To fully understand the phenomena at the microscale, a variety of theoretical studies are needed, both in fundamental understanding of physics, and in specification and optimization of design.
First, the physics need to be understood. We have studied pressure driven fluid flows, dielectrophoresis, AC electroosmosis, AC electrothermal effect, diffusion. Finding the correct set of equations to describe a particular microfluidic system is an important step in our microfluidic study framework. In some cases, improved models were needed . From those, exact or approximate solutions can be found. In the case of dielectrophoresis generated by interdigitated electrodes, we were able to derive analytical solutions  but in general, numerical simulations are needed. Our software of choice for finite element simulation is Comsol multiphysics. When a lack of tools for a specific type of simulation is observed, our group will develop its own numerical schemes .
Once the physical phenomena are well understood, it is possible to design and optimize new microfluidic devices that will be able to perform the basic operations for microfluidic processing (separation , concentration , mixing  , transport and reaction). Using a dynamical system approach, we develop methods to measure performance , optimize performance , allow controllability [2, 1, 11].
Our theoretical studies of microfluidic are tested and validated by experiments.
 Frederic Bottausci, Caroline Cardonne, Igor Mezic, and Carl Meinhart. An actively controlled micromixer: 3-d aspect. COURSES AND LECTURES- INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES, 466:129, 2006.
 Dong Eui Chang and Sophie Loire. Separation of bioparticles using the travelling wave dielectrophoresis with multiple frequencies. In Decision and Control, 2003. Proceedings. 42nd IEEE Conference on, volume 6, pages 6448–6453. IEEE, 2003.
 Dong Eui Chang, Sophie Loire, and Igor Mezic. Closed-form solutions in the electrical field analysis for dielectrophoretic and travelling wave inter-digitated electrode arrays. Journal of Physics D: Applied Physics, 36(23):3073, 2003.
 T John and I Mezic. Maximizing mixing and alignment of orientable particles for reaction enhancement. Physics of Fluids, 19:123602, 2007.
 S Loire and Mezic I. Spatial filter averaging approach of probabilistic method to linear second-order partial differential equations of the parabolic type. Journal of Computational Physics, 233(0):175 – 191, 2013.
 S Loire, P Kauffmann, I Mezic, and CD Meinhart. A theoretical and experimental study of ac electrothermal flows. Journal of Physics D: Applied Physics, 45(18):185301, 2012.
 George Mathew, Igor Mezic, and Linda Petzold. A multiscale measure for mixing. Physica D: Nonlinear Phenomena, 211(1):23–46, 2005.
 George Mathew, Igor Mezic, Radu Serban, and Linda Petzold. Optimization of mixing in an active micromixing device. In Technical Proc. 2004 NSTI Nanotechnology Conf. Trade Show, Boston, MA, volume 1, pages 300–303, 2004.
 Igor Mezic. Lectures on mixing and dynamical systems. In Analysis and Control of Mixing with an Application to Micro and Macro Flow Processes, pages 35–108. Springer, 2009.
 Marin Sigurdson, Dong-Eui Chang, Idan Tuval, Igor Mezic, and Carl Meinhart. Ac electrokinetic stirring and focusing of nanoparticles. In BioMEMS and Biomedical Nanotechnology, pages 243–255. Springer, 2007.
 Idan Tuval, Igor Mezic, Frederic Bottausci, Yanting T Zhang, Noel C MacDonald, Oreste Piro, et al. Control of particles in micro-electrode devices. 2005.