Abstract
In this chapter, a numerical study and assessment of the mixing efficiency of a novel microfluidic device for mixing two fluids are presented. The device under study consists of a two-dimensional straight microchannel with a square pillar centered across the channel. The main fluid flows through the microchannel from the main inlet to the outlet, while the second fluid is injected through the pillar as two small jets at its upstream corners. For different values of the Reynolds number, intensity ratio between the jets and the main channel stream and jets injection angle, the authors have conducted several numerical simulations to characterize both the mixing efficiency and the required input power to make the fluids flow. The optimum configuration has been revealed for high values of the Reynolds number, low intensity ratios, and high injection angles. Thanks to vortex shedding and the corresponding downstream oscillations, a mixing efficiency of around 90% can be reached. The worst mixing efficiency is obtained for a configuration without vortex shedding, having a mixing efficiency of only around 2%.
TopNomenclature
C0: Molar concentration of solute at channel inlet [mol/m3].
CD: Drag coefficient [-]
CL: Lift coefficient [-]
D: Mass diffusion coefficient [m2/s].
Fx: Streamwise, horizontal, force [N/m]
Fy: Spanwise, vertical, force [N/m]
H: Channel width [m].
I: Jet intensity ratio [-].
L: Channel length [m].
n: Number of grid nodes at the channel outlet.
p: Pressure [-].
P: Input power energy [-].
Pe: Péclet number [-].
: Average static pressure at channel inlet [-].
: Average static pressure at jet injections [-].
: Channel inlet mass flow rate [-].
: Jet injection mass flow rate [-].
: Reynolds number at inlet of the channel [-].
: Jet Reynolds number at the injections [-].
: Schmidt number [-].
: Strouhal number [-].
: Time [-].
: Mean velocity at channel inlet [m/s].
: Mean velocity at jet injections [m/s].
: Velocity vector [-].
: Side of the inner square pillar [m].
: Jet injection width [m].
: Mass fraction of one fluid [-].
: Mass fraction at outlet 
-grid cell [-].
: Average mass fraction at the outlet [-].
: Mixing efficiency [%].
𝜌: Density [kg/m3].
: Standard deviation of the mass fraction of one of the fluids [-].
: Maximum standard deviation in the system [-].
: Kinematic viscosity [m2/s].
Key Terms in this Chapter
Lab on a Chip (LOC): This term refers to a device which integrates functions of a laboratory in a microchip. Due to its small dimensions, small amount of fluids and with a very short time of response can be analyzed.
Microfluidics: This term is used to refer the study of fluids in flow paths with at least one dimension of the order of microns.
Micromixing: Process on which the mixing of two or more fluids takes place at microscale.
Vortex Shedding: When a stream of a fluid past a bluff object, above a certain fluid velocity, vortices, which are shed from the object, can be observed downstream and make the wake oscillatory and unsteady.
Computational Fluid Dynamics (CFD): It is the part of fluid mechanics that computationally (i.e., by means of computers) studies the flow and motion of fluids.
Reynolds Number: One of the most important dimensionless numbers in fluid mechanics. It compares the viscous forces versus the inertial ones. When the former are dominant, the Reynolds number will be low (laminar regime), and if the latter are more important, the Reynolds number will be high (turbulent regime).
Laminar Regime: The flow of a fluid is said to take place in laminar regime when the Reynolds number of the flow is low and below a critical value, which is usually around of few thousand.