Introduction - Micromixers Fundamentals Design and Fabrication - page 2

and requires a turbulent flow. Because of the dominant viscous effect in microscale, turbulence is not
possible in micromixers. Mixing based on eddy diffusion is therefore not relevant for micromixers.
Thus, the main transport phenomena in micromixers include molecular diffusion, advection, and
Taylor dispersion. Molecular diffusion is caused by the random motion of molecules. This transport
mechanism is characterized by the molecular diffusion coefficient. Advection is the transport
phenomena caused by fluid motion. A simple Eulerian velocity can lead to a chaotic distribution of the
mixed species. A stable and laminar flow can also lead to chaotic advection. Thus, chaotic advection
would be ideal for the laminar flow condition in micromixers. Taylor dispersion is advection caused by
a velocity gradient. Axial dispersion occurs due to advection and inter-diffusion of fluid layers with
different velocities. Due to this effect, mixing based on Taylor dispersion can be two or three orders
faster than that based on pure molecular diffusion.
Designing micromixers is a completely new engineering discipline, because existing designs in
macroscale cannot simply scale down for microscale applications. One of the main challenges
related to miniaturization is the dominance of surface effects over volume effects. Actuation
concepts based on volume forces working well in macroscale may have problems in microscale. A
magnetic stirrer is a typical example of the ratio between surface forces and volume forces. It
consists of a magnet bar and a rotating magnet or stationary electromagnets creating a rotating
magnetic field. The driving magnetic force is proportional to the volume of the magnet bar, while
the friction force is proportional to its surface. Scaling down the stirrer follows the so-called cube-
square law. This means shrinking down the stir bar 10 times would roughly decrease its volume by
1000 times and its surface only by 100 times. With its original size, the external magnetic field can
generate a force of the same order of the friction force and cause the stir bar to move. Scaling down
the size 10 times in the same magnetic field would create a small driving force, which is only 1/10th
of the friction force. As a consequence, the stir bar cannot move. A surface force-based actuation
concept would allow scaling down because the ratio between driving force and friction force would
remain unchanged.
The dominant surface phenomena in microscale also affect mixing processes with immiscible
interfaces. For a solid-liquid system, mixing starts with suspension of the solid particles. The dis-
solving process follows suspension. The large surface-to-volume ratio in microscale is an advantage
for the dissolving process, making it easily achievable. Thus, the main challenge is the suspension
process. Because of their relatively large sizes and the correspondingly small diffusion coefficient, the
particle can only be suspended in microscale with the help of chaotic advection. Therefore, the quality
of solid-liquid mixing in microscale is determined by the suspension process.
In a system of immiscible liquids , additional energy is needed to overcome interfacial tension. On
the one hand, dispersing the immiscible phases is a difficult task. On the other hand, surface tension
breaks the stretched fluid into segments and forms microdroplets. The advantage of microscale is that
the formation process can be controlled down to each individual droplet. Therefore, an emulsion with
homogenous droplet size can be achieved in micromixers.
Gas-liquid systems are other systems affected by the dominant surface phenomena. Some appli-
cations such as hydrogenation, oxidation, carbonation, and chlorination require gas-liquid dispersion.
Unlike liquid-liquid emulsion, gas molecules can be absorbed into the liquid phase. The gas-liquid
mixing process consists of two processes: dispersion of the gas bubble and absorption of gas mole-
cules. While absorption is promoted due to the larger available interfacial area, dispersion of tiny gas
bubbles is the main challenge in designing micromixers for a gas-liquid system.