Hi Chantelle,

You have a very interesting request, and although I am not an active
participant in this group, I am touched by your generosity to work abroad
and felt compelled to respond.

Let me attempt to put scaling issues in context.  Consider that an ant can
easily carry many times its weight, consider that flies can stick to walls
without falling, consider that water which flows very easily in rivers acts
like molasses in microchannels... these are all issues related to
dimensional scaling.  In other words, physical characteristics in the
microscale, i.e. the MEMS world, do not always parallel the expected
behavior of proportionally-sized devices in the human-sized world.

Consider a silicon beam supporting its own weight.  This beam will have a
"stiffness" proportional to w*t^3*L^4 with its load is proportional to
w*t*L, where w is the beam width, t is the beam thickness in the direction
of gravity, and L is the length.  Dividing load (F) by stiffness (k) gives
beam deformation (x), i.e. F/k = x.  You find that deformation is
proportional to 1/(t^2*L^3).  So if we scale all dimensions by a factor
1e-2, i.e. one-hundredth, keeping the material properties of the beam
constant, the deformation is reduced by 1/(100^5), which is 1e-10, not
1e-2!

In the study of fluid dynamics non-dimensional analysis is used to avoid
confusion during geometric scaling.  Non-dimensional analysis is fairly
general and can be applied to many other fields as well.  I do not have a
reference for you on non-dimensional analysis, but if you search on the
internet, I am sure you will find many hits.

So unfortunately, I do not have a three-sentence definition, but, perhaps,
based on my description and those of other respondents, you can tailor a
message appropriate for your audience.

Good luck,

Raj Gupta
Microcosm Technologies, Inc.
http://www.memcad.com



Chantelle Snyder wrote:
>
> Hello!
>     I am writing you this note in hopes that you are able to help me out
> a little.    My name is Chantelle Snyder and I am a Canadian currently
> teaching English at North China Institute of Technology (Taiyuan,
> Shanxi, China).  Some of my students have come to me requesting help in
> understanding their reading...so far I have been able to muddle my way
> through most of the technical jargon quite well, but one specific term
> still eludes me regarding the "Scaling Laws" of micromachined devices.
> I am completely unable to explain what "scaling laws" are or what they
> refer to.  I understand that the concept may be quite complex, but I was
> hoping that if someone had a moment that they could email me a short
> note with a brief explanation (3 sentence definition type of thing).
> English resources here are shockingly limited and I can't find an answer
> anywhere...so I turn to you for help.
>     Thank you in advance for any assistance you are able to give me.
> Thanks for your time and consideration...
>     Sincerely,
>     Chantelle Snyder
>     cplsnyder@263.net