Local evaporation rate

Other geometries can readily be worked out. As a useful analogy, the concentration c in equation 1 can be viewed as the electrostatic potential around a conductor of potential co. The analog to the local evaporation rate is the electric field, evaluated at the surface of the conductor. By this analogy a fresh set of intuitive ideas can be brought to bear on evaporation problems. For example, it is not surprising that the vapor density around an infinite cylindrical source drops logarithmically with radial distance, and that the evaporation rate varies inversely with the radius of the cylinder. Similarly, the vapor concentration above an infinite sea drops linearly with distance, whereas the evaporation rate is constant everywhere on the surface. 

Fig. 3.4 Local evaporation rates vctsus r, the dimensionless radial distance to the center of a droplet. The black dotted line shows experimental results while the others are calculated results from models [51], Adapted with permission from ref. [51], Copyright 2014 American Chemical Society...

Dehaeck, S., Rednikov, A., Colinet, P. Vapor-based interferometric measurement of local evaporation rate and interfacial temperature of evaporating droplets. Langmuir 30, 2002-2008 (2014)... 

Droplet Evaporation, Fig. 1 (a) Left side simulated vapOT concentratirai (grayscale encoded) above a spherical-cap-shaped droplet. Right side isolines of vapor concentration. The inset shows the local evaporation rate (J) as function of the radial coordinate. The large concentration gradient (narrow isolines) leads to a diverging flux close to the three-phase contact line, (b)... 

FI G U RE 6.18 Schematic of convection in liquid produced by the vapor recoil mechanism. The local evaporation rate increases at point P and decreases at point Q. 

The drying problem is solved in small time steps by removing some liquid at the local evaporation rates and subsequently relaxing the liquid with a volume-of-fluid approach as proposed by Stepanek et al. (1999). Space is discretized into voxels, and the distribution of solid, liquid and gas is described by the respective volume fractions in these voxels (, Jw and ). From these phase functions, normal vectors can be computed, for example... 

Initially, the void space between the particles is completely filled with liquid ( = 0 for all voxels). Evaporation from the liquid-gas interface and liquid relaxation into capillary equilibrium are then computed in an alternating sequence. For this simulation we assume a scale separation in time, i.e., that the evaporation occurs on a much slower time scale than the liquid motion. We resolve only the evaporation time scale, which yields a quasi-static approach in each evaporation step, liquid is removed according to the local evaporation rates computed from the solution of the vapor diffusion problem in the gas phase. Then the liquid is relaxed to the capillary equilibrium by volume-preserving mean curvature flow. This quasi-static approach is in contrast to a fully dynamic simulation (via computational fluid dynamics), but may come with considerably lower computational cost. Evaporation is modeled by vapor diffusion in the gas phase, with a no-flux condition at solid-gas interfaces and equilibrium vapor pressure imposed on liquid-gas interfaces (for more details, see [15]). The equilibrium liquid disttibution... 

A drum contains 42 gal of toluene. If the lid of the drum is left open (lid diameter = 3 ft), determine the time required to evaporate all the toluene in the drum. The temperature is 85°F. Estimate the concentration of toluene (in ppm) near the drum if the local ventilation rate is 1000 ft3/min. The pressure is 1 atm. 

Latent heat associated with phase change in two-phase transport has a large impact on the temperature distribution and hence must be included in a nonisothermal model in the two-phase regime. The temperature nonuniformity will in turn affect the saturation pressure, condensation/evaporation rate, and hence the liquid water distribution. Under the local interfacial equilibrium between the two phases, which is an excellent approximation in a PEFG, the mass rate of phase change, ihfg, is readily calculated from the liquid continuity equation, namely... 

Once the surface temperature distribution has been computed, using Eq. (151), the droplet evaporation rate is given by integrating the local mass flux over the droplet surface,... 

The desorption field is an ill defined quantity as this field depends on the rate of field evaporation the measurement is carried out. A d.c. evaporation field differs from the field needed in ns pulsed-field evaporation by as much as —15% as shown in Fig. 2.10h. The field evaporation rate depends on the local properties of the atom and the substrate under the influence of the applied high electric field and these influences are largely unknown. 

Leaf gas exchange rates are highly dependent on local climatic factors influencing C02 diffusion and evaporation rates, especially temperature lapse rates. The dependency of gas-exchange parameters on local climatic factors and leaf anatomy may account for the wide variability in leaf stomatal responses and stable isotope composition over elevation transects found in different species and different regions. 

In this chapter we develop formulas describing local vapor concentration and temperature fields for two juxtaposed drops in a gas-vapor mixture of infinite extent. Instantaneous growth or evaporation rates can be calculated straightforwardly from knowledge of the vapor concentration fields in the vicinity of the drop. Our primary and fundamental assumptions are that continuum transport theory is a valid approxima-... 

---