Raman Thermometry Measurements of Free Evaporation from Liquid Water Droplets Jared D. Smith, ²,‡ Christopher D. Cappa, ²,‡,§ Walter S. Drisdell, ²,‡ Ronald C. Cohen, ² and Richard J. Saykally* ,²,‡ Contribution from the Department of Chemistry, UniVersity of California, Berkeley, California 94720, and Chemical Sciences DiVisions, Lawrence Berkeley National Laboratory, Berkeley, California 94720 Received May 22, 2006; E-mail: saykally@berkeley.edu Abstract: Recent theoretical and experimental studies of evaporation have suggested that on average, molecules in the higher-energy tail of the Boltzmann distribution are more readily transferred into the vapor during evaporation. To test these conclusions, the evaporative cooling rates of a droplet train of liquid water injected into vacuum have been studied via Raman thermometry. The resulting cooling rates are fit to an evaporative cooling model based on Knudsen’s maximum rate of evaporation, in which we explicitly account for surface cooling. We have determined that the value of the evaporation coefficient (γ e) of liquid water is 0.62 ( 0.09, confirming that a rate-limiting barrier impedes the evaporation rate. Such insight will facilitate the formulation of a microscopic mechanism for the evaporation of liquid water. Introduction Interphase mass transfer at the liquid-vapor interface of water is a fundamental process that impacts many areas of physical science, engineering, and biology. However, despite intensive research, the underlying mechanisms and rates of evaporation and condensation remain poorly understood. Recent measure- ments of the temperature profile across the surface of a rapidly evaporating liquid-vapor interface exhibited a discontinuous temperature increase, wherein the vapor directly above the surface was as much as ∼7° warmer than the liquid surface itself. These measurements were interpreted as indicating that molecules in the high-energy tail of the Boltzmann distribution are those most often evaporating. 1 Molecular dynamics (MD) simulations have also shown that the evaporating water mol- ecules exhibit a non-Maxwellian distribution characterized by increased translational energies. 2 Such a conclusion is in contrast to the classical kinetic picture of evaporation, wherein it is assumed that the temperature of the vapor is less than or equal to that of the surface. 1,3 In fact, an elevated vapor temperature suggests there exists an energetic barrier to evaporation in excess of the enthalpy of vaporization. More recent results by Cappa et al. have shown that the relative evaporation rates of light and heavy isotopes of water are strongly composition dependent, which also evidences a barrier to the evaporation process. 4 The standard kinetic theory of evaporation was first derived by Hertz from analysis of the evaporation of mercury 5 and was later verified by Knudsen. 6 Under equilibrium conditions, the rate of evaporation is equal to the rate of condensation, as there is no net mass transfer between phases. The maximum rate of condensation (J c,max ) or evaporation (J e,max ) is then the number of molecular collisions per unit time per unit area with the liquid surface, as given by the Knudsen equation 7 where P 0 is the equilibrium vapor pressure, T is the liquid temperature, k B is Boltzmann’s constant, and m is the molecular mass. The parameter most often reported in evaporation studies is the evaporation coefficient (γ e ). The evaporation coefficient is the ratio of the observed rate to that given by the theoretical maximum (eq 1), 8,9 such that where J e,obs is the observed evaporation rate. Hence, an evaporation coefficient of unity implies the maximum possible evaporation rate. An evaporation coefficient less than unity indicates that there exists a barrier (energetic or entropic) that limits the rate of evaporation. ² University of California. ‡ Lawrence Berkeley National Laboratory. § Present address: NOAA Earth System Research Laboratory, Chemical Sciences Division and the Cooperative Institute for Research in Environ- mental Sciences, University of Colorado, Boulder, CO. (1) Fang, G.; Ward, C. A. Phys. ReV. E: Stat. Sphys., Plasmas, Fluids, Relat. Interdiscip. Top. 1999, 59, 417. (2) Tsuruta, T.; Nagayama, G. J. Phys. Chem. B 2004, 108, 1736. (3) Cercignani, C.; Fiszdon, W.; Fressotti, A. Phys. Fluids 1985, 28, 3237. (4) Cappa, C. D.; Drisdell, W. S.; Smith, J. D.; Saykally, R. J.; Cohen, R. C. J. Phys. Chem. B 2005, 109, 24391. (5) Hertz, H. Ann. Phys. 1882, 17, 177. (6) Knudsen, M. Ann. Phys. 1915, 47, 697. (7) Knudsen, M. The Kinetic Theory of Gases; Methuen: London, 1950. (8) Barrett, J.; Clement, C. J. Colloid Interface Sci. 1991, 150, 352. (9) Eames, I. W.; Marr, N. J.; Sabir, H. Int. J. Heat Mass Transfer 1997, 40, 2963. J c,max ) J e,max ) P 0  2πmk B T (1) J c,obs ) γ e J e,max ) γ e P 0  2πmk B T (2) Published on Web 09/12/2006 12892 9 J. AM. CHEM. SOC. 2006, 128, 12892-12898 10.1021/ja063579v CCC: $33.50 © 2006 American Chemical Society