Physics and Thermodynamics of Water and Ice. Ottmar Möhler

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1 Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Physics and Thermodynamics of Water and Ice Ottmar Möhler Institute for Meteorology and Climate Research (IMK-AAF) ESF workshop on Microbiological Meteorology, Avignon, March 1-3, 2006

2 Outline Basic properties of water and ice Vapour pressure of ice Vapour pressure of (supercooled) liquid water Phase transition liquid to ice (homogeneous freezing) Consequences of ice formation in liquid clouds

3 Basic Properties of Water and Ice Molecular structure of the water molecule Equilibrium O-H distance: Å H-O-H angle: Hydrogen bonds Formation of dimers Different radiative properties Different chemical reactivity SO 3 + (H 2 O) 2 H 2 SO 4 + H 2 O Crystal structure of ice Phase diagram Triple point (all three phases coexist): p = Pa T = C Melting curve has negative slope: C at atmospheric pressure Definition of Celsius scale Pressure (Pa) δ+ 57 Ice δ- H O Liquid Vapour Å H Schematic phase diagram of water (not to scale) Temperature (K)

4 Basic Properties of Water and Ice The density of liquid water and ice Maximum density of water at about +4 C: ρ = ρ ρ ( 4 C) ρ(0 C) 4 ρ(0 C) Density of ice lower than that of water 1 At T = 0 C: % ρ liq ρ ice ρ ρ = ρ = gcm = gcm ice ρ ρ liq liq ρ (g cm -3 ) Density of liquid water Bursting bottles, pipes, T (ºC)

the upper rim From Kenneth G. Libbrecht, Caltech http://www.its.caltech.

5 Basic Properties of Water and Ice Formation of ice cube spikes Expansion of ice freezing from the edge pushes water upward A channel forms with water freezing around the upper rim From Kenneth G. Libbrecht, Caltech See also recent paper by Charlie Knight, J. Glaciology, 2005.

6 Vapour Pressure of Ice Thermodynamic Basis (from Murphy and Koop, Q.J.R.Met.Soc, 2005) 1. Starting with Clausius-Clapeyron Equation: d lnp dt = Lice( T ) 2 RT L ice : Latent heat of sublimation R: Molar gas constant ( J mol -1 K -1 ) 2. Express L ice (T) as function of the difference in molar heat capacities for water vapour and ice (based on measurements) 3. Fit to the numerical integration of the Clausius-Clapeyron equation: p ice = exp( T ln( T ) T ) p ice in Pa, T in K (for T > 110 K)

7 Vapour Pressure of Ice Comparison with measurements p ice = exp( T ln( T ) T ) 10 3 Ice Vapour Pressure (Pa) Temperature (K) (from Murphy and Koop, Q.J.R.Met.Soc, 2005)

8 Vapour Pressure of Supercooled Liquid water Thermodynamic Basis (from Murphy and Koop, Q.J.R.Met.Soc, 2005) As for ice, starting with Clausius-Clapeyron Equation: d lnp dt = L liq RT ( T ) 2 L liq : Latent heat of sublimation R: Molar gas constant ( J mol -1 K -1 ) Measurements of molar heat capacity only for T > 235 K (supercooled liquid water) and T < 155 K (amorphous ice) Calculation more uncertain. ln( p liq ) ln( T ) T ) T tanh{0.0415( T 218.8)}( ln( T ) T ) T p liq in Pa, T in K (for 123 K < T < 332 K)

9 Vapour Pressure Ratio Liquid to Ice 2 Pressure Ratio p liq /p ice Supercooled solution droplets Region of ice supersaturation Supercooled water droplets Temperature (K)

10 Phase Transition Liquid to Ice Homogeneous nucleation rate of water droplets: Basic equations Nucleation rate J V G act ( T ) ( T ) = AT ( ) exp RT see e.g. Pruppacher&Klett, 1997 Free energy G of germ formation G act Nact Volume terms: -N Activation size Surface terms: N 2/3 Number N of molecules in solid germ 1/ 2 ρ wkt σi / w Gact ( T J = V ( T ) 2Nc exp ρih kt RT Rate of germ formation per liquid volume and time ) j = 1 cm -3 s -1 Pruppacher 1995 j = ice J V Droplet concentration c drop Mean droplet volume V drop V drop c drop Rate of ice formation per air volume and time -3-1 J (cm s ) v Droplets 100 cm -3 d = 10 µm j = 1 l -1 s Temperature (ºC)

11 Phase Transition Liquid to Ice Homogeneous nucleation rate of water droplets: Laboratory results Benz et al., 2005

Vapour Pressure Difference p liq - p ice Bergeron-Findeisen Mechanism of Ice Growth in Expense of Droplets Diffusional growth of ice crystals in expense of liquid droplets dn

12 Vapour Pressure Difference p liq - p ice Bergeron-Findeisen Mechanism of Ice Growth in Expense of Droplets Diffusional growth of ice crystals in expense of liquid droplets dn dt 4πaD( n ns ) const ( pliq pice) Maximum growth rate around -10 C Pressure Difference p liq - p ice (Pa) Temperature (K) Bergeron, 1935

Vapour Pressure Difference p liq - p ice Laboratory Example for the Bergeron-Findeisen Mechanism AIDA cloud chamber experiment starting with an aerosol mixture of 120 cm -3 bacterial cells from an

13 Vapour Pressure Difference p liq - p ice Laboratory Example for the Bergeron-Findeisen Mechanism AIDA cloud chamber experiment starting with an aerosol mixture of 120 cm -3 bacterial cells from an aqueous Snomax suspension (1mg/ml) and 3000 cm -3 residual particles from the dispersion of the suspension Welas Optical Particle Counter Ice particles Water droplets Start expansion cooling at -6 C Liquid cloud forms around -7 C Ice particles nucleate and grow between -7 and -8 C (maximum number conc. about 20 cm -3 )

14 A collection of natural (above) and designer (below) snow flakes (from K. G. Libbrecht, ) and real AIDA ice crystals (courtesy of Roland Schön)

15 AIDA Experiments Jan 2005: Aerosol Generation Setup Dispersion of aqueous bacterial suspension Evaporation of water in diffusion dryer Size distribution of single bacterial cells Addition of bacterial cells to AIDA chamber Start cloud expansion simulation Note: large number of residual particles Synthetic Air Atomizer To AIDA Bacteria Suspension Synthetic Air Diffusion Dryer VKL10 VKL10 APS SMPS CPC Exhaust Gases

Melting of ice particles:

Melting of ice particles: When ice particles fall below 0 C they begin to melt, but the process takes some time since heat transfer needs to occur (heat from ambient environment has to supply the latent