Slide 1

Kelvin Effect: Physical Cartoon Equilibrium vapor pressure is higher over a curved surface than a flat one. Important for nucleation of new particles, lifetime of small droplets.

Slide 2

Energy of converting vapor molecules to bulk liquid molecules Energy required to maintain a liquid-gas surface boundary X v X l Kelvin Effect: Energy of Droplet Formation

Slide 3

Rp*Rp* Radius at which G maximizes and beyond which droplet formation becomes possible S1 GG S = ratio of eq. vapor pressure around a droplet relative to to above a flat surface For a droplet to exist, S>1. p curved > p flat always How does S vary with R p ?

Slide 4

Kelvin Equation Relates molecular properties (molecular weight, surface tension, density) to the degree to which v.p. over curved surface is enhanced

Slide 5

Questions 1.Some organic compounds are highly surface active. That is, they prefer to reside at the gas-liquid interface, and lead to a lower surface tension. By how much would S change if the surface tension of a droplet changed from 75 dynes (pure water) to 35 dynes (surfactant coated water)? 2.Do you have a physical explanation to the above answer? 3.What is the surface tension of a cluster of 10 H 2 SO 4 molecules and 10 H 2 O? Is it the same as the surface tension for a 50 wt% H 2 SO 4 bulk solution?

Slide 6

RpRp RpRp Free Molecular or Non-continuum Regime Continuum Regime Transition Regime Continuum versus Free Molecular Dynamics

Slide 7

Mean Free Path In 1 second: red has swept through a volume For N molecules per cm 3, red-blue collisions per sec ~ The distance traveled between collisions:

Slide 8

Mean Free Path Increases with Altitude For 10 nm particle: Kn