Aerosol-cloud interaction Anatoli Bogdan Institute of Physical Chemistry, University of Innsbruck Austria and Department of Physics, University of Helsinki Finland

Contents - role of aerosol in cloud formation - ideal gas - vapor pressure and partial vapor pressure - Kelvin equation - hygroscopic aerosol particles - Raoults law - Kohler curves

Cloud condensation nuclei or CCNs or cloud seeds are small particles (typically 0.2 µm, or 1/100 th the size of a cloud droplet) about which cloud droplets coalesce. Water requires a non-gaseous surface to make the transition from a vapor to a liquid. In the atmosphere, this surface presents itself as tiny solid or liquid particles called CCNs. When no CCNs are present, water vapor can be supercooled below 0°C before droplets spontaneously form.

At T > 0 ºC, the air would have to be supersaturated to ~400% before the droplets could form. The concept of cloud condensation nuclei has led to the idea of cloud seeding, that tries to encourage rainfall by seeding the air with condensation nuclei. It has further been suggested that creating such nuclei could be used for marine cloud brightening, a geo-engineering technique.

Aerosol pollution over Northern India and Bangladesh - NASA

Warm Clouds Warm clouds consist entirely of droplets which have been formed by condensation onto aerosol particles. Aerosol particles respond to changes in humidity in different ways depending on their chemical composition and solubility. Particles which are soluble or hydrophilic take on water as humidity increases and increase in size.

Above a certain relative humidity soluble particles will deliquesce – the solid particle dissolves in the water it has taken on and becomes a tiny liquid drop, but not yet a cloud drop. For many soluble salts deliquescence happens at relative humidity around 60 – 80%. These droplets exist in equilibrium with water vapor in the surrounding air. The growth of such particles with increase in relative humidity is expressed by the Köhler equation and is a function of the size and chemical composition of the particle.

Prior to the consideration of the Kohler aquation, we will firstly consider several important notions needed for the understanding of the matter.

General about gases and vapors Perfect gas Atmosphere is a mixture of gases. Prier to the study of the real atmosphere (a mixture of real gases) we firstly will consider a notion of perfect (ideal) gas. Gas under very small pressure ( 1 atm) is a very good approximation of perfect gas. In perfect gas: i) the distance between molecules is much larger than the length of free path of molecules and ii)the interaction between molecules is restricted only to their collisions which are considered to be similar to that of the hard balls. Thus in the perfect gas, the molecules possess only kinetic energy whereas potential energy of interaction between the molecules is absent. As a result internal energy E of perfect gas is independent on pressure and volume, E E (p, V). Internal energy is determined only by the kinetic motion of molecules and can be easily changed by the addition (or withdrawing) of heat i.e., by changing its temperature. Thus E =E (T).

Vapor pressure of water Above the surface of liquid water there always exists some amount of vapor and consequently there is a vapor pressure. When a container containing water is open then the number of the escaping molecules is larger than the number of molecules coming back from the vaporphase (Fig. 1). In this case water vapor pressure is small and far from saturation. The atmosphere is a mixture of gases including water vapor

When the container is closed then the water vapor pressure above the surface increases (concentration of molecules increases) and therefore the number of molecules coming back increases too (Fig.2).

After a while, the number of molecules escaping the liquid and those coming back becomes equal. Such situation is called by dynamic equilibrium between the escaping and returning molecules (Fig. 3). In this case, the water vapor pressure over the liquid water is called saturated water pressure.

Saturated water vapor pressure is a function of temperature only and independent on the presence of other gases. The temperature dependence is exponential. In the case of water vapor, the semi empirical dependence reads as where temperature is in Kelvin and A = 77.34, B = -7235, C = - 8.2, D =

Kelvin equation: p s (r)/ p s () = exp ({2 σ w }/{ρ w R v Tr}) = exp (a/r) r = droplet radius p s (r) = the actual vapour pressure of droplet of radius r p s ()= the saturation vapour pressure over bulk water σ w = surface tension ρ w = water density R v - the universal gas constant, T - temperature Example: Saturation ratio Critical radius μm μm nm

What is going on with soluble aerosol particles, for example, such which are composed of NaCl, sea salt, ammonium sulfate etc.

Hygroscopy is the ability of a substance to attract water molecules from the atmosphere through either absorption or adsorption. Hygroscopic substances include sugar, honey, glycerol, ethanol, methanol, sulfuric acid, many salts, and many other substances.

Deliquescent materials (mostly salts) have a strong affinity for water. Such materials absorb a large amount of moisture (water vapor) from the atmosphere until it dissolves in the absorbed water and forms an aqueous solution. Deliquescence occurs when the vapour pressure of aqueous solution is smaller than the partial pressure of water in the atmosphere. All soluble salts will deliquesce if the air is sufficiently humid.

Fig. 6. Equilibrium partial pressures of the components of ideal and non-ideal binary solution as a function of the mole fraction X A. For the real solution, relationships between the pA, pB, and the mole fractions X A, X B are not linear as it is in the case of ideal solution where the linear relationships are shown by the straight dashed lines LR and KQ. When X A 1, then we have a dilute solution of B in A. In this region the Raoults law p A = X A p* A is applied for the component A. For the component B the Henrys law p B = K B X B is applied. In the region where X A 0, we have the Raoults law p B = X B p* B for B component and the Henrys law p A = K A X A for A component. The straight lines LM and KN depict the Henrys law.

The solutions, which obey the Raoults law throughout the whole composition range from pure A to pure B, are called ideal solutions. The solutions, which components are structurally similar, obey the Raoults law very well. In Fig. 6, the equilibrium partial pressures of the components A and B in the ideal solution are shown by dashed lines of LR and KQ. Solution is only ideal if is satisfied for each component. Dissimilar liquids (large difference in the liquid structures) significantly depart from the Raoults law. Nevertheless, even for these mixtures, the Raoults law is obeyed closely for the component in excess as it approaches purity i.e., when X A 1 or X A 0 (Fig. 6).

Raoults law: Mathematically, for a plane water surface the reduction in vapour pressure due to the presence of a non-volatile solute is expressed: p* ()/p s () = 1 – (3νm s M w )/(4 πM s ρ w r 3 ) = 1 - b/r 3 where p* () - the saturation vapour pressure of pure water p s * () - the saturation vapour pressure of bulk solution M s - molecular weight of the solute M s - mass of the solute Ν- degree of dissociation

Combining the Kelvin equation and the expression from the Raoults law, we can obtain so called Kohler equation.

Köhler Curve = Kelvin equation + Raoults law p*(r)/p s () = (1 - b/r 3 )·exp(a/r) 1 + a/r - b/r 3 where a ~ /T [m] b ~ i M s /m s [m 3 /mol] M s = molecular mass of salt [kg/mol] m s = mass of salt [kg] The critical radius r c and critical supersaturation S c are calculated as r c = (3b/a) 1/2 and S c = (4 a 3 /[27 b]) 1/2

Kohler curves show how the critical diameter and critical supersaturation are dependent upon the amount of solute.

As humidity increases, aerosol continues to swell, even after vapor saturation is reached. Once a critical supersaturation is reached, corresponding to the peak of the Köhler curve for that particle, a particle becomes activated as a cloud droplet. Activated particles are no longer in stable equilibrium with the vapor phase, but are able to continue to grow by vapor deposition provided that conditions remain supersaturated.

Droplet size is determined by the number of particles activated and the amount of water vapor available for condensation which is generally determined by the vertical height of an adiabatic ascent. If droplets are able to grow to a sufficient size and the cloud exists for a sufficient length of time droplets will coalesce as they collide with each other through random motion, gravitational settling, or motion within the dynamics of the cloud system.