When   Friday, May 15, 2009   Time   2:00 PM - 3:00 PM  
Where   Technological Institute M 416 2145 Sheridan Rd.   map it
Audience   - Faculty/Staff - Student - Public
Contact   Molly E Scanlon   +1 847 491 5586  
Group   McCormick-Colloquia Engineering Sciences and Applied Mathematics

Applied Math Colloquium

Title: Rain in a test tube?

Speaker:  Juergen Vollmer, Max-Planck Institute

Abstract:

In clouds the adiabatic cooling drives uprising air across the cloud point and hence causes the nucleation of cloud droplets which subsequently coarsen and eventually lead to rain. In clouds nucleation is due to seeds (mostly small salt particles) such that droplets have to grow from a submicrometer to millimeter scale. Typical cloud diameters are hundreds of meters.

Surprisingly, a very similar scenario leading to precipitation is also observed when subjecting binary liquid mixtures to a shallow temperature ramp. In that case, however, the absence of seeds entails that critical nuclei are two orders of magnitude smaller, and gravity becomes noticeable when droplets have grown to a size of tens of microns. Consequently the resulting ``clouds'' fit into test tubes with lateral dimensions of a few centimeter. This allows us to follow the evolution of phase-separating mixtures for very long times under carefully controlled conditions. Upon slow cooling the mixtures repeatedly go through cycles of nucleation, coarsening and sedimentation.

We suggest a set of PDEs describing the evolution of the mixtures, and discuss its instability towards nucleation and convection. This approach also provides a minimal model explaining the arising of periodic precipitation, and it allows us to discuss physical mechanisms leading to precipitation. Similarities and differences to rain formation in clouds are discussed in the outlook of the talk.