A simple method for evaluating and predicting chaotic advection in microfluidic slugs

A simple method for evaluating chaotic advection in slug micromixing is reported in this paper. We consider a slug moving in a slit microchannel (w⪢h)(w⪢h) and flow field in a plane far from the boundary walls is modelled as a two-dimensional low-Reynolds-number flow (Stokes flow). Analytical solution for normalised velocity field in the slug is derived. The two-dimensional analytical solution is compared with the two-dimensional slice from the three-dimensional numerical solution of the slug velocity field. Boundary conditions mimicking the motion of the slugs in microchannel geometries, in Lagrangian frame of reference, is used to track the passive tracer particles using Lagrangian particle tracking method. Poincaré sections and dye advection patterns are used to analyse chaotic advection of passive tracer particles using statistical concepts such as ‘variance’, ‘Shannon entrophy’ and ‘complete spatial randomness’. Results for boundary conditions mimicking constant-velocity straight-channel flow, constant-velocity normal-meandering channel flow are compared. A method for finding new channel geometries which enhance chaotic mixing is also proposed.