TMIXER,wid,vel,dcoef,sel
Design of a T-shaped microfluidic mixer

wid       width of the primary channel in µm
vel        fluid velocity in the channel in mm/s
dcoef    diffusion coefficient in m²/s
sel        number denoting the selected result.
Use 1 for minimum length of channel and 3 for mixing time

Notes

In laminar flow typically encountered in microfluidics, the flow will not be turbulent enough to permit mixing. Mixing by diffusion is typically slow. To facilitate mixing of two fluids and minimize mixing time, a T shaped microchannel is often used. A cross sectional view of a rectangular T shaped micromixer is shown in figure. It is sometimes called as T-mixer, T sensor or Y-mixer.

Two fluids A and B are forced into a T junction. The width of the channels reduces beyond the intersection. Fluid A being the solute, moves side by side with solvent B. Diffusion of fluid A molecules into fluid B happens as it flows along the primary channel. Based on the diffusion coefficient, fluid velocity and available time for diffusion, proper mixing happens. To ensure that there is enough time for mixing, the length of the primary channel needs to be designed.

This design form can be used to estimate the minimum length of the primary channel for proper mixing. The velocity of the fluid can be estimated for the microchannel based on its shape from the section under Mechanics > Fluidics > Microchannels. The diffusion coefficient can be calculated from the section under Mechanics > Fluidics > Diffusion > Diffusion coefficient.

The plot shows the concentration field of fluid A molecules along a line drawn close to the farther edge of the channel. This is shown by the blue line in the figure above. At the T intersection, the fluid A particle concentration is nearly zero, which then gradually increases as it flows along the channel. When proper mixing has taken place, enough fluid A molecules should have crossed over to the fluid B side so that the fluid A concentration reaches 0.5 in the normalized scale. The length downstream of the channel at that point should be the required length of the channel. The results obtained analytically nearly matches this result. The 2D surface plot shows the diffusion profile of the solute over the length and width of the T mixer channel.

Assumptions

-The Reynold's number is small
-The channels are long, rigid and wide.
-The fluids have constant viscosity.