Kinetics of Evaporation
Kinetics of Evaporation
Kinetics of Evaporation
N 1301-9724
Vol.8, (No1), pp.1-14, March-2005
Payam Rahimi
Department of Mechanical Engineering,
University of Alberta, Edmonton, AB, T60 208, Canada
Charles A. Ward
Depar1ment of Mechanical and Industrial Engineering,
University of Toronto, ON, MSS 308, Canada
Abstract
Currently there are three theoretical approaches to study evaporation: Continuum
Mechanics, Classical Kinetic Theory, and recently Statistical Rate Theory (SRT). The
assumptions being used and the predictions resulting from the first two methods have not
been supported by experimental results which are in agreement with the SRT predictions. It
seems that SRT can predict the conditions existing at the interface during evaporation
better than other methods. This paper reviews some of the published evaporation studies,
par1icularly evaporation rate, thermocapillary convection, and temperature discontinuity at
the interface during evaporation and compares the results of different approaches.
Keywords: Evaporation, rate of phase change, surface temperature, convection, statistical
rate theory
l
that had been predicted from classical kinetic
theory.
Hisatake et al. (1993) used a 127 m-
diameter thermocouple to measure the
temperature profile in both phases as water
evaporated into air. The temperature profile in
water shows the temperature decreasing as the
thermocouple approached the interface from
within the liquid and then a very sharp increase
as it crossed the interface and entered the vapor- Evaporation Water from a
air mixture. Chamber syringepump
.
t Uniform-
particularly those of Carnmenga et al. (1983) and
Schreiber and Cammenga (1981) measures were ,,.
\,. __IemperatureLayer Liquid
I
JLv = 2Kesinh(LlSLv/k) (6) substance evaporating,Psat, YsatL and yLV; and the
molecular properties of the evaporating
where k is the Boltzmann constant. Local
substance, m, roL and q,;b"For water, all of the
equilibrium is assumed valid in each phase; and
material and molecular properties have been
if the chemical potential at the interface in phase-
; is denoted as ; and the temperature by T;, then previously and independently determined; thus
the expression for the evaporation flux does not
the function LlSLvmay be written as
containany fitting parameters.
LlSLV=(L _ V )+ h V
TL TV TV TL
(-J
___
J") (7) To examine the expression for the
evaporation flux, one would ideally measure the
local equilibrium properties in each phase and
where h v is the intensive enthalpy in the vapor the local evaporation flux and then compare the
phase at the interface" The thermodynamic predicted flux with that measured at each point
function K, may be expressed by on the interface, but a method to measure
pressure at a point has not yet proven possible,
P,a1 (TL)exp(:;{ (P,;"-P,a 1 (TL))) nor has measuring the local evaporation flux"
However, the average evaporation flux can be
Ke ----"'?==~--~ (8)
determined using the apparatus shown
..f21tmkTL ,
schematically in Figure l" The total evaporation
where the pressure P/ is determined as the flux can be measured with an accuracy of
iterative solution of approximately 05% (by measuring the
Ward C. A., 1983, "Effect of Concentration on Ward C. A., Stanga D., 2001, "Interfacial
the Rate of Chemical Reaction", J. Chem. Phys., conditionsduringevaporationor condensationof
Vol. 79, pp 5605. water", Physical Rev. E, Vol. 64, pp 05159091-
05159099.
Ward C. A., 1977, "The Rate of Gas Absorption
at a Liquid Interface", J. Chemical Phys., Vol. Ward C. A., Tikuisis P., Tucker A. S., 1986,
67, pp 229. "Bubble Evolution in Solutions with Gas
Concentrations Near the Saturation Value", J.
Ward C. A., Duan F., 2004, "Turbulent Colloid Inte,face Sci., Vol. 113, pp 388.
Transition of Thermocapillary Flow Induced by
Water Evaporation", Physical Rev. E, Vol. 69, pp Wylie K. F., Brodkey R. S., 1972, "Transport
056308-1. Phenomena at the Liquid-Vapor Interface of
Mercury Using a Radioactive Tracer", Progress
Ward C. A., Elmoslehi M. B., 1988, "The in Heat and Mass Transfer, Vol. 6, pp 195.
Coverage Dependence of the Heat of Adsorption
and the Predicted Wavelength of Surface Young J. B., 1991, "The Condensation and
Luminescence", Suif. Sci., Vol. 203, pp 463. Evaporation of Liquid Droplets in Pure Vapor at
Arbitrary Knudsen Number", Int. J. Heat Mass
Ward C. A., Elmoslehi M. B., 1986, "Molecular Transfer, Vol. 34, pp 1649.
Adsorption at a Well Defined Gas-Solid