"In droplet-based microfluidics, the elementary units transporting reagents from one functional site to another (mixer, sensor or analyzer) are droplets, which are carried by an inert wetting fluid. This research project aims at the development of numerical models of flowing droplets in thin spatially extended microchannels, designed at avoiding the exponential complexity of parallelized 1-D networks. We aim at simulating the trajectory of droplets transported by a pressure-driven carrier fluid, as they evolve in a surface energy gradient, generated by channel depth variations or surface tension inhomogeneities.To this end, we exploit the remarkable aspect ratio of these microfluidic devices to propose a depth-averaged description of the pancake shaped droplets. The resulting equations, called Brinkman's equations, combine the 2D Stokes equations with 2D Darcy potential-flow-like equations. Their diphasic simulation relies on the adaptation of existing algorithms to this particular free interface problem. Pressure corrections due to the thickness variations of the lubricating thin films will also be included.Surfactant and heat dynamics will then be added to model thermo- and soluto-capillary forcing. The depth-averaged model will be finally generalized to account for arbitrary depth variations, so as to add dynamics to the quasi-static description of droplets moving along successive minimal surface energy locations.A specific part of the project is also devoted to the development of an experimental expertise: it is indeed essential to the success of the project to conduct fundamental microfluidic experiments in order to validate our new models. While SIMCOMICS aims at shrinking the gap between present computations of droplets flowing in microchannels and the increasing number of application-oriented experimental studies, it both raises fundamental questions and opens promising perspectives for the engineering design of new microcarved microchannels."