Predicted penetration rates

FLOW INTO CAPILLARY GAPS 10.1.1 Predicted penetration rates 

The idealised flow of non-reactive liquids in smooth channels has been considered by founding physicists such as Newton and Poiseuille and is well understood. Slow flow of a liquid is laminar or streamlined while rapid flow is turbulent with the transition occurring when the Reynolds number - the dimensionless parameter (Udphf) in which U is the velocity of the liquid, p and i] are the density and 

The Reynolds numbers for the flow of a molten metal along a capillary braze gap are usually less than 1000 as will be shown later, and the theoretical laminar flow rates for such configurations have been calculated by Milner (1958) for both horizontal and vertical joints. He regarded the flow into a horizontal joint induced by capillary attraction as being impeded only by viscous drag, and derived a simple parabolic expression to describe such behaviour, 

The predicted behaviour of individual liquid metals depends on their specific physical properties, such as those listed in Table 10.1 for Hg and a number of solder and braze metals and alloy solvents. Substitution of these values into 

Differentiation of equation (10.1) to obtain a value of dl/dt, U, permits the Reynolds number to be rewritten as equal to (ffLvCos0Ypd2/(6/72l)). Assuming the workpieces are completely wetted, substitution of Table 10.1 data yields Reynolds numbers for a typical braze joint 0.1 mm wide and 10 mm long, (Schwartz 1995), ranging from 49.5 for A1 to 117 for Au and even smaller numbers are obtained if the workpieces are not completely wetted so that cos()Y is less than 1. These values are much smaller than that needed to induce a transition in flow behaviour, and 

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Differences in the predicted penetration rate and depth of a pollutant plume depend not only on the choice of transport coefficients, but also on whether the contaminants are retained or retarded . The choice and nature of the transport coefficients used in the prediction model will describe the expected distribution and attenuation of the contaminants with time and space. Whether the attenuation is by retention or retardation mechanisms becomes the critical consideration and issue. In the first instance (i.e. retention), the attenuation of contaminants will lead to a successful containment of the pollutants in the substrate. In contrast, in the second instance (retardation), the retardation transport mechanism will result only in a postponement of the time for contamination of the aquifer, i.e. a ticking time bomb problem or a health hazard waiting to happen. 

In the context of skin sensitization bioavailability can be seen as the capacity of the compound to reach the viable epidermis, where it interacts with keratinocytes and Langerhans cells. This capacity is dependent on its molecular weight and solubility in polar and apolar solvents [115]. Importantly, potency prediction solely on the basis of cell culture models (steps 3 and 4) does not account for skin penetration rate and may thus wrongly predict potency in vivo. Possible in vitro approaches to detect allergic capacity of chemicals/pharmaceuticals are presented in Table 18.5. 

The addition of various surfactants and micelle forming agents on the biphasic hydroformylation of olefins was also considered as a tool for enhancement of the reaction rate. The relation between the extent of emulsification of the reaction mixture and the performance of hydroformylation reaction was also investigated. Mass transfer effects in biphasic hydroformylation of 1-octene in the presence of cetyltri-methylammoniumbromide (CTAB), was studied by Lekhal etal. [33], A mass-transfer model based on the Higbie s penetration theory was proposed to predict the rate of hydroformylation in a heterogeneous gas-liquid-liquid system under... 

The optimization of a gel formulation of ketoprofen has been described by Takayama and Nagai (4). They studied the effect of t/-limonene and ethanol in their formulation on the penetration rate of the drug through the skin of the rat in vivo. They also measured the lag time and the skin irritation. A central composite design with 4 centre points was used and predictive second-order equations were obtained by multi-linear regression. 

As illnstrated in Fignre 15.7, differences between species in the dependence of permeability coefficients can cause the relative order of penetration rates to change with For example, for a chemical with MW = 100 and log = 4, the predicted order for the permeability coefficients is snake > hairless mouse > human for a chemical with MW = 100 and log = -2.0, the predicted order is hairless mouse > human > snake. However, when MW = 300, the relative order among these three species is predicted to be independent of log These plots show clearly that relative rankings of permeability coefficients in different species may depend on chemical properties of the penetrant. 

Although more predictive approaches may be possible in the future, with the ethical considerations of utilizing humans in studies with pesticides, currently the laboratory rat appears to be a suitable model. Dermal absorption studies with the rat allow the calculation of a penetration rate and hence, assist in the estimation of a potential body burden in man. Indeed, the extrapolation of a dermal penetration rate in the rat to man may represent a worst case approximation. Studies with one pesticide, malathion, in the rat and man have revealed the absorption/ penetration rate in the rat to be approximately 3-fold higher than man ( ). 

The other problem with trying to predict the chloride penetration rate is defining the initial concentration, as chloride diffusion produces a concentration gradient not a front . In other words we can use the square root relationship for the carbonation front as the concrete either is or is not carbonated, but we cannot use it so easily for chlorides as there is no chloride fronf , but a concentration profile in the concrete. A typical chloride profile is shown in Figure 3.2. This particular profile is a very convincing fit to a diffusion curve but show no error bars. Many profiles show far more scatter. The calculation of chloride diffusion rates is discussed more fully in Chapter 8. 

Liquid penetration rates. Comparison of experimental values and model predictions. ... 

Experience shows that at least duplicate test specimens should be exposed in each test. Under laboratory tests, corrosion rates of duplicate specimens are usually within 10 % of each other, when the attack is uniform. Occasional exceptions, in which a large difference is observed, can occur under conditions of borderline passivity of alloys that depend on a passive film for their resistance to corrosion. If the rate difference exceeds 10 %, re-testing should be considered, unless it is observed that localized attack is predominant. Corrosion rates are calculated assuming a uniform loss of metal, and therefore when specimens are attacked non-uniformly, the calculated corrosion rates indicate only the relative severity of attack and should not be used to predict the performance of an alloy to the test solution. In such cases, weight loss per unit of surface area may be used to avoid implying a uniform penetration rate. 

Because the electrode surface area is usually between 1 and 0.03 mm, which is approximately 2 to 4 orders of magnitude less than that of a typical LPR probe or a typical electrochemical noise (EN) probe, the prediction of penetration rate or localized corrosion rate by assuming uniform corrosion on the small electrode is realistic in most applications. CMAS probes have been used for monitoring localized corrosion of a variety of metals and alloys in the following environments and conditions ... 

Considerable effort will be made to predict the onset of overpressures ahead of the drill bit. The most reliable indioations are gas readings, porosity - depth trends, rate of penetration and shale density measurements. 

Note that both the penetration and the surface-renewal theories predict a square-root dependency on D. Also, it should be recognized that values of the surface-renewal rate s generally are not available, which presents the same problems as do 6 and t in the film and penetration models. 

The predictions of correlations based on the film model often are nearly identical to predictions based on the penetration and surface-renewal models. Thus, in view of its relative simphcity, the film model normally is preferred for purposes of discussion or calculation. It should be noted that none of these theoretical models has proved adequate for maldug a priori predictions of mass-transfer rates in packed towers, and therefore empirical correlations such as those outlined later in Table 5-28. must be employed. 

Localised corrosion The various forms of localised corrosion are a greater source of concern to the plant designer (and operator) since it is usually difficult to predict an accurate rate of penetration, difficult to monitor, and consequently can be (especially in the case of stress-corrosion cracking) catastrophically rapid and dangerous. 

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