Logarithmic Law Research Articles

Hair relaxation after shaping - A kinetic approach.

Hair fibres have been shaped via either a thermal route or via a chemical route. The time-relaxation transients of the shaped hairs in air, and in water, respectively, were evaluated. The collected data were kinetically modelled in order to reveal information about the rate controlling mechanism of the recovery process. Hair fibres were thermally shaped at different temperatures between heated plates and left to relax in an environment of controlled humidity and temperature. Different hair fibres were chemically shaped and left to relax in water of different controlled temperatures. Relaxation data were used for modelling the kinetics of the recovery processes by using exponential and logarithmic kinetic laws. The fitting of the models to the two sets of data has been checked by using the residual sum of squares for matching the proper model to each set of data. The processes of shaping and recovery were assimilated with a sequence of two successive quasi-chemical reactions, occurring at the used temperatures. Based on chemical and physical assumptions, the two groups of experiments were modelled by two different laws: an exponential law, suggesting a first-order process as the rate-determining step of the relaxation of thermally shaped fibres, and a logarithmic law, suggesting a slow relaxation, based on percolation theory, for the chemically shaped fibres. This allowed use of chemical kinetics tools for calculating the values of the activation energy in each case. The evaluated values of activation energy of the relaxation processes for both thermal and chemical shaping were found to be close to each other, in spite of the different methods of shaping. The kinetic analysis suggests that despite different reaction sequences occurring during the different shaping-relaxation processes, the rate-controlling mechanism that manages the recovery process is the same in all cases; and this process is proposed to be the thiol-disulphide reformation of intra-protein bonds inside hair.

Combined Logarithmic and Linear Law for Double-Averaged Flow Velocity Profiles over Two-Dimensional Fixed Dunes

Combined Logarithmic and Linear Law for Double-Averaged Flow Velocity Profiles over Two-Dimensional Fixed Dunes

Effects of electric field and device size on the electron velocity in p-i-n GaAs semiconductor

This paper introduces the investigation of the influence of electric field and device size on the drift velocity of electrons in GaAs semiconductor using ensemble Monte Carlo simulation method under limited size conditions. We employed a GaAs diode device model with p-i-n structure, consisting of p-type and n-type semiconductor layers with uniform size of 20 nm, and a variable-sized intrinsic (i) semiconductor layer in between. We show that in the absence of external electric field, the damped velocity will diminish as the size of the (i) layer ranges from 100 nm to 800 nm. And the damped oscillation period of the electron velocity is a linear function of the device size. Additionally, by examining the maximum value of electron velocity under the influence of an external electric field, our observed results are consistent with those reported by Saraniti et al. (2002) [22] in low electric field below 50 kV/cm; while at higher electric fields, the maximum velocity gradually increased to a saturation value. Furthermore, the maximum velocity vmax is found to follow a simple logarithmic law as a function of i-layer size S as vmax=aln⁡(bS). The coefficients of this relation equation were derived using least-square approximation technique yielding a high determination coefficient R2 up to 0.998.

River Discharge Inversion Algorithm Based on the Surface Velocity of Microwave Doppler Radar

Non-contact methods, which are of great significance to the measurement of river discharge, can not only improve the efficiency of measurement but can also ensure the safety of equipment and personnel. However, owing to their inherent drawbacks such as the requirement of riverbed topography measurements and the difficulty in determining hydrological parameters such as equivalent roughness height, velocity index, etc., there are still challenges for measuring river discharge with high levels of efficiency and accuracy using non-contact methods. To overcome the aforementioned challenges, a new river discharge inversion method is proposed in this paper. In this method, vertical velocities are divided into inner and outer region velocities which can be described by the logarithmic law and the parabolic law, respectively. Applying the river surface velocities collected by microwave Doppler radar and the vertical velocity distributions, the water depths are estimated according to the continuity of the vertical velocities and the shear stresses, and then, the river discharges are obtained by the velocity–area method. The proposed method not only has a simple formula but also comprehensively considers the influence of different hydrological conditions, making it suitable for different river widths and water depths. In this paper, surface velocities collected by microwave Doppler radar on the Yangtze River and the San Joaquin River are used to invert the river discharge, and the results show that for wide–shallow, wide–deep, and narrow–shallow river conditions, the mean percent error (MPE) values of the discharges invertedby the proposed method are 3.91%, 3.82%, and 3.6%, respectively; the root mean square error (RMSE) values are 4.53%, 5.19%, and 4.81%, respectively; and the maximum percent error (MaPE) is less than 15%. The results prove that the proposed method can invert the river discharge with high efficiency and high accuracy under different river widths and water depths without measuring water depth in advance, making it is possible to automatically measure the river discharge in real time.

High temperature oxidation behaviour of polycrystalline and single crystal Ta stabilized γ'-strengthened Co-Ni-Al-Ta-Cr alloys

Isothermal oxidation was carried out on the polycrystalline and single crystal γ'-strengthened Co-Ni-Al-Ta-Cr alloys at 800–1000 ℃. The oxidation kinetic of both alloys follows logarithmic, cubic and parabolic law at 800 ℃, 900 ℃ and 1000 ℃, respectively. The polycrystalline alloy exhibits superior oxidation resistance at 800–1000 ℃, which can be explained by the effects of grain boundary. Grain boundary diffusion enhances the formation of the protective spinel oxides layer at 800–900 ℃. The beneficial effect of the grain boundary on the spallation resistance of oxides results that the polycrystalline alloy maintains better oxidation properties at 1000 ℃.

Boundary layer measurements of the flow along a streamwise-oriented circular cylinder using particle tracking velocimetry

Particle tracking velocimetry (PTV) measurements of an axisymmetric turbulent boundary layer (ATBL) around a long circular cylinder in axial flow were carried out in a large-scale water tunnel at different velocities and at different measurement positions along the cylinder. A relatively thick ATBL developed with ratios of δ/a between 4.6 and 8.1 and a/δν between 313 and 1027, where δ is the boundary layer thickness, δν the viscous length scale and a the cylinder radius. At ratios of δ/a above unity and a/δν above 250, transverse curvature effects are known to influence the boundary layer in the outer region. This was observed in the measured mean velocity profiles as the profiles fall below the planar logarithmic law of the wall. Shape factors close to unity with a rather full velocity profile were determined that explain the relatively high skin friction coefficient known to be present for such ATBL flows. Additionally, measurements of the turbulence intensity and Reynolds stress profiles are presented. The non-intrusive PTV measurement approach allowed to gather near-wall velocity data down to a wall-distance below 10 wall-units. The present study provides valuable information regarding ATBL flows along streamwise-oriented cylinders in the flow regime indicated above by the ranges of δ/a and a/δν. In particular, it fills a gap in the literature as far as experimentally obtained higher-order statistical quantities are concerned, such as root-mean-square velocity fluctuations and Reynolds stresses.

Prediction of back-layering length in subway tunnel with on-fire train running

The exploitation and utilization of urban underground space effectively contribute to the sustainable development of society. Tunnel fire safety is necessary to ensure normal operation. Motion train fire is more serious and complex than stationary fire in tunnels due to the influence of unsteady piston wind. This study investigates the smoke back-layering characteristics of a burning subway train during emergency braking. A three-dimensional unsteady numerical model adopting the dynamic mesh technique is built to investigate the smoke diffusion characteristics of motion train fire. Experimental tests are conducted based on a 60 m-long scaled-down experimental setup to verify the accuracy of the numerical model. On this basis, the dynamic characteristics of smoke back-layering length as the longitudinal wind pressure is less than the critical value are studied, considering the influence of heat release rate (HRR), train speed, and train deceleration. The results indicate that the maximum back-layering length follows the logarithmic law with the variation of longitudinal wind pressure. An empirical model is proposed to predict the maximum back-layering length at various longitudinal wind pressure, and it is helpful to the optimization design of ventilation systems for tunnel motion fire.

Improved Modelling of Vertical Velocity Profiles at a Tidal Energy Site

The Minas Passage, one of the Bay of Fundy’s tidal channels, located in Nova Scotia, Canada, presents significant potential for tidal energy development because of its highly energetic flows. As development in the region gains traction, the implementation of floating tidal energy platforms is a topic of growing interest. Tidal energy deployments in Minas Passage have historically been bottom-mounted and stationary, and the transition to arrays of floating turbines requires additional considerations. Particularly, this new application demands characterization of flow over the entire water column, including near the free surface. Complete vertical velocity profiles are essential for the successful deployment of floating tidal turbines, allowing for the estimation of key metrics such as tidal power and shear across turbine blades. Here we explore adaptations to the well-established logarithmic law of the wall with the goal of extending the vertical range over which a fitting regime based in classical turbulence theory can capture the observational records of flow in Minas Passage.
 Observational site characterization efforts in Minas Passage have primarily consisted of stationary, bottom mounted Acoustic Doppler Current Profiler (ADCP) deployments. Using historical ADCP records collected in Minas Passage between 2008 and 2021, we fit the vertical profiles of velocity using three methods: logarithmic law of the wall, power law, and an adapted logarithmic law of the wall which includes a “wake function” to improve fits in the upper water column. We find that although the law of the wall results in well-fitted estimations of the vertical velocity profiles near the seabed, observational profiles consistently deviate from the fitted curves in the middle and upper water column, recording significantly faster flow speeds than predicted by the law of the wall. The adapted model, which is rooted in turbulence theory and includes a wake term, is successful in capturing flow in the outer layer of the water column and allows for reverse shear to be captured in the profile. The resulting fits show a sizeable reduction in error throughout the entirety of the water column compared to the law of the wall profiles, and consistently reduce the error in the vertical profile fits when compared to power law fits. In addition to resulting in low error for both individual and averaged vertical profiles of flow, the physical quantities estimated from the adapted model, including drag coefficient, agree well with those computed from the law of the wall, demonstrating the physical usefulness of the adapted model.

Analysis of dielectric resonator antenna using natural fiber reinforced polymer composites

This work aims to demonstrate the viability of replacing natural fiber reinforced polymer composites for hard ceramics in millimeter-wave dielectric resonator antennas (DRA). The dielectric characteristics of three novel natural fiber reinforced polymer composites were determined using the Lichtenecker logarithmic mixing law. Using two commercial antenna design software packages, CST Studio and ANSYS HFSS, the resulting dielectric characteristics were utilized to study a probe-fed rectangular DRA. Natural fiber-reinforced polymer-based DRAs offer a wider bandwidth than ceramic-based DRAs. Close coupling is obtained by the three natural fiber-reinforced polymer-based antennas and the ceramic DRA. In all cases, the impedance bandwidths observed are the consequence of quasi-TM111 mode radiation. HFSS studies indicate that the resonance frequency of the natural fiber reinforced polymer based DRAs is roughly 75 percent higher than that of the ceramic DRA. CST results indicate that the resonance frequency of the natural fiber polymer-based DRA is approximately 88 percent higher than that of the ceramic DRA. Natural fiber reinforced Polymer-based DRAs have three times the −10 dB impedance bandwidth of ceramic-based DRAs.

A universal velocity transformation for boundary layers with pressure gradients

The logarithmic law of the wall does not capture the mean flow when a boundary layer is subjected to a strong pressure gradient. In such a boundary layer, the mean flow is affected by the spatio-temporal history of the imposed pressure gradient; and accounting for history effects remains a challenge. This work aims to develop a universal mean flow scaling for boundary layers subjected to arbitrary adverse or/and favourable pressure gradients. We derive from the Navier–Stokes equation a velocity transformation that accounts for the history effects and maps the mean flow to the canonical law of the wall. The transformation is tested against channel flows with a suddenly imposed adverse or favourable pressure gradient, boundary layer flows subjected to an adverse pressure gradient, and Couette–Poiseuille flows with a streamwise pressure gradient. It is found that the transformed velocity profiles follow closely the equilibrium law of the wall.

Propeller-Induced Jet Impact on Vegetated Flow Fields: Complex Coupled Effect towards the Velocity Profile

The failure of swirling ship propellers in marine environments can lead to huge repair costs. One of the main causes of such failure is when propellers tangle with vegetation, especially in shallow flow environments like ports, harbours, or shipyards. In order to understand the above-mentioned issue, this study proposes an analytical approach to explore efficient predictions and provide a flow guideline with respect to the co-existence of vegetation and propeller swirling effects. More specifically, we intend to investigate the full-depth theoretical velocity profile to represent propeller-induced flow under submerged vegetation conditions. This paper first investigates the modified logarithmic law approach to determine its suitability to represent the regional vegetated flow zone before implementing it into a three-layer analytical model. It was found, using the benchmark of literature measurements, that the modified log law improved the near-bed velocity calculation by nearly 70% when compared to an existing model. A propeller jet impact computation coupled into the vegetation analytical model was then investigated in different locations within the vegetated flow, i.e., at free-flow, water–vegetation interface, and vegetation-hindered zones, to study their complex velocity distribution patterns. The results demonstrate adequate validation with the vegetated flow and measured propeller jet data from the literature. This proves the potential of the proposed analytical approach in representing a real-world propeller jet event submerged in water flow with the existence of vegetation. The proposed novel method allows costless computation, i.e., as compared to conventional numerical models, in representing the complex interaction of the propeller jet and vegetated flow.

Hydrometallurgical recycling of lithium-titanate anode batteries: Leaching kinetics and mechanisms, and life cycle impact assessment

Since the inception of Li-ion batteries, the chemistry of cathode and anode materials has changed time-to-time. In recent times, the lithium-titanate (LTO) anode material has gained attention due to a higher surface area (100 m2/g) than the usual graphite-made anode (3 m2/g). The development of a new recycling strategy, in particular, to deal with spent LTO batteries, is therefore urgently needed as plenty of batteries deployed in electric vehicles are near to completing their lifespan. Herein, we demonstrate the recycling of spent LTO batteries by optimizing the parametric influence of H2SO4 concentration, H2O2 dosage, agitation speed, temperature, and time for lithium and titanium leaching from the anode material. About 92% titanium and 98% lithium were efficiently leached from the anode powder using a 3.5 mol/L H2SO4 solution with 25 vol% H2O2 at a pulp density of 5 wt./vol.%, temperature 120 °C, and time 120 min. The leaching examined in the temperature range between 60 °C and 120 °C with respect to time showed the best fits to the kinetic model governed by the logarithmic rate law. The apparent activation energies of titanium (78.9 kJ/mole) and lithium (11.3 kJ/mole) indicated two different mechanisms governed by chemically controlled and diffusion-controlled reactions, respectively. It indicated that both metals’ leaching proceeded through lixiviant diffusion on the LTO surface, which was corroborated by the instrumental analyses of the untreated LTO sample and the leached residues. A life-cycle assessment suggests the need for discharge acid for recycling within the system due to a terrestrial ecotoxicity of 97.09 kg DCB-eq; however, the ionizing radiation and eutrophication potential are found to be negligible.

The development and validation of the Inhomogeneous Wind Scheme for Urban Street (IWSUS-v1)

Abstract. The layout of urban buildings shows significant heterogeneity, which leads to the significant spatial inhomogeneity of the wind field in and over the canopy of urban street canyons. However, most of the current urban canopy models do not fully consider the heterogeneity of the urban canopy. Large discrepancies thus exist between the wind speeds simulated by the current urban canopy models and those observed in the street canyon. In this study, a parameterization scheme for wind fields, Inhomogeneous Wind Scheme for Urban Street (IWSUS), is developed to better characterize the heterogeneity of the urban canopy. We use a computational fluid dynamics method to generate the IWSUS scheme and compare it with observations of the wind profile and turbulent flux in and over the street canyon for validation. In IWSUS, the wind speed vertical profiles at six representative positions located in a typical street canyon (i.e., the windward or leeward side of a long straight street or the inflow or outflow end) are parameterized separately. The wind profile by IWSUS thus can better describe the horizontal heterogeneity of the urban near-surface wind field, e.g., the dynamic drag effect of buildings in the lower atmospheric layer over the urbanized land use. The validation based on observations shows that the performance of simulation results by IWSUS is better than that by the exponential–logarithmic (exp-log) law widely used in the current urban schemes. We consider typical building arrangement and specific street orientations in IWSUS for wind field simulations, which can better match the distribution characteristics of street canyons around the observation point in the street canyon. The averaged wind profiles and turbulence energy fluxes in the model grids of urban areas by IWSUS are also nearer to the observations than those by the exp-log law. The normalized mean errors (NMEs) between the simulated and the observed vertical average wind speed are 49.0 % for IWSUS and 56.1 % for exp-log law in the range from the ground to 4 times the average height of the buildings and 70 % for IWSUS and 285.8 % for exp-log law in the street canyon (range from the ground to building top). This study proves that the accuracy of simulations of land surface processes and near-ground meteorological processes over the urban canopy can be improved by fully considering the heterogeneity of the urban canopy layout structures and the inhomogeneity of wind field distributions in and over the street canyon. IWSUS is expected to be coupled with mesoscale atmospheric models to improve the accuracy of the wind field, land surface energy budget, meteorological and atmospheric chemistry simulations.

Spin-wave analysis of the ferromagnetic-ferromagnetic Heisenberg spin bilayer with intralayer single-ion anisotropy and interlayer antiferromagnetic interaction

In this paper, the spin wave theory is applied to the Heisenberg spin bilayer with intralayer ferromagnetic interaction [Formula: see text], intralayer single-ion anisotropy D and interlayer antiferromagnetic interaction [Formula: see text]. It is found that the effects of both D and [Formula: see text] on the thermodynamic quantities give rise to the two different low-temperature asymptotic behaviors with and without exponential law. For [Formula: see text], the interlayer antiferromagnetic interaction can induce the appearance of the maximum of the layer magnetization at finite temperatures. At the location of the layer magnetization maximum, the approximate behaviors (such as the power, linear, rational, exponential and logarithmic laws) which are driven by the temperature or the anisotropy, are obtained for the low-temperature thermodynamic properties. It is shown that the presence of antiferromagnetic interlayer interaction [Formula: see text] clearly induces more quantum fluctuations than the case where the interlayer interaction [Formula: see text] is ferromagnetic. Our results of the layer magnetization agree with the experimental data of the layered van der Waals crystal FeCl2 at low temperatures. In the monolayer case of [Formula: see text], our results are in agreement with the findings obtained by the existing theories and the quantum Monte Carlo data.

A Strong Limit Theorem of the Largest Entries of a Sample Correlation Matrices under a Strong Mixing Assumption

We are interested in an n by p matrix Xn where the n rows are strictly stationary α-mixing random vectors and each of the p columns is an independent and identically distributed random vector; p=pn goes to infinity as n→∞, satisfiying 0<c1≤pn/nτ≤c2<∞, where τ>0, c2≥c1>0. We obtain a logarithmic law of Ln=max1≤i<j≤pn|ρij| using the Chen–Stein Poisson approximation method, where ρij denotes the sample correlation coefficient between the ith column and the jth column of Xn.

Mechanism and kinetics of high-temperature oxidation of medium- and high-entropy carbides in air

Medium- and high-entropy carbides (MECs and HECs) have a wide range of advanced applications and, in many cases, outperform monocarbides. However, the behavior, oxidation mechanisms, and factors defining oxidation resistance of some popular HECs at high temperatures have not been studied in detail yet. In this study, the oxidation behavior of MEC and HECs including (Ta,Ti,Nb,Zr)C, (Ta,Ti,Nb,Zr,Mo)C, (Ta,Ti,Nb,Zr,Hf)C, and (Ta,Ti,Nb,Zr,W)C was investigated under both non-isothermal and isothermal conditions at temperatures up to 1200 °C, and a possible oxidation path was described. It was found that under non-isothermal heating conditions, the oxidation of HECs occurred in three stages, each governed by first-order chemical reactions, and was limited by the formation of ZrO2, Me2Me6O17, and MeMe2O7 oxides, respectively. In the case of isothermal heating, the oxidation of (Ta,Ti,Nb,Zr)C, (Ta,Ti,Nb,Zr,Mo)C, and (Ta,Ti,Nb,Zr,Hf)C follows a logarithmic law and was limited by the formation of a protective Me2Me6O17 layer. In contrast, isothermal oxidation of (Ta,Ti,Nb,Zr,W)C followed a linear law due to the formation of volatile WO3. The results of the study have a high potential for practical application for the production of HEC ceramics for various high-temperature purposes and could be used for further understanding of functional characteristics and development of the new ceramic compositions.

Modeling of drag coefficient under emergent and submerged flexible vegetated flow

In an open-channel flow, vegetation study is crucial to be investigated with any type of plants including trees, shrubs, and grasses, which are growing within or near the channel banks and beds in natural or artificial waterways, such as rivers, streams, and canals. These plants are different in height, size, shape, and arrangements, which have a big impact on the turbulence and flow resistance structures. In this paper, a regression analysis has been used based on collected experimental data to improve a specific equation for the drag coefficient for rigid vegetation stems and expanded to flexible stem types under emergent and submerged flow conditions. The equation suggests a length scale metric that, by analogy with the log wake law, normalizes velocity profiles of the depth-limited open channel flow with submerged, rigid vegetation. It has been formulated by drawing regression analysis for each parameter including (Re) Reynolds number, (h*) submergence ratio, and (λ) vegetation density by considering the (Fr) Froude number ranges for the water flows and vegetated channel flows. Using the Reynolds number, which is determined by the height and diameter of the vegetation, the results demonstrate an increase and decrease in the drag coefficient. For assessing the impact of vegetation on flow resistance at the surface layer, the notion of the drag coefficient is introduced. It shows better performance than other length scales in collapsing resistance data gathered under a variety of vegetation circumstances. The proposed scaling is more accurate than those based on the logarithmic, velocity-defect, and power laws in collapsing regression analysis for the studied parameters.

The reaction mechanism and interfacial crystallization of Al nanoparticle-embedded Ni under shock loading

The shock-induced reaction mechanism and characteristics of Ni/Al system, considering an Al nanoparticle-embedded Ni single crystal, are investigated through molecular dynamics simulation. For the shock melting of Al nanoparticle, interfacial crystallization and dissolution are the main characteristics. The reaction degree of Al particle first increases linearly and then logarithmically with time driven by rapid mechanical mixing and following dissolution. The reaction rate increases with the decrease of particle diameter, however, the reaction is seriously hindered by interfacial crystallization when the diameter is lower than 9 nm in our simulations. Meanwhile, we found a negative exponential growth in the fraction of crystallized Al atoms, and the crystallinity of B2–NiAl (up to 20%) is positively correlated with the specific surface area of Al particle. This can be attributed to the formation mechanism of B2–NiAl by structural evolution of finite mixing layer near the collapsed interface. For shock melting of both Al particle and Ni matrix, the liquid-liquid phase inter-diffusion is the main reaction mechanism that can be enhanced by the formation of internal jet. In addition, the enhanced diffusion is manifested in the logarithmic growth law of mean square displacement, which results in an almost constant reaction rate similar to the mechanical mixing process.

Logarithmic scaling of higher-order temperature moments in the atmospheric surface layer

A generalized logarithmic law for high-order moments of homogeneous passive scalars is proposed for turbulent boundary layers. This law is analogous to the generalized log law that has been proposed for high-order moments of the turbulent longitudinal velocity and is derived by combining the random sweeping decorrelation hypothesis with a spectral model informed by the attached eddy hypothesis. The proposed theory predicts that the high-order moments of passive scalar fluctuations within the inertial sublayer will vary logarithmically with wall-normal distance (z), and is evaluated using high frequency time-series measurements of temperature and streamwise velocity fluctuations obtained in the first meter of the atmospheric surface layer (ASL) under near-neutral thermal stratification. The logarithmic dependence with z within the inertial sublayer is observed in both the air temperature and velocity moments, with good agreement to the predictions from the proposed theory. Surprisingly, the proposed theory appears to be as, if not more, valid for transported passive scalars than for the longitudinal velocity.

Time-Dependent Passivation Performance of Plasma Sprayed FeCrMoCBY Amorphous Coating

The relationship between passive film growth behavior and passivation time for plasma-sprayed Fe48Cr15Mo14C15B6Y2 amorphous coating in borate buffer solution has been thoroughly studied. The morphological characteristic and structural feature of as-spayed amorphous coating were estimated by scanning electron spectroscopy (SEM), X-ray diffraction (XRD) and transmission electron spectroscopy (TEM). The influence of passivation time on the film evolution properties was measured by electrochemical impedance spectra (EIS), Mott–Schottky curves, atomic force microscope (AFM) and X-ray photoelectron spectroscopy (XPS). The results revealed that both corrosion resistance and self-repairing capacity of passive film greatly increased with time based on high electric field assumption. Reductions in donor density and flat band potential were accountable for a lower conductivity of passive film. An increment in Cr2O3 oxide as the inner barrier layer derived from the dehydration reaction of Cr(OH)3 contributed to the gradually densified structure of passive film. The extracted passive film thickness d increment with passivation time t conformed to the logarithm law on the basis of effective capacitance hypothesis: d=0.43lnt+52.06−2.18 (nm). Passivation mechanism within 600 s was ascribed to the adsorption of mechanical mixtures between metal ions and electrolytes, possibly leading to mechanical stress and rupture of passive film in the later growth procedure. The cation vacancy condensation process at the interface of coating/film was propitious in stabilizing the growth rate of passive film.