3.155j/6.152j lecture 20 fluids lab testing...fluids lab report follow the letters format purpose:...
TRANSCRIPT
3.155J/6.152J Lecture 20: Fluids Lab Testing
Prof. Martin A. SchmidtMassachusetts Institute of Technology
11/23/2005
Outline
� Review of the Process and Testing � Fluidics
� Solution of Navier-Stokes Equation � Solution of Diffusion Problem
� Lab Report Guidance � References
� Senturia, Microsystems Design, Kluwer � 6.021 Web Site on Microfluidics Lab � Plummer, Chapter 7, p.382-384
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 2
Process Flow - Overview
Si Unexposed SU-8 (100 µm) Surface treatment &
casting PDMS
photolithography
UV light
Si
mask Si
PDMS
removing elastomer from master
development
Si “master”
Our process was changed
here
PDMS
tubing
seal against glass after plasma treatment and insert tubing
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 3
The Mixer
Width = 250µm, 500 µm Depth = 100 µm Inlet Length = 25 mm Outlet Length = 35 mm
Images: Prof. D. Freeman
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 4
Courtesy of Dennis Freeman.
Courtesy of Dennis Freeman.
Packaging/Testing
Images: Prof. D. Freeman Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 5
Courtesy of Dennis Freeman.Courtesy of Dennis Freeman.
Experiment
� Gravity feed of fluids � Requires ‘priming’ of channel
� Particles for velocity measurement � We will attempt this
� Dye for diffusion experiments � Measurements
� Particle velocity
� Diffusion
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 6
Navier-Stokes
� The Navier-Stokes equation for incompressible flow:
� U = velocity
� P* = pressure (minus gravity body force)� ρm = fluid density (103 kg/m3 for water)� η = viscosity (10-3 Pa-s for water)
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 7
Poiseuille Flow
� Assume width (w) >> height (h)� Neglect entrance effects (L >> h)
h
w
L
y
x
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 8
Simplify to our problem
� No time dependence � d/dt = 0
� Flow is constant in x-direction (and 0 in z) � U = f(y)
� Pressure is only a function of x � A linear pressure drop
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 9
Poiseuille Flow
� ‘No-Slip’ Boundary conditions � Ux(y=0) = 0 � Ux(y=h) = 0
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 10
τw
τw
High P Low P
h
y
Umax
Ux
ILLUSTRATING POISEUILLE FLOW
Figure by MIT OCW.
Solution
� Solution is a quadratic polynomial � Ux = a + by + cy2
� Using boundary conditions and substitution
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 11
Parabolic Flow Profile
� Maximum velocity
� Flow rate
� Average velocity
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 12
τw
τw
High P Low P
h
y
Umax
Ux
ILLUSTRATING POISEUILLE FLOW
Figure by MIT OCW.
Pressure drop over length
∆P = ρgH
H = height of waterg = gravity
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 13 Courtesy of Dennis Freeman.
Flow Issues
� Edge effects� Flow rate
� Particle location in channel � Dimensions � Merging of channels
� How to model
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 14
Courtesy of Dennis Freeman.
The Mixer – Mixing by diffusion
Width = 250µm, 500 µm Depth = 100 µm Inlet Length = 25 mm Outlet Length = 35 mm
Images: Prof. D. Freeman
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 15
Courtesy of Dennis Freeman.
Courtesy of Dennis Freeman.
Diffusion Image Sequence
Think of this axis as length or time
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 16
Imaging System Output
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 17
Diffusion
� Same problem as diffusion in an epi layer � As in the case of the design problem
n+
Dopant Concentration
- silicon
n - epi
Solution in Plummer, Chapter 7, p.382Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 18
Solution
� Initial Conditions
� Identical to Infinite Source Problem:
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 19
C
0x
Initial Profile
Diffused Profile
Figure by MIT OCW.
Reference: Plummer, J., M. Deal, and P. Griffin. Silicon VLSI Technology: Fundamentals, Practice, and Modeling. Upper Saddle River, NJ: Prentice Hall, 2000. ISBN: 0130850373.
An ‘Intuitive’ way to look at it…
� Think of the uniform concentration as a sum of dopant ‘pulses’
� Each ‘pulse’ has a Gaussian diffusion profile � Dose = C ∆x
� Apply superposition since diffusion is linear
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 20
Refer to Plummer, J., M. Deal, and P. Griffin. Silicon VLSI Technology: Fundamentals, Practice, and Modeling. Upper Saddle River, NJ: Prentice Hall, 2000. ISBN: 0130850373.
Figure removed for copyright reasons.
Solution
� Taking the limit of ∆x
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 21
Solution
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 22
Error Function Solution
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 23
Refer to Plummer, J., M. Deal, and P. Griffin. Silicon VLSI Technology: Fundamentals, Practice, and Modeling. Upper Saddle River, NJ: Prentice Hall, 2000. ISBN: 0130850373.
Figure removed for copyright reasons.
Diffusion Issues
� Fitting ideal curve to measured profiles � Scaling time to position � Choice of velocity � Non-ideal flow profiles
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 24
Fluids Lab Report
� Follow the Letters format � Purpose: Characterization of a Liquid
Micromixer� Report Flow Velocity� Compare to calculated
� Estimate errors � Extract an effective diffusion coefficient
� Utilize ‘best estimate’ for flow velocity � Compare to expected (D ~ 2x10-6 cm2/s)
� Identify relevant non-idealities
Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 20 – Slide 25