In this project, we aim to control the short- and long-term evolution of a wall-bounded immiscible Rayleigh-
Taylor Instability (RTI). The control is done using an external DC electric field excitation which is applied 
either vertically or horizontally with respect to the initial interface position. Here we apply two complementary 
methodologies namely theoretical analysis and numerical simulation. In the theoretical study we start with 
existing viscous theory for linear electrohydrodynamic RTI and extend it in the nonlinear regime and for a 
wall-bounded domain. In the developed model, the two fluids are perfect dielectrics with constant electric 
permittivities/conductivities and the imposed electric field is assumed of constant intensity but variable 
orientation with respect to the initial interface position. For the numerical study, we base on the available in-
house Smoothed Particle Hydrodynamics (SPH) code in which the well-known Leaky Dielectric Model (LDM) 
is developed and validated for single droplet deformation. After comparison of this model with the developed 
theory in non-linear regime, we extend the solver to Perfect Dielectric (PDM) and Charge Conservative 
Models (CCM) to remove some constraint of LDM. CCM will be compared to LDM and to the developed 
theory, and the capacity of each model will be investigated. Finally, through extensive case studies, effect of 
relevant parameters such as confinement ratio, electrical field strength, direction, as well as fluid 
hydrodynamical and electrical properties will be inspected in details. Once the knowledge is available, it is 
transferable to other hydrodynamical instabilities such as Kelvin-Helmholtz and Saffman-Taylor instabilities, 
which may develop between two fluids respectively with velocity/viscosity difference, in particular in porous 
media and may have direct impact on different energetic systems for multiphase pipe-line transport and 
polymer membrane formation. 

We are looking for a potential candidate with the good background in developing numerical code, 
understanding theoretical background, and performing multiphase flow analysis for the advertised position. 
Interested candidate should already finished his/her Master thesis (or engineering degree) in the field of 
Mechanical/Energy/Mathematical Engineering or the defence date should not be later than the end of 
September 2023. Good communication skills, profound mathematical appetite and good knowledge of code 
development using C/Fortean or any other scientific programming languages are pre-requisite. If interested, 
please send your CV along with 2 letters of recommendations to Dr. Shadloo at msshadloo@coria.fr or Dr.  
Renoult at renoultm@coria.fr .