52
G. K. Ananthasuresh
comb drives (marked a to d). Thus, it is modular design with four kinds of building
blocks. Two DaCMs amplify the motion of the proof mass at the center. The purpose
of 12 compliant sliders is to decouple the movements of the proof mass in x- and
y-directions and transmit that to two sensing combs (a and b) though two DaCMs.
Four more compliant sliders prevent the motion of the sensing combs in unintended
directions. The other two combs (c and d) are used for self-test through actuation.
Once we see the intent of each building block, the function of the entire device
becomes clear and the interoperability of this modular design becomes clearer. It
also makes it easy to arrive at the parameters of all the building blocks.
10 Hierarchy in Flow Paths and Solid Structures
What holds true at one size scale might change slightly or a lot at another size scale.
Scaling arguments are popular in MEMS and nanotechnology [36, 37]. That line
effects (e.g., surface tension) and surface effects (e.g., heat exchange) dominate over
volume effects (e.g., inertia) at micro- and nano-scales is well known. Quantitatively
speaking, length is the largest at the small scales as compared to area, and area looks
larger than volume. This reversal of sequence as compared to the macro-size brings
in interesting consequences in many physical and chemical phenomena [38]. There
is much more to size effects within a given MEMS device. That has to do with
hierarchy in a design.
Hierarchical design is most evident in Nature. The circulation paths of blood flow
comprise a prime example. From the big aorta, the arteries multifurcate into small
vessels and end up in small capillaries, only to unite later to veins and then vena
cava. It is a tree structure. A big flow path divides into small, and then smaller flow
paths. They combine in reverse. Andrian Bejan calls it constructal law [39]. A tree
is another example. From the trunk up, branches emerge and then divide into subbranches and twigs and then to leaves. Trunk down, the root system too has this
hierarchy. For flowing from one source point to multiple points with least resistance
requires a hierarchical tree structure [40]. Such a design also helps in mixing because
microflows are known to have extremely low Reynolds number and hence are hard
to mix otherwise. As we go down a tree structure, the cross-sectional area of the
flow path decreases. This has to be calculated carefully; optimization helps and also
points what is optimal under what conditions [40].
Hierarchy in structural design is much older and dates back to at least Gustave
Eiffel [41, 42]. Eiffel exploited structural hierarchy by making his designs optimally
porous. That is, he used beam segments crisscrossing with another rather than using
a solid piece. If we examine the Eiffel tower, we see cross-beams with smaller
cross-beams inside them. It resembles fractal-like design. While Eiffel took it to
three levels of hierarchy in the famous tower in Paris, Nature has exploited it up
to five levels [41]. Trabecular bone is made of collagen molecules making fibrils,
fibrils combining to become fiber, fibers forming lamella, and lamella leading to
cancellous bone. All five size scales have their own unique design unlike Eiffel’s
G. K. Ananthasuresh
comb drives (marked a to d). Thus, it is modular design with four kinds of building
blocks. Two DaCMs amplify the motion of the proof mass at the center. The purpose
of 12 compliant sliders is to decouple the movements of the proof mass in x- and
y-directions and transmit that to two sensing combs (a and b) though two DaCMs.
Four more compliant sliders prevent the motion of the sensing combs in unintended
directions. The other two combs (c and d) are used for self-test through actuation.
Once we see the intent of each building block, the function of the entire device
becomes clear and the interoperability of this modular design becomes clearer. It
also makes it easy to arrive at the parameters of all the building blocks.
10 Hierarchy in Flow Paths and Solid Structures
What holds true at one size scale might change slightly or a lot at another size scale.
Scaling arguments are popular in MEMS and nanotechnology [36, 37]. That line
effects (e.g., surface tension) and surface effects (e.g., heat exchange) dominate over
volume effects (e.g., inertia) at micro- and nano-scales is well known. Quantitatively
speaking, length is the largest at the small scales as compared to area, and area looks
larger than volume. This reversal of sequence as compared to the macro-size brings
in interesting consequences in many physical and chemical phenomena [38]. There
is much more to size effects within a given MEMS device. That has to do with
hierarchy in a design.
Hierarchical design is most evident in Nature. The circulation paths of blood flow
comprise a prime example. From the big aorta, the arteries multifurcate into small
vessels and end up in small capillaries, only to unite later to veins and then vena
cava. It is a tree structure. A big flow path divides into small, and then smaller flow
paths. They combine in reverse. Andrian Bejan calls it constructal law [39]. A tree
is another example. From the trunk up, branches emerge and then divide into subbranches and twigs and then to leaves. Trunk down, the root system too has this
hierarchy. For flowing from one source point to multiple points with least resistance
requires a hierarchical tree structure [40]. Such a design also helps in mixing because
microflows are known to have extremely low Reynolds number and hence are hard
to mix otherwise. As we go down a tree structure, the cross-sectional area of the
flow path decreases. This has to be calculated carefully; optimization helps and also
points what is optimal under what conditions [40].
Hierarchy in structural design is much older and dates back to at least Gustave
Eiffel [41, 42]. Eiffel exploited structural hierarchy by making his designs optimally
porous. That is, he used beam segments crisscrossing with another rather than using
a solid piece. If we examine the Eiffel tower, we see cross-beams with smaller
cross-beams inside them. It resembles fractal-like design. While Eiffel took it to
three levels of hierarchy in the famous tower in Paris, Nature has exploited it up
to five levels [41]. Trabecular bone is made of collagen molecules making fibrils,
fibrils combining to become fiber, fibers forming lamella, and lamella leading to
cancellous bone. All five size scales have their own unique design unlike Eiffel’s