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Simulation of droplets in complex microchannels

Final Report Summary - SIMCOMICS (Simulation of droplets in complex microchannels)

In the last decade, micro-channels have become a preferred solution for droplet-based lab-on-the-chip applications: the elementary units transporting reagents from one functional site to another (mixer, sensor or analyzer) are droplets, which are transported by an inert wetting carrier fluid avoiding contact with the circuits walls and environment. This research project aimed at the development and implementation of numerical models for flowing droplets in thin microchannels of arbitrary geometry, which allows to avoid the exponential complexity of 1-D networks designed for parallelization.

Although appearing as round or oval across a microscope, a transported microfluidic droplet is indeed everything but a simple pancake. It is inherently multiscale, with a radius one order of magnitude larger than the depth, itself an order of magnitude larger than the lubrication layer. Thanks to intense experimental and numerical efforts conducted in parallel, we have provided the first one-to-one comparison of dynamical film thickness measurements in an upscaled experiment and their numerical prediction, using a dedicated in-house 3D boundary element solver. We have discovered the existence of two lateral regions where the lubrication film is the thinnest and demonstrated that most of the recirculation takes place across the thin direction.

These observations have been rationalized by solving the lubrication equations in the thin gap region, using a dedicated finite-element solver. During the course of its development, we have revisited several thin-film coating problems, including for instance the coating of the interior of a sphere or of a cylinder, elucidating the competition between the stabilizing effect of gravity associated to drainage and its destabilizing effect associated to hydrostatic pressure gradient.

Our understanding of the dynamic thin film deformation has allowed us to simulate the trajectory of droplets transported by a pressure-driven wetting carrier fluid. To this end, we have first exploited a remarkable feature of these microfluidic devices, namely their aspect ratio, and proposed a depth-averaged description of the flow involving pancake shaped droplets confined in one direction while allowed to move in the two others. The resulting equations, called Brinkman's equations, combine the 2D Stokes equations with 2D Darcy potential-flow-like equations. We have implemented an open-source tool to solve them when two phases are in contact, using boundary element methods, including lumped interface corrections due to the thickness variations of the lubricating thin films and of the associated meniscii.

We have simulated the trajectory and capture of droplets as they evolve in a surface energy gradient, generated by channel depth variations. In the flow regime where surface tension dominates over viscosity, droplets are indeed attracted to a location where they can lower their surface energy, or equivalently their surface area. This has enabled us to propose a rational description of bubble propped auto-catalytic conical micromotors. Other external driving forces have been also modelled like gravity, or Marangoni effects, raising unforeseen hydrodynamic instability questions.

We have thereby contributed in shrinking the gap between available computations of droplet flowing in microchannels and the increasing number of experimental studies and applications.