Thickness as function of time

Passive Oxide Thickness as Function of Time An important point associated with the passive oxide growth rate, as expressed by Equation 5.40, is that the growth rate dx/dt depends on the oxide thickness x. Thus, the oxide growth rate is constantly changing as the oxide grows thicker In order to understand exactly how the oxide thickness increases with time, it is necessary to integrate Equation 5.40. Integrating over the dummy variables x and t from ji/ = 0 to =x and from f = 0 to t = t yields... 

To minimize end effects, spherically shaped containers were utilized in the experimental apparatus. These containers were of soft aluminum (2S), having an outer diameter of 5.375 in. and a wall thickness of 0.029 in. Each sphere was fitted with a standpipe welded into its top. Two types of experiments were performed. These were (1) the determination of frost formation rates and thicknesses as functions of time, and (2) the determination of liquid oxygen vaporization rates and subsequent heat transfer rates under varying ambient conditions of temperature, pressure and humidity. 

Figure 6 shows the averaged values of the frost layer thickness as functions of time and specific humidity. Sloughing of the frost from the container surface seriously affected the thickness readings after elapsed times of 2 hr hence, no data are shown for values in excess of this time. In this figure, comparisons are also made with data obtained experimentally by Ruccia [4] and analytically by Loper [3]. The method of measurement limited observations to a local area of the surface of the condensate layer and hence the measurements were considered to represent the average thickness existing over the total surface of the container. Despite such limitations, these data compare favorably with the above cited studies. It should be noted diat both of these works include wind velocity and values of humidity in excess of those used in this study. 

In this process, final membrane thickness is only a fraction of the as-cast thickness owing to solvent loss and the resultant Increase in the concentration of polymer per unit volume. However, because of the inclusion of voids, the final membrane thickness is substantially greater than the thickness of a dense membrane containing an equivalent amount of polymer. The weight and thickness as functions of evaporation time for a typical CN membrane casting are shown in Table I. 

The numerical model we used was originally developed by Gill and Clyne [6] and has been modified to handle multi-layered deposits. It is a 1-dimensional model and consists of two parts thermal profile calculation and stress calculation. By regarding the torch motion as a fluctuation in the heat and mass flux onto a reference point on the substrate and assuming biaxial stress state, the program calculates both the through-thickness thermal profile and stress distribution during thermal spray as functions of time. 

Darkening and fading of photochromic glass (Coming, Photogray, thickness 2 mm) as function of time. 

Figure 9.6 Plots of scale thickness (a) and weight change (b) as functions of time for erosion-oxidation. The diagrams correspond on a common time base.

Figure 5 Experimental lithium loss and estimated SEI thickness (symbols) as functions of time and temperature for HE prototype cells stored at a float potential of 3.9 V at temperatures of 30 C and 60"C. Solid lines represent one parameter linear fits of the data in accord with Eq. (53).

Chouvenc et al. (2004a) was compared with the predictions of the two previously quoted MTM models. The position of the sublimation interface and the thickness of the dry layer, denoted were estimated as functions of time by simple mass balances. Chouvenc et al. (2004a) observed that the Rp values derived from the three models were similar for < 6 mm and slightly lower than the few literature values. Moreover, experimental data correlation lines pass close to the axis origin, so that no significant crust effect was present in the experimentally investigated crystalline system (mannitol), in contrast to what is observed with concentrated vitreous systems that can present relatively large crust effects. 

The formation of the reaction zone in the pressure-volume plane is shown in Figure 1.8 that in the pressure-distance plane in Figure 1.9. The steady-state reaction zone profiles of pressure, temperature and mass fraction are shown in Figure 1.10. The shock-front pressure and reaction zone thickness are shown as functions of time in Figure 1.11. Formation of an approximately stable reaction zone profile requires many ( 10) reaction zone lengths. 

The formation of an overdriven detonation by a piston, whose initial velocity of 0.4 cm/yusec is decreased to 0.3 cm/jisec when complete decomposition occurs at the pis-ton/nitromethane interface, was computed using a 5-A mesh and realistic viscosity values. The initial reaction zone was about 100-A thick, and the shock-front pressure was 360 kbar. The steady-state reaction zone thickness for a 0.3 cm/yusec piston is 620-A, the shock-front pressure is 272 kbar as described in section 1.1. The formation of the reaction zone in the pressure-volume plane is shown in Figure 1.13. The shock-front pressure and the reaction zone thickness are shown as functions of time in Figure 1.11 for the 0.3 cm//isec constant-velocity piston, and for the 0.4/0.3 cm/yitsec stepped-velocity piston. The 0.4/0.3 stepped-velocity piston results in a reaction zone thickness of 100-A at 3 x 10 /isec which increases to a maximum of 920-A at 4.25 x 10 /itsec and then decreases to 610-A by 7 X 10 /isec. The 0.4/0.3 stepped-velocity piston produces an initial shock-front pressure of 365 kbar, which decreases to 248 kbar by 1.5 x 10 /itsec and remains almost constant for the next 10 /isec during this time the reaction zone thickness increases from 300 to 600-A. Once the reaction zone thickness exceeds the steady-state thickness, the shock-front pressure begins to increase toward the steady-state shock-front pressure. 

FIGURE 12.35. Growth of YSZ film thickness by EVD as function of time. (From de Vries, K.J., Kuipers, R.A., and de Haart, L.G.J., Proceedings of the Second International Symposium on Solid Oxide Fuel Cells, Gross, F., Zeghers, P., Singhal, S.C., and Iwahara, H., Eds., Office for Official Publications of the European Communities, Luxembourg, 1991, 135-143. With permission.)... 

Adsorption of biologically important materials, such as fibrinogen from plasma proteins and barbiturates, " and organic molecules including corrosion inhibitors have been studied, often as functions of potential of the substrate, by ellipsometry in situ. Jovancicevic, Yang, and Bockris used time-resolved ellipsometry to measure the thickness, refractive index, and extinction coefficient of the adsorption layer of l-octyne-3-ol on iron as functions of time. They showed that the layer thickness increased stepwise, due to change of the adsorption configuration from flat... 

Figure 3.6 Calculated average molecular weight as functions of time for two different sets of parameters showing they give same prediction for samples with a thickness of 0.3 mm.

Wiles and Carlsson published a number of papers concerning the photooxidation of isotactic polypropylene. They determined by I.R. ATR, OOH groups (3400 cm l) and C=0 groups (1715 cm ) as function of time (film thickness 22vi). Figures 14 and 15 show the normalized O.D. values as function of time and depth of penetration. The concentration of -OOH groups is at a maximum at the film surface. See also Reich and Stivala in this respect. ... 

The pressure drop through the filter is a function of two separate effects. The clean filter has some initial pressure drop. This is a function of filter material, depth of the filter, the superficial gas velocity, which is the gas velocity perpendicular to the filter face, and the viscosity of the gas. Added to the clean filter resistance is the resistance that occurs when the adhering particles form a cake on the filter surface. This cake increases in thickness as approximately a linear function of time, and the pressure difference necessary to cause the same gas flow also becomes a linear function with time. Usually, the pressure available at the filter is limited so that as the cake builds up the flow decreases. Filter cleaning can be based, therefore, on (1) increased pressure drop across the filter, (2) decreased volume of gas flow, or (3) time elapsed since the last cleaning. 

Figure 20 Calculated critical burst time /< as function of the halved sample thickness.

Fig. 12.22 Chromised low-carbon steel coating thickness as a function of time temperature...

The influence of temperature on coating thickness is shown in Fig. 12.21 which relates to a 4h treatment at temperature. Figure 12.22 shows the variations of thickness as a function of time at a constant temperature of 1 1(X)°C. This curve is in good agreement with the third of Fick s equations (12.15) ... 

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