Curvatures radius

No MWD or LWD equipment exist to date to log these wells. However, service companies are developing equipment for MWD purpose in 40-ft (12-m) curvature radius or 1.5°/ft (4.6°/m). The equipment consists of articulated mud motors and inclination and azimuth sensors. 

In this section we present the system of quasi-one-dimensional equations, describing the unsteady flow in the heated capillary tube. They are valid for flows with weakly curved meniscus when the ratio of its depth to curvature radius is sufficiently small. The detailed description of a quasi-one-dimensional model of capillary flow with distinct meniscus, as well as the estimation conditions of its application for calculation of thermohydrodynamic characteristics of two-phase flow in a heated capillary are presented in the works by Peles et al. (2000,2001) and Yarin et al. (2002). In this model the set of equations including the mass, momentum and energy balances is ... 

Capillary phenomena are due to the curvature of liquid surfaces. To maintain a curved surface, a force is needed. In Eq. (8), this force is related to the second term in the integral. The so-called Laplace pressure due to the force to maintain the curved surface can be expressed as, Pl = 2-yIr, where r is the curvature radius. The combination of the capillary effects and disjoining pressure can make a liquid film climb a wall. 

Thomson-Freundlich equation relates the solubility of a particle to its curvature radius (e.g., Swalin, 1962). Using this equation, Kirkaldy and Young (1987) show how periodic precipitation may result from the capillary resistance of the matrix to grow small precipitates. Formally, the conditions read... 

Within these coordinates the visual-acoustic installation The Heart (2006-2007) becomes precisely this kind of curvature radius that is the basis of heterogeneity in our space as the history and physiology of civilization. The vectors of observing the latest artistic reality that are parallel in classical art,... 

Equations (1) and (2) hold true when the curvature radius, Rcurv, of the body taken out of the liquid paste is much greater than the capillarity constant, i.e. when ... 

The shape of the metal specimen considered is obviously related to the kind of system to be modelled. For SERS and the others SE phenomena, the presence of curved surfaces, with a curvature radius on the nanometric scale, is fundamental for the enhancement. Thus, spheres, ellipsoids, ensembles of spheres, spheres close to planar metal surfaces and planar metal surfaces with random roughness have been considered. We refer to the review by Metiu [57], which describes most of these analytically solvable models. More recently, the modelling of the electric field acting on the point molecule has moved to more realistic shapes (including fractal metal specimen) [59] which require numerical methods to be tackled. The aim of these approaches is usually to calculate the total electric field around the metal particle, and the molecule does not even appear explicitly in the calculations. Interested readers are referred to some recent reviews on the subject [60] (see also Chapters 2 and 5 of ref. [56]). 

The flatness problems comes from similar considerations. The Einstein equations cannot of course predict the value of the curvature K, or of the curvature radius Rc = a/yf K. What is known observationally is that the curvature radius is very large H l > a/ J K. Using Eq. (7.24), this can be translated at any epoch (subscript 0 denotes today) ... 

In other word, as any physical length, the curvature radius grows as a, that is more slowly than the Hubble radius. In order for the curvature radius to be larger than the Hubble radius today it has to be immensely larger than the Hubble radius at earlier times. Again, this is unexpected. One would for example prefer that at Planck epoch, both the curvature radius and the Hubble radius were of same order of magnitude. 

The equilibrium between two fluids at different pressures (for example, liquid and its vapor, at PL and P8, respectively) in a spherical interface of curvature radius, r, and surface tension, y, is given by the Laplace equation... 

The conversion of the mean curvature radius (rm) to pore size involves assuming a model of pore shape and also knowing the contact angle (0) between the capillary condensed phase and the... 

Figure 3.28 Sketch of the plateau border in a surfactant foam. Due to the curvature (radius r) a suction effect in the direction of the arrows results.

Detjaguin approximation. For the present comparisons with experiment, the Derjaguin approximation is considered to be applicable, since the curvature radius of the surface (cylindrical surface) is much larger than the separation between the (20) two surfaces (105 times). 

The lower the surface free energy of the shell chemistry, the smaller is the contact angle hysteresis on the closely packed surface arrays. Further the contact angles varied with increasing height roughness. A possible explanation for this behaviour is that the vertical roughness influences the curvature radius of the liquid in trapped air pockets at the solid-liquid interface as was already assumed in the literature for nanostructured metal surfaces and paraffin-coated steel balls. 

It should be noted here that both the curvature radius and local density of states are canceled out by taking the ratio between o and rr(). This means that the frequency A as a function of conductivity a, presents an inverse parabolic curve when it is plotted with a logarithmic scale. This is consistent with the curves shown in Fig. 14, if we consider that the height required to keep a... 

Here ps is the saturated vapor pressure at temperature T, y the surface tension, Vm the molar volume of the liquid, and the curvature radius r is conventionally taken as negative for concave interfaces. Kelvin equation for a non-ideal multicomponent mixture was derived by Shapiro and Stenby (1997). 

The nanotube network was successfully investigated in our laboratory by Dalmas et al. (63), in terms of distribution of radius of curvature. Indeed, the 2D apparent nanotube segment curvature radius distribution was then measured on TEM bright field images acquired on the composites (see Figure 3.8). The experimental curvature... 

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