chapter 9: Scaling, Actuators and Power in Miniaturized Systems

9.1 Explain in detail scaling laws for flying and swimming.

9.2 Explain the DC breakdown voltage versus electrode distance curve and how it is relevant to dry etching. How is miniaturization of an electrode set equivalent to creating a local vacuum?

9.3 Demonstrate that d/d_T ~ Pr ^1/2

9.4 How does velocity scale with size (ignore drag/damping)? (A short 2 or 3 equation answer—the solution may be surprising.)

9.5 A simple and accurate viscometer can be made from a length of capillary tubing.  If the flow rate and pressure drop are measured, and the tube geometry is known, the viscosity can be computed.  A test of a certain liquid in a capillary viscometer gave the following data:

•        flow rate:                           880 mm³/s

•        tube diameter                    500 mm

•        tube length:                       1 m

•        pressure drop                    1.0 MPa

Determine viscosity of the liquid.

9.6 The accepted transition Reynolds number for flow in a circular pipe is Re ≈ 2300.  For flow through a 6 cm diameter pipe, at what velocity will this occur at 20°C for (a) airflow and (b) water flow?

9.7 Piezoelectric materials produce _______when they are deformed by a force. Silicon [] is or [] is not piezoelectric. Viscosity of a fluid is the tendency of the fluid to resist _____. Large field strength can be used to produce large ______ with smaller _____. __________________ is the major loss mechanism in microactuators. Shape memory alloys recover the shape they are given when they are heated to a temperature that is higher than the _____________________.

9.8 Scaling laws

Mass scales with a factor of _________

Stress scales with a factor of _________

Natural frequency scales with a factor of ______

Viscous damping scales with a factor of _______

 Coulomb damping scales with a factor of _______

Elastic coulomb damping scales with a factor of ____

Surface adhesion scales with a factor of _______

Power scales with a factor of_____________

9.9 What is the primary assumption of continuum mechanics? Give examples where continuum theory breaks down and how MEMS, in some cases, may take advantage of this breakdown.

9.10 You want to model flow of blood through a 100X50 mm² micro channel in Si.  The channel was formed by bulk KOH etching resulting in a trapezoidal profile.  For the lack of a better "simple" theory, you use Navier-Stokes equations. List 4 assumptions that introduce potential errors when modeling flows through such a channel?  Why?

9.11 What conclusions can one draw regarding flows on the microscale from the currently available microscale flow data in the literature? When does turbulence occur on the macroscale?  Microscale? How could you achieve good mixing of two chemicals in a micro reactor?

9.12 In the miniaturization of analytical instruments, scaling laws and breakdown of scaling laws often determine whether miniaturization will favor sensitivity or not. What will happen to the sensitivity of the following techniques upon miniaturization: (a) the optical path in UV spectrometer; (b) a potentiometric sensor (e.g., a pH sensor); (c) an amperometric sensor (e.g., an oxygen gas sensor); (d) the column in a GC.

9.13 If you miniaturize an absorption-based optical analytical instrument and one based on luminescence, which one scales down more favorably? Explain why.

9.14 List all the electrokinetic effects taken advantage of in the MEMS field and list one application for each approach.

9.15 If a 100 bp long DNA is to be sequenced in a microfabricated channel, calculate the length of a channel needed to get single base pair separation. What voltage (E field) would you pick to perform the separation in a polyacrylamide gel. Make the necessary assumptions! The width and height of the channel is 20µm X 20µm

Professor Rashid Bashir, Purdue University

9.16 List 7 different methods to propel fluids through micro channels. Rank the methods according to their desirability in terms of scaling, power, manufacturing ease, and cost.

9.17 Why is there a lower limit to the size of an uncharged particle one can move with dielectrophoresis (~ 14 nm) and not on the size of a charged particle one can move in electrophoresis? What types of particles (size and charge) can one move with electro-osmosis?

9.18 What is electronic stringency? Discuss two types of DNA amplification means? Example 9.3 illustrates the breakdown of continuum theory, explain why? How could one take advantage of the same effect in other applications?

9.19 What is GMR? Where is it being used?

9.20 What MEMS power would you put into a micro robot? A micro rocket? A micro submarine? A micro butterfly?

9.21 Complete similarity between a ship model and a full-sized ship requires the same Reynolds and Froude numbers. Suppose that

Re = rVL/µ= 11X10⁸ and Fr^-1 = gL/V² = 33.25.

Assuming a model 1/100 the size of the ship, can you design an experiment having full similarity?

9.22 Compare/contrast how separation is achieved in chromatography and electrophoresis.

9.23 Why are more theoretical plates achievable in capillary electrophoresis than in the following separation techniques.

(a) Slab electrophoresis

(b) Liquid chromatography