Charged disk model

In addition, the phenomenon of potential attenuation has been theoretically included as a cmde approximation as predicted by the Charge Disk and Uhlig models. Both models exhibit similar potential profiles. RnaUy, sets of formulae used in cathodic protection are given as mathematical recipes for practical purposes in the field of corrosion prevention. 

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

The atomic model in 1911. A Japanese scientist, Hantaro Nagaoka, proposed a similar, disk-shaped model with electrons orbiting a positively charged nucleus, in 1904. Rutherford notes in his 1911 paper that his results would be the same if Nagaoka s model were correct. 

The thickness of the disk of the galaxy is of order 300 pc = 1000 light years, which is much shorter than the characteristic propagation time of 10 million years. The explanation is that the charged particles are trapped in the turbulent magnetized plasma of the interstellar medium and only diffuse slowly away from the disk, which is assumed to be where the sources are located. Measurements of the ratio of unstable to stable secondary nuclei (especially 10Be/9 lie) are used to determine resc independently of the product np resc and hence to constrain further the models of cosmic-ray propagation. 

Further results of the overlap model [61] are as follows (iv) The prefactor that determines the strength of the exponential repulsion has no effect on Fj at fixed normal load L, (v) the lateral force scales linearly with L for any fixed lateral displacement between slider and substrate, (vi) allowing for moderate elastic interactions within the bulk does not necessarily increase Fj, because the roughness may decrease as the surfaces become more compliant, and (vii) the prefactor of F for nonidentical commensurate surfaces decreases exponentially with the length of the common period 5 . This last result had already been found by Lee and Rice [62] for a yet different model system. We note that the derivation of properties (iv) and (v) relied strongly on the assumption of exponential repulsion or hard disk interactions. Therefore one must expect charged objects to behave differently concerning these two points. 

Clays of the montmorillonite family are lamellar aluminosificates [46] used in many industrial processes and in products such as paints, softeners, and composite materials [47]. They swell when brought into contact with water, which is due to the insertion of water molecules between the sheets. Complete exfoliation can be induced leading to dispersions of disk-like particles of 10 A thickness and 300-3000 A in diameter, depending on the variety of clay used. These clay platelets bear a rather large surface electrical charge so that electrostatic interactions between them must be considered and are actually responsible for the colloidal stability of these dispersions. These suspensions have been widely studied as model colloids and also because they form physical thixotropic gels. 

Figure 5. Theoretical estimate of the transport of propidium iodide (Pi) across an artificial planar bilayer membrane. The molecule was treated as a circular disk with charge zs = +2. Only transient aqueous pores are used in this version of the model Future versions should include metastable pores and estimates of the contributions of diffusion and convection.

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