Diffusion-deflection model

Rutherford s experiment demonstrated that the total positive charge in an atom is localized in a very small region of space (the nucleus). The majority of a particles simply passed through the gold foil, indicating that they did not come near a nucleus. In other words, most of the atom is empty space. The diffuse cloud of electrons (which has a size on the order of 10 8cm) did not exert enough force on the a particles to deflect them. The plum pudding model simply did not explain the observations from the experiment with a particles. 

Several elementary aspects of mass diffusion, heat transfer and fluid flow are considered in the context of the separation and control of mixtures of liquid metals and semiconductors by crystallization and float-zone refining. First, the effect of convection on mass transfer in several configurations is considered from the viewpoint of film theory. Then a nonlinear, simplified, model of a low Prandtl number floating zone in microgravity is discussed. It is shown that the nonlinear inertia terms of the momentum equations play an important role in determining surface deflection in thermocapillary flow, and that the deflection is small in the case considered, but it is intimately related to the pressure distribution which may exist in the zone. However, thermocapillary flows may be vigorous and can affect temperature and solute distributions profoundly in zone refining, and thus they affect the quality of the crystals produced. 

As soon as one is concerned with wrinkled fronts and/or inhomogeneous flows, the flame cannot be described by a pure reaction-diffusion model. Because of the gas expansion produced by the temperature increase in the preheated zone, the streamlines are deflected across the tilted front and a strong coupling with hydrodynamics is developed. When the size A of the wrinkles of the front is large compared to the flame thickness d, the corresponding fluid mechanical effects can be splitted in two distinct parts ... 

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