Vortical flow and mixing in rotating milli- and micro-chambers

The complex flow in rotating milli- and micro-chambers, with wide applications in bio-MEMS, has not been fully understood; and this forms the basis of our investigation. A time-and-grid size validated numerical model has been developed to study the fluid mechanics and mass transfer of mixing by the vortical flow being induced from continuously transient angular acceleration-deceleration of the chamber. A primary vortex, responsible for mixing fluids in the radial-circumferential planes of the chamber, is generated from the inertial effect with the temporal change of vorticity directed opposite to that of the rotating chamber. This dominant vortex has been confirmed by an analytical approach assuming quasi-equilibrium under constant acceleration-deceleration. In addition, a pair of toroidal vortices, responsible for mixing fluids in the radial-axial planes of the chamber, is generated from the Coriolis acceleration acting on the fluid motion from the primary vortex. The resultant three-dimensional (3D) spiral toroidal vortex (STV) provides effective momentum and mass transfer in the chamber. Different transient rotation speed schemes have been used to realize the continuous acceleration-deceleration; and the most effective scheme is the linear change of angular speed over time with chamber accelerating linearly to maximum rotation speed Ω_M, and subsequently decelerating linearly to zero speed in a total time duration of 2δ. t. Experiments and simulations demonstrate that more effective mixing with smaller specific mixing time (SMT), attributed to higher vorticity and lower viscous friction, can be obtained from higher angular acceleration/deceleration and with large chamber (longer radial extent, taller height, and wider angular span). A similitude study on both numerical and experimental data using the dimensionless groups obtained from the Buckingham-π analysis reveals that an empirical scale-up law can be developed with the dimensionless mixing time τ/(ro2/υ) being well correlated with the driving potential Φ which is made up of the five dimensionless variables, ratio of transient acceleration time of chamber to momentum diffusion time δt/(ro2/υ), rotational Reynolds number ReR=ro2ΩM/ν, ratio of half height to outer radius h/. r_o, ratio of inner to outer radius r_i/. r_o, and angular span θ of the rotating chamber. Higher Φ is required to create sufficiently high vorticity overcoming increasing viscous resistance offered from the top, bottom, radial and end walls of the milli- and micro-chamber so that effective mixing can be achieved.