Diffusion-controlled evaporation

The selection of diffusion equation solutions included here are diffusion from films or sheets (hollow bodies) into liquids and solids as well as diffusion in the reverse direction, diffusion controlled evaporation from a surface, influence of barrier layers and diffusion through laminates, influence of swelling and heterogeneity of packaging materials, coupling of diffusion and chemical reactions in filled products as well as permeation through packaging. 

Ozawa K. and Nagahara H. (2000) Kinetics of diffusion-controlled evaporation of Fe-Mg olivine experimental study and implication for stability of Fe-rich olivine in the solar nebula. Geochim. Cosmochim. Acta 64, 939-955. 

The vapor cloud of evaporated droplets bums like a diffusion flame in the turbulent state rather than as individual droplets. In the core of the spray, where droplets are evaporating, a rich mixture exists and soot formation occurs. Surrounding this core is a rich mixture zone where CO production is high and a flame front exists. Air entrainment completes the combustion, oxidizing CO to CO2 and burning the soot. Soot bumup releases radiant energy and controls flame emissivity. The relatively slow rate of soot burning compared with the rate of oxidation of CO and unbumed hydrocarbons leads to smoke formation. This model of a diffusion-controlled primary flame zone makes it possible to relate fuel chemistry to the behavior of fuels in combustors (7). 

The rate at which each fan circulates air can be varied by changing the pitch of the fan blades. In final drying stages, in which diffusion controls or the product is light and powdery, the circulation rate is considerably lower than in the initial stage, in which high evaporation rates prevail. In the majority of applications, air flows through the... 

This represents a special case of high-level turbulence at a surface by the formation of steam and the possibility of the concentration of ions as water evaporates into the steam bubbles . For those metals and alloys in a particular environment that allow diffusion-controlled corrosion processes, rates will be very high except in the case where dissolved gases such as oxygen are the main cathodic reactant. Under these circumstances gases will be expelled into the steam and are not available for reaction. However, under conditions of sub-cooled forced circulation, when cool solution is continually approaching the hot metal surface, the dissolved oxygen... 

Diffusion-Controlled Bubble Growth S. G. Bankoff Evaporative Convection... 

The following reactions have been employed in the syntheses of tri-and tetrametaphosphimates. Since most often the compounds are very soluble in water, single crystals were grown by evaporation of the solvent or by diffusion controlled addition of an organic solvent such as acetone, ethanol, or methanol. 

Diffusion-Controlled Bubble Growth S. G. Bankoff Evaporative Convection John C. Berg, Andreas Acrivos, and Michel Boudart... 

At the air-water interface, water molecules are constantly evaporating and condensing in a closed container. In an open container, water molecules at the surface will desorb and diffuse into the gas phase. It is therefore important to determine the effect of a monomolecular film of amphiphiles at the interface. The measurement of the evaporation of water through monolayer films was found to be of considerable interest in the study of methods for controlling evaporation from great lakes. Many important atmospheric reactions involve interfacial interactions of gas molecules (oxygen and different pollutants) with aqueous droplets of clouds and fog as well as ocean surfaces. The presence of monolayer films would thus have an appreciable effect on such mass transfer reactions. 

Solvents are selected such that some will escape relatively quickly from paint films to prevent excessive flow, while others will escape slowly to provide film leveling and adhesion. With typical alkyd coatings, the first 30% of solvent has been observed to evaporate as quickly as the neat solvents, essentially at a constant rate which is dependent on volatility. Later stage evaporation occurred several times more slowly and was rate-controlled by solvent diffusion to the surface of the paint film. The transition point between this behavior was defined as the resin solids content at which the evaporation rate due to volatility equaled that due to diffusion. Transition points have been observed to typically occur at a resin solids content of 40-50% v/v. Thus alkyd paints, normally formulated at 27-40% v/v resin solids, generally exhibit rapid initial solvent-release driven by volatility while high solids coatings (usually 65-75% v/v resin solids) dry solely by a diffusion-controlled process with negligible influence by solvent volatility (Ellis, 1983). 

As with water-based latex paints, the substrate on which the solvent-based paint is applied will influence the emission rates of VOCs. Kwok et al. (2003) showed that emission rates of aromatic VOCs from a polyurethane lacquer in the first 10 hours were 65% greater when the substrate was aluminum rather than plywood. VOCs from the former were emitted in an evaporation process, while from the latter they emitted largely in a diffusion-controlled process. 

As we are considering an evaporation/growth process that is predominantly diffusion controlled, we adopt Pick s and Fourier s laws in the following form (I) ... 

Wang J., Davis A. M., Clayton R. N., and Hashimoto A. (1999) Evaporation of single crystal forsterite evaporation kinetics, magnesium isotope fractionation, and implications of mass-dependent isotopic fractionation of a diffusion-controlled reservoir. Geochim. Cosmochim. Acta 63, 953-966. 

Even with a permeable wood diffusion assumes increasing importance as the average moisture content approaches the irreducible moisture content indeed, in every part of the board where the moisture eontent approaehes this value drying is diffusion controlled. Permeable and impermeable timbers of similar densities should dry from fibre saturation at about the same rate. The behaviour of mixed heart/sapwood boards is eomplieated sinee, at first, there is both an evaporative interface near the sapwood surfaee and one in the interior at the zonal boundary between heart and sapwood. For a board with only a slither of heartwood along one face, mass flow can only move to the sapwood faee so in effeet the board appears to be twice the width than it aetually is. Pang et al. (1994) predieted that such a 50 mm thick board would dry from green to 6% moisture eontent using a 140°C/90°C schedule in 14 hours, compared to 10 hours for sapwood and 11 hours for heartwood. 

Lead hydroxide is filtered off, converted to lead nitrate, and stored. The sodium azide in solution is recovered by evaporation and recrystallization. The reaction of lead azide with sodium hydroxide is diffusion controlled with basic lead salts forming on the crystal surface and slowing the reaction rate. Within days the reaction goes to completion. A flow diagram for the method is given in Figure 1. 

---