# Microfluid Mechanics/Introduction

## Motivation

The microelectromechanical systems (MEMS) and devices comprising fluid flow can be called as microfluidic devices and systems. Micro-and nano devices are technologically attractive because of their small dimensions and consequently low inertia. These two simple properties are the basis for many attractive applications. Already being small means that very low volumes of fluid are necessary in these systems. When very small amounts of fluid or samples with very less concentration of molecules are available for a reaction or detection process, it is clear that only with comparably small size of fluidic device, the successful realization of this process is possible. Owing to the small size of the devices it is possible to conduct massively parallel fluidic operations, which would save enormous amount of time. High spatial resolution especially in the fields of sensing and actuation is a natural advantage of microdevices. In summary, operations conducted in small dimensions offers the possibilities to have the sample substance to be portable and to conduct multitasking and parallel fluidic operations. Low inertia of microdevices results in high temporal resolution of any sensing and actuating elements, fast response of these devices, high sensitivity of sensing devices and low-energy consumption. Of course exploitation of these advantages is only possible when the small devices can economically be produced. In the meantime many microdevices were developed and commercially available.

With the introduction of microfluidic devices it was realized that the fluid flow does not behave similar to macro flow owing to the dominance of surface forces on the body forces. The consequences of this unexpected behavior is summarized by Karniadakis et al. (2005) as follows:

 "In microgeometries, the flow is granular for liquids and rarefied for gases, and the walls move." [1].

For example, the viscous stresses damps the inertial effects in the flow, gas flows can be rarefied in microconduits, or the surface tension starts to drive the flow. It was very soon understood that simple downscaling is not sufficient to mimic the operation of the device in the macro world. Intensive research has been conducted to understand unexpected flow phenomena in micro and nano scales and to exploit the observed effects in different applications. The academic publications shows a rapid increase of the 1990s. This increase can fairly be accepted as the projection of high commercial interest in this field. According to Nguyen(2004)[2], the research and development in microfluidic devices focus on:

• miniaturization of conventional systems
• applications of new effects and forces which are only feasible in microdevices
• finding new application areas for the microdevices

State of the art fluid mechanics education should comprise the flow phenomena and its analysis. In this course, efforts were undertaken to provide physical understanding of the underlying flow processes in micro devices and to introduce theoretical numerical and experimental analysis methods of these processes.

Benefits of micro devices

Academic references on micro and nano flows

## Surface forces vs. body forces

Microdevices tend to behave differently from the objects we are used to handling in our daily life[3] [4] because of a simple reason: The influences of forces, which are functions of wetted area, decreases slower than those, which are functions of fluid volume.

Let ${\displaystyle \displaystyle p_{1}(A)}$  and ${\displaystyle \displaystyle p_{2}(V)}$  are any two property which scales with wetted area ${\displaystyle \displaystyle (A)}$  and fluid volume ${\displaystyle \displaystyle (V)}$ . Their change relative to eachother with decreasing lengh scale of the system ${\displaystyle \displaystyle (L)}$  can be written as:

${\displaystyle \displaystyle {\frac {p_{1}(A)}{p_{2}(V)}}\propto {\frac {L^{2}}{L^{3}}}\propto {\frac {1}{L}}}$

Typical order of magnitude is ${\displaystyle \displaystyle 10^{6}\,{\text{m}}^{2}/{\text{m}}^{3}}$ . In other words, surface forces clearly dominates the body forces.

The unexpected effects starts to appear because the intermolecular forces either dominate or loose their influence. The former case appears to happen in liquid and multi-phase flows and the decrease of molecular forces happens mainly in rarefied gas flows. Therefore, it is important to understand these flows in terms of their molecular behavior. A key nondimensional parameter for microflows is the Knudsen number:

${\displaystyle \displaystyle Kn={\frac {\lambda }{L}}}$

where ${\displaystyle \displaystyle \lambda }$  is the mean free path of the molecules.

Owing to decreasing ${\displaystyle \displaystyle L}$

• Reynolds number number decreases ${\displaystyle \displaystyle (Re<1)}$ .
• Knudsen number increases ${\displaystyle \displaystyle (Kn>1)}$ .

## Examples of microdevices

### Man made microdevices

 Some of the microdevices, which are developed are: microchannels and pipes, microjets, micropumps, microfilters, micro heat pipes, micro heat exchangers, micromixers with chaotic advection, microreactors, micro gas turbines, microrockets, microthrusters, microengines, microsensors, microactuators, microair vehicles, microdialysis systems, microfluidic chips (lab-on-a-chip), microfluidic circuits, ...All these systems can be classified under microelectromechanical systems (MEMS). The MEMS devices comprising fluid flow can be classified as microfluidic devices. Microreactor technologies developed at LLNL use micromachining techniques to miniaturize the reactor design. Applications include fuel processors for generating hydrogen, chemical synthesis, and bioreaction studies.

### Natural micro devices

 In nature, almost all living creatures formed by micro structures and devices. For example, a tree sucks water from soil via its roots composed of micron sized cells and distributes the water throughout its body by vanes which can be again in the order of a few hundred microns on its leaves. Micron-sized hair-like appendages (Trichome) can be seen on a leaf. These hairs have multiple functions: For example they can keep the frost away from the living surface cells. In windy locations, hairs break-up the flow of air across the plant surface, reducing evaporation. Dense coatings of hairs reflect solar radiation, protecting the more delicate tissues underneath in hot, dry, open habitats. In locations where much of the available moisture comes from cloud drip, hairs appear to enhance this absorption of water from air.[5]   Willow tree   Root tip at microscope 10x Vein sceleton hydrangea   Scanning electron microscope image of Nicotiana alata upper leaf surface, showing tricomes and a few stomates.

Insects are autonomous creatures which have been adopted themselves to the physical effects dominating in the micron world. For example, water strider stays over the water surface owing to the surface tension. The bee flight is totally different than many of the birds.

The locomotion of sperms is not similar to that of big fishes. The alveoli in the lungs ranges between 200 to 300 µm and responsible for the gas exchange. Reinflation of the alveoli following exhalation is made easier by pulmonary surfactant, which is protein mixture that reduces surface tension in the thin fluid coating within all alveoli.

Planktons provide a crucial source of food to larger, more familiar aquatic organisms such as fish and marine mamals.

 Honey bee Human sperm
 Phytoplankton are the foundation of the oceanic food chain.

## Historical perspective

 Miniaturization is continuously progressing field, which has strong commercial impact and scientific attraction. The first attempts of miniaturization can be found in the jewelery making. Watch is a very good example of miniature mechanical system with moving parts.   Timeline of technical miniaturizaiton Example fine jewelery piece.   Fine mechanics in a pocket watch.

## References

1. Karniadakis, G., Beşkök, A., Aluru, N. R.: Microflows and nanoflows: fundamentals and simulation, Springer, New York, 2005.
2. Nguyen, N.-T.: Mikrofluidik: Entwurf, Herstellung und Charakterisierung, Teubner Verlag, 2004.
3. Gad-el-Hak, M.: The ﬂuid mechanics of microdevices. J. Fluids Eng., 12(1):5–33, 1999.
4. Ho,C. M.and Tai, Y.C. :Micro-electro-mechanical systems (MEMS)and ﬂuidﬂows, Ann. Rev. Fluid Mech., 30:579–612, 1998.