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Reply to comments on 'EPR study of He-implanted Si' by P. Pivac, B. Rakvin, R. Tonini, F. Corni, G. Ottaizani, Published in Mater. Sci. Eng. B73 (2000) 60-63 - Written by M. Kakazey, M. Vlasova, and J.G. Gonzalez-Rodriguez - Reply to discussion
No full textReply to comments on 'EPR study of He-implanted Si' by P. Pivac, B. Rakvin, R. Tonini, F. Corni, G. Ottaizani, Published in Mater. Sci. Eng. B73 (2000) 60-63 - Written by M. Kakazey, M. Vlasova, and J.G. Gonzalez-Rodriguez - Reply to discussio
Heat and mass transfer modelling of water droplets in non-viscous steady-state gaseous environment
No full textThe Influence of Curvature on the Modelling of Droplet Evaporation at Different Scales
No full textThe evaporation of liquid drops in stagnant gaseous environment is modelled, accounting for the effect of drop curvature and size at the macro- and microscopic scales. At the macro-scale level, the validity of the conjectured dependence of the local fluxes on the drop surface curvature is analysed. Analytical solutions to the gas-phase conservation equations for five drop shapes (sphere, oblate and prolate spheroids and inverse oblate and prolate spheroids), under uniform Dirichlet boundary conditions, are used to calculate the local vapour and heat fluxes. The analysis shows that in general non-dimensional fluxes do not solely depend on local curvature, but possibly the effect of the whole drop shape must be taken into account. At the micro-scale level, the equilibrium vapour pressure at a convex curved surface is higher than that at a flat surface, thus leading to a considerable enhancement of the evaporation rate for nanometre sized droplets. To model the increase in equilibrium vapour pressure, we consider the Kelvin correction. Our analysis shows that the Kelvin correction is strictly required for droplet radii below 20 Å, as typically encountered for modelling the growth of critical clusters in phase transition processes initiated by homogeneous nucleation. At these conditions, it is mandatory to consider also the repartition of molecules in the different phases, in order to prevent a significant overestimation of the equilibrium vapour pressure
Sturm–Liouville Problems
No full textIn Chap. 3 we have seen how the separability of PDEs leads to ordinary differential equations problems, usually of second order. The problem is complemented with B.C.s and the reduction of the initial PDE to second order ODEs often yield a so-called Sturm–Liouville (SL) problem (named after the French mathematicians Jacques Charles François Sturm, 1803–1855, and Joseph Liouville, 1809–1882)
Introduction to Constitutive Equations
No full textWhen the conservation equations for mass, chemical species, momentum and energy were derived in the previous chapter, it became soon evident that the number of unknown functions was far larger than that of the equations. To allow the closure of the problem some quantities need to be related to others and to the properties of matter, and these are the diffusive mass fluxes, j(p), the deviatoric stress tensor, τjk, the internal energy per unity of mass, u^ (or the specific enthalpy, h^ ) and the heat flux, q. The laws that describe these quantities are known as constitutive equations, and in thermo-fluids they are inherently empirical, although they must satisfy some requirement based upon first principles, like the condition of material objectivity (material properties must be independent of observer), the symmetry properties of a material body and the law of thermodynamics (particularly, the entropy inequality)
Elements of Differential Geometry of a Surface
No full textWhen dealing with multiphase systems, like evaporating liquid drops or vapour bubbles in a liquid, etc., interfaces are present and they can be schematised as surfaces separating two different phases
Drop Evaporation Under Unsteady Conditions
No full textIn the previous two chapters we have investigated models of drop evaporation under steady-state conditions, an assumption widely used, although clearly unphysical: a mass source inside the drop is needed to maintain the drop shape unchanged during evaporation. To relieve this assumption a time dependent problem must be set and solved, increasing the complexity of analytical approaches. In particular, even for a spherical drop shrinking by evaporation, a moving boundary problem must be solved, which is known to be a challenging task, even for the simplest geometries. In this chapter we will see how it is possible to account for unsteadiness of the heat and mass transfer processes and still approach the modelling by analytical methods
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