Microfluid Mechanics/Introduction

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Surface forces vs. body forces
Microdevices tend to behave differently from the objects we are used to handling in our daily life  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 $$ \displaystyle p_1(A) $$ and $$ \displaystyle p_2(V)$$ are any two property which scales with wetted area $$ \displaystyle (A)$$ and fluid volume $$ \displaystyle (V) $$. Their change relative to eachother with decreasing lengh scale of the system $$ \displaystyle(L)$$ can be written as:

$$ \displaystyle \frac{p_1(A)}{p_2(V)}\propto\frac{L^2}{L^3}\propto\frac{1}{L} $$

Typical order of magnitude is $$ \displaystyle 10^6\,\text{m}^2/\text{m}^3 $$. 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:

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

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

Owing to decreasing $$ \displaystyle L $$


 * Reynolds number number decreases $$ \displaystyle (Re<1) $$.


 * Knudsen number increases $$ \displaystyle (Kn>1) $$.

Natural micro devices
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.