Continuously driven phase separation: size distributions and time scales in droplet growth

by Martin Rohloff
Doctoral thesis
Date of Examination:2015-07-16
Date of issue:2015-09-09
Advisor:Prof. Dr. Vollmer Jürgen
Referee:Prof. Dr. Marcus Müller
Referee:Prof. Dr. Vollmer Jürgen
Persistent Address: http://dx.doi.org/10.53846/goediss-5247

 

 

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Abstract

English

Phase separation arises in mixtures when temperature, pressure or concentrations of the mixture is changed such that a new macroscopic phase emerges. Typically the domains of the new phase take the form of droplets, bubbles or solid particles. Many phenomena such as the synthesis of monodisperse colloidal particles, rain formation or geysers are caused by continuously driven phase separation where a sustained change of temperature, pressure or concentrations induces a continuous increase of the volume occupied by the domains. I use here (i) laboratory experiments on phase separation of liquid binary mixtures, (ii) numerical investigation of droplet assemblies evolving with overall volume growth, and (iii) theoretical modelling to study the evolution of the domain size distributions and the emerging time scales in the domain growth. Depending on the driving strength I identify a crossover from coarsening dynamics (Ostwald ripening) to size focussing in the domain size distributions. I give analytic expressions for the evolution of the size distribution in the size focussing regime that arises for sufficiently strong driving and I show that the size distribution can be rescaled for all times onto the initial distribution. These findings have immediate consequences for size distributions in nano-particle synthesis. When the droplets have grown to sizes where their motion is affected by buoyancy, sedimentation and collisions cause a runaway growth. The runaway leads to precipitation of the droplet volume out of the fluid and resets the system. For a sustained driving new droplets start to grow and eventually they will be removed by another wave of precipitation. We denote this oscillatory response to a continuous thermodynamic driving as episodic precipitation. The time scale of precipitation is set by the crossover from diffusive to collisional growth. The measured time scales collapse on a master curve predicted by an analytic model that is also developed in the thesis. Applying the model to the formation of warm rain gives reasonable values for the rain initiation time. The application of concepts developed in the present thesis to describe continuously driven phase separation thus provides valuable new insights for a wealth of different phenomena.
Keywords: phase separation; binary fluids; ripening; cloud physics; precipitation; monodisperse colloids; size focussing; synchronisation
 
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