47228-G9
Simulating the Spontaneous Emulsification of Oil/Water/Surfactant Mixtures
The goal of this project is to understand the fundamental mechanisms in spontaneous emulsification by means of coarse-grained computer simulations. This involves exploring the growth laws and the morphology of the internal interfaces in the different stages of the emulsification process. These interfaces are characterized by energy scales comparable to the thermal energy, so that a consistent description of thermal fluctuations is needed. We use a particular mesoscale technique for microemulsions, which was recently developed in our group. This method is a generalization of the algorithm introduced by Malevanets and Kapral which is often called Multi-Particle Collision Dynamics (MPC). MPC incorporates hydrodynamic interactions and thermal fluctuations; it is simple enough to allow many analytic calculations which are hard to do for other mesoscale methods. In our algorithm, the fluid consists of two particle species with labels A and B, where particles of different labels undergo multi-particle ``reflections''. This creates an effective repulsion between A-B particles which can lead to phase separation. In order to simulate microemulsions, dimers were included which act as surfactants and consist of rigidly connected A and B particles. In this first year of the project, I developed and implemented a constrained-dynamics algorithm which efficiently handles surfactants of arbitrary shape made of many rigidly connected particles. This generalization was tested for long rod-shaped surfactants. Furthermore, I was able to analytically derive the transport coefficients of the MPC-algorithm for A and B particles by means of a new kinetic theory approach. Previously, we had calculated the mean field phase-diagram of the MPC-method, but were not able to consistently derive the gradient terms in the Ginzburg-Landau free energy functional, which are essential to determine the surface tension. This year, I derived the gradient terms for different versions of the algorithm: one version works with a hexagonal grid and the other uses two grids rotated to each other by an angle of 45 degrees. Originally, an underlying cubic grid was used, but new versions became necessary in order to achieve better isotropy and exact thermodynamic consistency on the level of the surface tension. The support from this grant helped financing my summer research at the Max-Planck Institute for Complex Systems in Dresden, Germany, and allowed me to attend an international conference. The broader impact of the research includes an invitation to co-author a comprehensive review article in ``Advances in Polymer Science'' about MPC. The grant also allowed me to hire two research assistants who started working on this project this Fall 2008.
