." Chemie Ingenieur Technik 88, no. 9 (August 29, 2016): 1372–73. http://dx.doi.org/10.1002/cite.201650098.

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20

White, P., R. G. Brower, J. T. Sylvester, T. Permutt, and S. Permutt. "Influence of diffusion on estimations of protein reflection coefficient by double-indicator method." Journal of Applied Physiology 75, no. 4 (October 1, 1993): 1734–39. http://dx.doi.org/10.1152/jappl.1993.75.4.1734.

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In isolated perfused organs, vascular protein reflection coefficients (sigma) can be calculated from the changes in hematocrit and perfusate protein concentration (CP) that occur during edema formation. This technique requires the assumption that transvascular protein flux by diffusion is negligible. To assess diffusion-induced errors in calculations of sigma, we derived an expression for CP that includes determinants of diffusive protein flux: protein permeability-surface area product (PS), transvascular fluid flux (J), true sigma, and transvascular protein concentration. We used this expression to obtain values of CP under various experimental conditions and then calculated values of sigma (measured sigma) for those conditions. Diffusion causes measured sigma to be lower than true sigma. The diffusion-induced error is larger and potentially substantial when J/PS is low and when true sigma is high. Diffusion-induced error is also larger when the amount of edema formation is greater. In recent isolated canine lung experiments where J/PS was approximately 2.7, diffusion-induced errors in measured sigma for albumin would have been approximately 0.06 (at true sigma = 0.5) and approximately 0.18 (at true sigma = 0.9). When J/PS was higher, the potential for diffusion-induced errors was much smaller. We conclude that diffusion causes underestimation of true sigma and that the error in measured sigma may be substantial when J/PS is < 5 and when true sigma is > 0.5.

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21

Shankar, Usha, Neminath B. Naduvinamani, and Hussain Basha. "A generalized perspective of Fourier and Fick’s laws: Magnetized effects of Cattaneo-Christov models on transient nanofluid flow between two parallel plates with Brownian motion and thermophoresis." Nonlinear Engineering 9, no. 1 (April 23, 2020): 201–22. http://dx.doi.org/10.1515/nleng-2020-0009.

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AbstractPresent research article reports the magnetized impacts of Cattaneo-Christov double diffusion models on heat and mass transfer behaviour of viscous incompressible, time-dependent, two-dimensional Casson nanofluid flow through the channel with Joule heating and viscous dissipation effects numerically. The classical transport models such as Fourier and Fick’s laws of heat and mass diffusions are generalized in terms of Cattaneo-Christov double diffusion models by accounting the thermal and concentration relaxation times. The present physical problem is examined in the presence of Lorentz forces to investigate the effects of magnetic field on double diffusion process along with Joule heating. The non-Newtonian Casson nanofluid flow between two parallel plates gives the system of time-dependent, highly nonlinear, coupled partial differential equations and is solved by utilizing RK-SM and bvp4c schemes. Present results show that, the temperature and concentration distributions are fewer in case of Cattaneo-Christov heat and mass flux models when compared to the Fourier’s and Fick’s laws of heat and mass diffusions. The concentration field is a diminishing function of thermophoresis parameter and it is an increasing function of Brownian motion parameter. Finally, an excellent comparison between the present solutions and previously published results show the accuracy of the results and methods used to achieve the objective of the present work.

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Inoue, Ryuichiro, Hidekatsu Yamazaki, Fabian Wolk, Tokihiro Kono, and Jiro Yoshida. "An Estimation of Buoyancy Flux for a Mixture of Turbulence and Double Diffusion." Journal of Physical Oceanography 37, no. 3 (March 1, 2007): 611–24. http://dx.doi.org/10.1175/jpo2996.1.

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Abstract Microstructure measurements were made in the Mixed Water Region of the Oyashio/Kuroshio/Tsugaru currents system where both turbulence and double diffusion are involved in mixing. While intense turbulence is observed near the front between the Oyashio and the Tsugaru Current, double diffusion occupies a noticeable fraction in both the Tsugaru Water and the Mixed Water between the Oyashio and the Kuroshio. After determining a criterion to distinguish double diffusion from turbulence, vertical diffusivities and buoyancy fluxes are estimated using microstructure data. When turbulence is weak, double diffusion is observed around temperature and salinity anomalies, partly due to interleaving, and dominates the buoyancy flux. Vertical diffusivities due to double diffusion are parameterized as a function of the 10-m-scale density ratio. The 10-m-scale diffusivity estimates are consistent with the microstructure data when an appropriate criterion to reproduce a probability density function for the Turner angle is applied. A weighted-average diffusivity model is proposed to account properly for turbulence and double diffusion simultaneously.

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Shivakumara, I. S., K. R. Raghunatha, and G. Pallavi. "Intricacies of coupled molecular diffusion on double diffusive viscoelastic porous convection." Results in Applied Mathematics 7 (August 2020): 100124. http://dx.doi.org/10.1016/j.rinam.2020.100124.

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Li, Yuehua, and Trevor J. McDougall. "Double-Diffusive Interleaving: Properties of the Steady-State Solution." Journal of Physical Oceanography 45, no. 3 (March 2015): 813–35. http://dx.doi.org/10.1175/jpo-d-13-0236.1.

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AbstractDouble-diffusive interleaving is examined as it progresses from a linear instability toward finite amplitude. When the basic stratification is in the “finger” sense, the initial series of finger interfaces is unstable and one grows in strength at the expense of the others. At an intermediate stage of its development, the interleaving motions pass through a stage when every second interface in the vertical is stable to double diffusion. At a later time this interface turns into a “diffusive” double-diffusive interface. This study takes the fluxes of heat and salt across both the finger and diffusive interfaces to be given by the laboratory flux laws, and the authors ask whether a steady state is possible. It is found that the fluxes across the diffusive interfaces must be many times stronger relative to the corresponding fluxes across the finger interfaces than is indicated from existing flux expressions derived from laboratory experiments. The total effect of the interleaving motion on the vertical fluxes of heat and of salt are calculated for the steady-state solutions. It is found that both the fluxes of heat and salt are upgradient, corresponding to a negative vertical diffusion coefficient for all heat, salt, and density. For moderate to large Prandtl numbers, these negative effective diapycnal diffusivities of heat and salt are approximately equal so that the interleaving process acts to counteract some of the usual turbulent diapycnal diffusivity due to breaking internal waves.

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YAN, JIANWU, and JICHENG ZHOU. "ELEMENTAL DIFFUSION IN Ni–Cr FILMS FABRICATED BY DOUBLE-TARGETS MAGNETRON SPUTTERING." International Journal of Modern Physics B 21, no. 12 (May 10, 2007): 1981–96. http://dx.doi.org/10.1142/s0217979207037132.

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By controlling the sputtering power, rotated speed of substrate and sputtering time, Ni – Cr films with appropriate composition were fabricated by double-target magnetron co-sputtering techniques. The cross-sectional micrograph and element diffusion of Ni – Cr films deposited on stainless steel substrates by magnetron sputtering have been analyzed by scanning electron microscope (SEM) and energy dispersive spectroscope (EDS). The results indicate that the according compositions of Ni – Cr films are 58 wt.% Ni and 42 wt.% Cr when the sputtering powers of Ni and Cr targets are 288 W and 280 W, respectively. In the same time, the diffusions of Ni , Fe and Cr were revealed and the diffusion distances of Ni and Cr are calculated by Fick's second law with a Pile-Up law model. The largest diffusion distance is about 885 nm, beyond which the content of Ni and Cr detected by EDS is the same as the substrate.

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26

WANG, CHANGQING, YU JIA, XUEQING WANG, XINJIAN LI, XING HU, and SONGYOU WANG. "MOLECULAR DYNAMICS SIMULATIONS OF SINGLE Si ADATOM DIFFUSION ON THE Si(001) SURFACE AND ACROSS SINGLE-LAYER Si(001) STEPS." Modern Physics Letters B 22, no. 02 (January 20, 2008): 117–25. http://dx.doi.org/10.1142/s0217984908014602.

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By using the Stillinger–Weber atomic interactional potential, we have carried out molecular dynamics simulations of single Si adatom diffusing on the Si(001) surface and single-layer Si(001) steps at temperatures ranging from 1000 K to 1300 K. We have presented one new diffusion pathway of a single Si adatom diffusing on the Si(001) along the direction perpendicular to dimer rows, that can weaken the diffusion anisotropy. We have investigated the process of the single Si adatom diffusing across single-layer Si(001) steps as well and given adatom diffusion pathways of step-flow and transformation of single-layer into double-layer steps. Our results show that the exchange between an adatom and a surface atom plays an important role in the adatom diffusion process above 1000 K.

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Dayananda, Mysore A. "Selected Analyses and Observations in Multicomponent Diffusion." Defect and Diffusion Forum 297-301 (April 2010): 1451–60. http://dx.doi.org/10.4028/www.scientific.net/ddf.297-301.1451.

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Selected isothermal diffusion studies in ternary and quaternary systems are reviewed in order to present analytical and experimental approaches adopted for the determination of interdiffusion fluxes of components, interdiffusion coefficients, diffusional interactions among components, and internal consistency in the experimental data. Several interesting phenomena and observations including uphill diffusion, zero-flux planes and flux reversals, and double serpentine diffusion paths are illustrated with selected single phase Cu-Ni-Zn, Fe-Ni-Al and Cu-Ni-Zn-Mn diffusion couples. The main challenges involved in the experimental determination of interdiffusion data from multicomponent diffusion couples and in the application of such data are also addressed.

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Radko, T., J. D. Flanagan, S. Stellmach, and M. L. Timmermans. "Double-Diffusive Recipes. Part II: Layer-Merging Events." Journal of Physical Oceanography 44, no. 5 (April 24, 2014): 1285–305. http://dx.doi.org/10.1175/jpo-d-13-0156.1.

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Abstract This study explores the dynamics of thermohaline staircases: well-defined stepped structures in temperature and salinity profiles, commonly observed in regions of active double diffusion. The evolution of staircases in time is frequently characterized by spontaneous layer-merging events. These phenomena, the authors argue, are essential in regulating the equilibrium layer thickness in fully developed staircases. The pattern and mechanics of merging events are explained using a combination of analytical considerations, direct numerical simulations, and data analysis. The theoretical merger model is based on the stability analysis for a series of identical steps and pertains to both forms of double diffusion: diffusive convection and salt fingering. The conceptual significance of the proposed model lies in its ability to describe merging events without assuming from the outset specific power laws for the vertical transport of heat and salt—the approach adopted by earlier merging models. The analysis of direct numerical simulations indicates that merging models based on the four-thirds flux laws offer adequate qualitative description of the evolutionary patterns but are less accurate than models that do not rely on such laws. Specific examples considered in this paper include the evolution of layers in the diffusive staircase in the Beaufort Gyre of the Arctic Ocean.

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Carpenter, J. R., T. Sommer, and A. Wüest. "Simulations of a double-diffusive interface in the diffusive convection regime." Journal of Fluid Mechanics 711 (September 14, 2012): 411–36. http://dx.doi.org/10.1017/jfm.2012.399.

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AbstractThree-dimensional direct numerical simulations are performed that give us an in-depth account of the evolution and structure of the double-diffusive interface. We examine the diffusive convection regime, which, in the oceanographically relevant case, consists of relatively cold fresh water above warm salty water. A ‘double-boundary-layer’ structure is found in all of the simulations, in which the temperature ($T$) interface has a greater thickness than the salinity ($S$) interface. Therefore, thin gravitationally unstable boundary layers are maintained at the edges of the diffusive interface. The $TS$-interface thickness ratio is found to scale with the diffusivity ratio in a consistent manner once the shear across the boundary layers is accounted for. The turbulence present in the mixed layers is not able to penetrate the stable stratification of the interface core, and the $TS$-fluxes through the core are given by their molecular diffusion values. Interface growth in time is found to be determined by molecular diffusion of the $S$-interface, in agreement with a previous theory. The stability of the boundary layers is also considered, where we find boundary layer Rayleigh numbers that are an order of magnitude lower than previously assumed.

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30

Frischauf, Leon, Melanie Melching, and Otmar Scherzer. "Diffusion tensor regularization with metric double integrals." Journal of Inverse and Ill-posed Problems 30, no. 2 (January 5, 2022): 163–90. http://dx.doi.org/10.1515/jiip-2021-0041.

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Abstract In this paper, we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting, which are defined appropriately. The regularization functionals are defined as double integrals, which are equivalent to Sobolev semi-norms in the Euclidean setting. We extend the analysis of [14] concerning stability and convergence of the variational regularization methods by a uniqueness result, apply them to diffusion tensor processing, and validate our model in numerical examples with synthetic and real data.

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Methot, Vincent, Patricia Ulloa, and Martin A. Koch. "Pore size estimation from double diffusion encoding." Current Directions in Biomedical Engineering 3, no. 2 (September 7, 2017): 627–30. http://dx.doi.org/10.1515/cdbme-2017-0131.

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AbstractDouble diffusion encoding is a magnetic resonance technique with applications in measuring microstructure. In many tissues, cell size (which is of a few micrometers) is an important biological parameter. Estimating an arbitrary pore size distribution from a diffusion attenuated signal usually relies on varying a single experimental setting. This inversion process is numerically unstable. Numerical simulations are presented, where multiple experimental settings are varied concomitantly. The inversion’s results show good agreement with ground truth.

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32

Zou, Liang-Jian, D. K. Campbell, and H. Q. Lin. "Spin diffusion dynamics in double exchange manganites." Journal of Applied Physics 87, no. 9 (May 2000): 5499–501. http://dx.doi.org/10.1063/1.373384.

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33

KITANO, Michio, Hideaki KOBAYASHI, and Nobuhiko NISHIKI. "Sooting limit of a double diffusion flame." Transactions of the Japan Society of Mechanical Engineers Series B 55, no. 515 (1989): 1979–84. http://dx.doi.org/10.1299/kikaib.55.1979.

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34

Seymour, I. D., A. Tarancón, A. Chroneos, D. Parfitt, J. A. Kilner, and R. W. Grimes. "Anisotropic oxygen diffusion in PrBaCo2O5.5 double perovskites." Solid State Ionics 216 (May 2012): 41–43. http://dx.doi.org/10.1016/j.ssi.2011.09.002.

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Azeem, N. Ameer Ahamad, Maughal Ahmed Ali Baig, N. J. Salman Ahmed, and Sarfaraz Kamangar. "Conjugate Double Diffusion: Effect of Buoyancy Ratio." Materials Today: Proceedings 24 (2020): 1410–15. http://dx.doi.org/10.1016/j.matpr.2020.04.459.

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36

Tarancón, Albert, Alexander Chroneos, David Parfitt, and John Kilner. "Oxygen Diffusion in Ordered/Disordered Double Perovskites." ECS Transactions 35, no. 1 (December 16, 2019): 1151–54. http://dx.doi.org/10.1149/1.3570097.

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37

Balducci, Anthony, Pan Mao, Jongyoon Han, and Patrick S. Doyle. "Double-Stranded DNA Diffusion in Slitlike Nanochannels." Macromolecules 39, no. 18 (September 2006): 6273–81. http://dx.doi.org/10.1021/ma061047t.

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38

Biebl, M., M. Bianco, K. Ehinger, H. v.Philipsborn, and H. Klose. "Ultrashallow emitter-base profiles by double diffusion." Microelectronic Engineering 19, no. 1-4 (September 1992): 347–50. http://dx.doi.org/10.1016/0167-9317(92)90451-v.

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39

Yang, Grant, Qiyuan Tian, Christoph Leuze, Max Wintermark, and Jennifer A. McNab. "Double diffusion encoding MRI for the clinic." Magnetic Resonance in Medicine 80, no. 2 (December 19, 2017): 507–20. http://dx.doi.org/10.1002/mrm.27043.

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40

Ganapathy, R. "Double Diffusion from a Horizontal Line Source." ZAMM 79, no. 9 (September 1999): 635–40. http://dx.doi.org/10.1002/(sici)1521-4001(199909)79:9<635::aid-zamm635>3.0.co;2-#.

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Li, Yuanfei, and Xuejiao Chen. "Spatial decay bound and structural stability for the double-diffusion perturbation equations." Mathematical Biosciences and Engineering 20, no. 2 (2022): 2998–3022. http://dx.doi.org/10.3934/mbe.2023142.

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<abstract><p>In this paper, we study the double-diffusion perturbation equations when the flow is through a porous medium. If the initial conditions satisfy some constraint conditions, the Saint-Venant type spatial decay of solutions for double-diffusion perturbation equations is obtained. Based on the spatial decay bound, the structural stability for the double-diffusion perturbation equations is also established.</p></abstract>

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42

Anncy, Maria, Thadathil Varghese Joseph, and Subbarama Pranesh. "Linear and non-linear analyses of double-diffusive-Chandrasekhar convection coupled with cross-diffusion in micropolar fluid over saturated porous medium." Multidiscipline Modeling in Materials and Structures 17, no. 1 (June 28, 2020): 211–36. http://dx.doi.org/10.1108/mmms-11-2019-0201.

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PurposeThe problem aims to find the effects of coupled cross-diffusion in micropolar fluid oversaturated porous medium, subjected to Double-Diffusive Chandrasekhar convection.Design/methodology/approachNormal mode and perturbation technique have been employed to determine the critical Rayleigh number. Non-linear analysis is carried out by deriving the Lorenz equations using truncated Fourier series representation. Heat and Mass transport are quantified by Nusselt and Sherwood numbers, respectively.FindingsAnalysis related to the effects of various parameters is plotted, and the results for the same are interpreted. It is observed from the results that the Dufour parameter and Soret parameter have an opposite influence on the system of cross-diffusion.Originality/valueThe effect of the magnetic field on the onset of double-diffusive convection in a porous medium coupled with cross-diffusion in a micropolar fluid is studied for the first time.

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43

Mishra, Manoranjan, A. De Wit, and Kirti Chandra Sahu. "Double diffusive effects on pressure-driven miscible displacement flows in a channel." Journal of Fluid Mechanics 712 (October 9, 2012): 579–97. http://dx.doi.org/10.1017/jfm.2012.439.

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AbstractThe pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.

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44

Legare, Sierra, Andrew Grace, and Marek Stastna. "Double diffusive instability with a constriction." Physics of Fluids 35, no. 2 (February 2023): 024109. http://dx.doi.org/10.1063/5.0135159.

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Confined geometries have an effect on hydrodynamic instabilities, and this provides opportunities for controlling the rate of mixing in flows of engineering relevance. In multi-component fluids, differential diffusion allows for novel types of hydrodynamic instability that have finite amplitude manifestations even in millimeter-scale channels. We present numerical simulations that demonstrate that localized channel constrictions can serve to partially “catch” the manifestations of double diffusive instabilities. The fluid collects just above the narrowest point of the constriction and eventually undergoes a secondary instability. We study this secondary instability, focusing on its chaotic nature and on the way in which flow into the region below the constriction is controlled by the constriction amplitude and shape.

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Ji, Yang, Jeffrey Paulsen, Iris Yuwen Zhou, Dongshuang Lu, Patrick Machado, Bensheng Qiu, Yi-Qiao Song, and Phillip Zhe Sun. "In vivo microscopic diffusional kurtosis imaging with symmetrized double diffusion encoding EPI." Magnetic Resonance in Medicine 81, no. 1 (September 9, 2018): 533–41. http://dx.doi.org/10.1002/mrm.27419.

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46

Mahajan, Amit, and Mahesh Kumar Sharma. "Double-diffusive convection in a magnetic nanofluid layer with cross diffusion effects." Journal of Engineering Mathematics 115, no. 1 (March 18, 2019): 67–87. http://dx.doi.org/10.1007/s10665-019-09992-8.

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47

San Antolín Plaza, Miguel Ángel, Josep L. Pelegrí, Francisco José Machín, and Verónica Benítez Barrios. "Inter-decadal changes in stratification and double diffusion in a transatlantic section along 7.5°N." Scientia Marina 76, S1 (September 3, 2012): 189–207. http://dx.doi.org/10.3989/scimar.03616.19g.

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48

Konopliv, Nathan, and Eckart Meiburg. "Double-diffusive lock-exchange gravity currents." Journal of Fluid Mechanics 797 (May 24, 2016): 729–64. http://dx.doi.org/10.1017/jfm.2016.300.

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Double-diffusive lock-exchange gravity currents in the fingering regime are explored via two- and three-dimensional Navier–Stokes simulations in the Boussinesq limit. Even at modest Reynolds numbers, for which single-diffusive gravity currents remain laminar, double-diffusive currents are seen to give rise to pronounced small-scale fingering convection. The front velocity of these currents exhibits a non-monotonic dependence on the diffusivity ratio and the initial stability ratio. Strongly double-diffusive currents lose both heat and salinity more quickly than weakly double-diffusive ones, and they lose salinity more quickly than heat, so that the density difference driving them increases. This differential loss of heat and salinity furthermore results in the emergence of strong local density maxima and minima along the top and bottom walls in the gate region, which in turn promote the formation of secondary, counterflowing currents along the walls. These secondary currents cause the flow to develop a three-layer structure. The late stages of the flow are dominated by currents flowing oppositely to the original ones. Three-dimensional simulation results are consistent with the trends observed in a two-dimensional parametric study. A detailed analysis of the energy budget demonstrates that strongly double-diffusive currents can release several times their initially available potential energy, and convert large amounts of internal energy into mechanical energy via scalar diffusion. Scaling arguments based on the simulation results suggest that even low Reynolds number double-diffusive gravity currents are governed by a balance of buoyancy and turbulent drag.

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Nagai, Takeyoshi, Gandy Maria Rosales Quintana, Gloria Silvana Durán Gómez, Fuminori Hashihama, and Kosei Komatsu. "Elevated turbulent and double-diffusive nutrient flux in the Kuroshio over the Izu Ridge and in the Kuroshio Extension." Journal of Oceanography 77, no. 1 (January 11, 2021): 55–74. http://dx.doi.org/10.1007/s10872-020-00582-2.

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AbstractWhile the Kuroshio is known to be a nutrient stream, as these nutrients are in dark subsurface layers, they are not immediately available for photosynthesis unless they are supplied to the sunlit surface layers. Recent microstructure observations have revealed that strong diapycnal mixing caused by the Kuroshio flowing over topographic features and double diffusion in the subsurface layers of the Kuroshio. However, it is still unclear how much nutrient flux can be provided by these microscale mixing processes. In this study, using an autonomous microstructure float and nutrient samplings, nutrient flux caused by the Kuroshio over the Izu Ridge, and that caused by double diffusion in the Kuroshio Extension are quantified. The nitrate diffusive flux is estimated to be $$>1 \,\hbox {mmol} \,\hbox {N}\,\hbox {m}^{-2}\hbox {day}^{-1}$$ > 1 mmol N m - 2 day - 1 over a distance, 20–30 km near the Izu Ridge and $$>0.1 \,\hbox {mmol} \,\hbox {N}\, \hbox {m}^{-2}\hbox {day}^{-1}$$ > 0.1 mmol N m - 2 day - 1 , which persists further downstream direction over 100 km along the Kuroshio, increasing the subsurface chlorophyll-a concentration in the region 200 km downstream. The double-diffusion-induced nitrate flux is estimated to be 1-$$10 \,\hbox {mmol} \,\hbox {N} \,\hbox {m}^{-2}\hbox {day}^{-1}$$ 10 mmol N m - 2 day - 1 in the pycnostad 26–$$26.5\,\hbox {kgm}^{-3}$$ 26.5 kgm - 3 of the Kuroshio Extension, suggesting that whether this double-diffusion-induced nutrient flux in the subsurface layers can ultimately contribute to surface primary production depends on additional eddy up- and northward fluxes.

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Fam, M., and J. C. Santamarina. "Coupled diffusionfabric-flow phenomena: an effective stress analysis." Canadian Geotechnical Journal 33, no. 3 (July 2, 1996): 515–22. http://dx.doi.org/10.1139/t96-074.

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Concentration diffusion, fluid flow and fabric changes are coupled phenomena in fine soils. Indeed, experimental results previously presented by the authors showed the presence of a pressure front advancing ahead of the diffusing high-concentration front in bentonite and kaolinite specimens. This note presents a simple analysis of diffusionfabric-flow coupling, based on elementary double-layer repulsion and attraction. Model predictions adequately agree with experimental data. High specific surface, high initial void ratio, and low initial pore-fluide concentration increase the sensitivity of soils to changes in pore-fluid concentration and enhance the potential development of pore pressure fronts. Key words: coupling, diffusion, clay, pore pressure, interparticle forces.

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