1. Class 2 Principles of Microfluid Mechanics
Jack Merrin
Institute of Science and Technology Austria
May 8, 2017

2. What is microfluidics?
Consequences of miniaturization of fluids in physics, mathematical physics, chemistry, biology, and engineering
Physics – Description of flow through micro pipes, effects of viscosity, diffusion, heat transfer, simulations of velocity fields
Chemistry – Mini chemical reactions, catalysis, single molecule
Biology – Manipulation of single cells, environment of cells, assays, screening, physical limitations of living matter
Engineering – Automation, parallelization, elimination of pipetting, lab on a chip, microfabrication of devices that solve science problems
Approach of Course: Start with basic engineering and physics then apply what we know to biology and biochemistry

3. Engineering Point of View
A channel with an inlet and an outlet is the simplest microfluidic device. Most devices are some variation of this, with more channels and more ports.
We will build up to understanding the flow through a circular pipe while it is actually easy to make rectangular pipes
In future classes, we will discuss various methods to produce master molds depending on the length scale you are trying to construct at.

4. Experimental Physics Point of View
Linear Phenomenon
Time Independent
Laminar
Nonlinear
Turbulent
Complicated Time
Dependence

5. Theoretical Physics Point of View
Navier-Stokes Equation – Everything you want to describe fluids
Nonlinear equation – velocity repeats twice in one term
Describes time dependent spatial flows like turbulence
Great unsolved problem of classical physics – Millennium Prize
PHYSICS GOAL – Understand all symbols in the NS equation and resulting simplifications for microfluidics
What you really need to know for microfluidics is much easier

6. Non calculus symbols Density Pressure
Viscosity – Fluids that drag and dissipate energy like honey
Velocity of the fluid at each point

7. Differential Calculus
Regular Derivative
Partial Derivatives
Chain Rule for Composition of Multiple Variable Functions

8. Vector Calculus – Understanding the Symbols
A vector has a magnitude and direction
Dot product
Del operator and Gradient
Chain Rule
Laplacian

9. Viscosity Newton defined dynamic viscosity as Kinematic viscosity
You can hear viscosity, cold or boiling water pouring
Velocity is zero on the boundaries

10. Comparison of NS with Newton’s Law
Newton’s Second Law
Transition to liquids uses density not particles
Liquids are incompressible
Just add the other types of forces, pressure, viscous forces or external

11. Reynolds Number by Dimensional Analysis
Inertial Forces
Pressure, viscous, and external forces
If Re is small then the terms
on the left are negligible. Ratio of inertial to viscous forces.
Removes the time dependence
Turbulence not possible
Result is called laminar flow
L is the conventional length scale
V is the average velocity
Also depends on density and viscosity

12. Scaling Laws
Work with models
in a wind tunnel

13. Now We Can Solve the Microflow Through a Pipe!
Integrate twice and apply the boundary conditions

14. Flow rate through the pipe
Hagen-Poiseuille Flow at
Low Reynolds Number
Working this out for a rectangular
channel is much more complicated,
but qualitatively similar

15. Electronics Analogy Microfluidic Resistance
Electrical Resistance of a wire
Channels in Series
Channels in Parallel
Capacitance
Example Microballoon

16. Resistance in series can be effectively the smallest constriction

17. Taylor Dispersion and Qualitative Limitations of Laminar Pipe Flow
If you reverse the flow the green dye goes back and spreads to the left

18. Plug Flow

19. Diffusion of chemicals and heat in fluids
Mixing in microfluidics occurs primarily by diffusion
Transporting temperature is analogous to diffusion
Brownian motion and random walks

20. Gradient by flow or diffusion

21. Chaotic Micromixer

22. Hydrodynamic Focusing

23. Christmas Tree Device

24. H Filter

25. Surface Tension

26. Contact Angle

27. Capillary Action

28. Hydrophobic and Hydrophilic Inside Channel

29. Spin Coating General formula for an ideal fluid
Power laws for photoresist that evaporates

30. Effect of Pressure on Protein Function
At the bottom of the ocean P = 110 MPa
High pressure tends to force water into hydrophobic core of proteins
Life at the bottom of the ocean near thermal vents is adapted to high pressures and high temperatures

31. Experimental setup for temperature-regulated fluorescence anisotropy measurements at high pressures.
Jack Merrin et al. PNAS 2011;108:
©2011 by National Academy of Sciences

32. Fluorescence Anisotropy of RecA with ssDNA
Thermus thermophilus
E. coli

33. Effect of temperature on RecA DNA binding
Denaturation
Aggregation
Without RecA

34. Effect of T and P on RecA function

35. Theoretical Fit
Hyperbola or
Ellipse

36. E. coli vs T. thermophillus
Bottom
Ocean P