A Study of Droplet Evaporation

Abstract

We investigate the problem of the vaporization of a liquid droplet in a hotter environment of the same fluid. The Navier-Stokes equations are solved for a physical model which assumes spherical symmetry and laminar conditions in the quasi steady case. The study is mainly characterized by the fact that the equation of conservation of momentum is effectively taken into account and the velocity of the drop is not always uniform. Recession laws which are different from the classical law can be derived from the zeroth order approximation solution. Additional assumptions on the thermodynamical properties of the gas phase in subcritical conditions restore the classical law and permit the determination of an analytic expression for the vaporization ratio K. The analysis of the evolution of the temperature, the density and the velocity in the droplet and in the gaseous phase reveals the existence of shock waves which develop from the center of the droplet towards its boundary and an unbalanced energetic layer attached to the interface when the velocity is not uniform in the drop.

Water-In-Oil Emulsion as Boiler Fuel for Reduced NOx Emissions and Improved Energy Saving

“…The problems with pure liquid droplet evaporation or burning in a high temperature environment have been fully ascertained through both theoretical and experimental studies. The theories from the early [15] (Law et al, 1980) to the recent [16] (Sagna et al, 2013) studies were based on the d 2 -law model. In addition, the evaporation of multi-component droplets has also been studied.…”

Environmental Pollution due to the Operation of Gasoline Engines: Exhaust Gas Law

“…It is mostly due to human activities, especially in urban areas and industrial areas, and the massive use of automobiles based on gasoline engines. The results show that this pollution is due in part to the existence of the mass and thermal discontinuity characterized by shock waves which occur during the evaporation process, precursor of the incomplete combustion in the combustion chamber of the engines [1,2]. By analytical approach, we establish in this paper the law ϕ of the exhaust gases in poor and rich reaction media during combustion in the combustion chambers of gasoline engines in order to propose the ranges of adequate proportions of additive elements to the petrol.…”