Hemispherical diffusion

Polytetrafluoroethylene (Teflon) - [Ref. 19] (Total diffuse hemispherical reflectance)... 

Different situations are summarized in Fig. 20.12. When radial diffusion boundary layers totally overlap, i.e. when the diffusion hemisphere is larger than the mean... 

The emissivity of a material is defined as the ratio of the radiation per unit area emitted from a real or from a grey surface (one for which the emissitivity is independent of wavelength) to that emitted by a black body at the same temperature. Emissivities of real materials are always less than unity and they depend on the type, condition and roughness of the material, and possibly on the wavelength and direction of the emitted radiation as well. For diffuse surfaces where emissivities are independent of direction, the emissivity, which represents an average over all directions, is known as the hemispherical emissivity. For a particular wavelength X this is given by ... 

Urbach H, Flacke S, Keller E, Textor J, Berlis A, Hartmann A, Reul J, Solymosi L, Schild HH. Detectability and detection rate of acute cerebral hemisphere infarcts on CT and diffusion-weighted MRI. Neuroradiology 2000 42 722-727. 

FIG. 1 (a) Schematic of the hemispherical diffusion-field established for the steady-state diffusion-... 

This article presents a brief account of theory and practical aspects of rotating hemispherical electrodes. The fluid flow around the RHSE, mass transfer correlations, potential profile, and electrochemical application to the investigations of diffusivity, reaction rate constants, intermediate reaction products, passivity, and AC techniques are reviewed in the following sections. 

The RHSE has the same limitation as the rotating disk that it cannot be used to study very fast electrochemical reactions. Since the evaluation of kinetic data with a RHSE requires a potential sweep to gradually change the reaction rate from the state of charge-transfer control to the state of mass transport control, the reaction rate constant thus determined can never exceed the rate of mass transfer to the electrode surface. An upper limit can be estimated by using Eq. (44). If one uses a typical Schmidt number of Sc 1000, a diffusivity D 10 5 cm/s, a nominal hemisphere radius a 0.3 cm, and a practically achievable rotational speed of 10000 rpm (Re 104), the mass transfer coefficient in laminar flow may be estimated to be ... 

Harrison, T. M. (1981). Diffusion of40Ar in hornblende. Contrib. Mineral. Petrol., 78,324-31. Hart, S. R. (1984). A large-scale isotope anomaly in the Southern Hemisphere mantle. 

Figure 6 Typical cyclic voltammogram obtained at a spherical (or hemispherical) (micro)electrode under experimental conditions such that only radial diffusion is operative...

In addition, one must choose the most appropriate geometrical form for such an electrode. The most common forms for fast voltammetric techniques are the planar geometry and the spherical (or hemispherical) geometry. In this regard, we have seen (Chapter 1, Section 4.2.2) that the simplest theoretical relationships describing the kinetics of electrode processes are valid under conditions of linear diffusion (even if we have briefly discussed also radial diffusion). 

The DigiSim program enables the user to simulate cyclic voltanunetric responses for most of the common electrode geometries (planar, full and hemispherical, and full and hemicylindrical) and modes of diffusion (semiinfinite, finite and hydrodynamic diffusion), with or without inclusion of IR drop and double-layer charging. 

However, at the highest frequencies the diffusion layers are muchthiimer, the microdroplets tend to behave as independent hemispherical microelectrodes and the response differs significantly from the theory of the thin-film electrode [49]. 

When the charge-transfer step in an electrodeposition reaction is fast, the rate of growth of nuclei (crystallites) is determined by either of two steps (I) the lattice incorporation step or (2) the diffusion of electrodepositing ions into the nucleus (diffusion in the solution). We start with the first case. Four simple models of nuclei are usually considered (a) a two-dimensional (2D) cylinder, (b) a three-dimensional (3D) hemisphere, (c) a right-circular cone, and (d) a truncated four-sided pyramid (Fig. 7.2). 

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