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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.

This year, I was able to generalize the well-known Chapman-Enskog kinetic theory of regular fluids to multi-particle collision models. To demonstrate the power of this new approach, I derived the constitutive relation with accurate expressions for all transport coefficients for the simplest MPC model. While this is not the first theory for MPC, the new approach is generalizable to more complicated models where the macroscopic hydrodynamic equations contain unusual nonlinear terms. This achievement has been recognized by invitations as plenary speaker to two international conferences, DSFD 2009 in China, and MESOSOFT 2009 in Germany.

The support from this grant enabled me to hire two graduate students, Alemayehu Gebremariam and Bekele Gurmessa, who are being trained in C-programming and the development of simulation methods for complex fluids.

Recently, it became clear that angular momentum conservation is relevant for particle-based algorithms of fluid mixtures. Therefore, Bekele incorporated angular momentum conservation in our MPC model in two different ways and is currently comparing their numerical efficiency. Alemayehu is involved in the numerical verification of the kinetic theories I am developing; he presented the results of our research at the 2009 March meeting of the American Physical Society.