2-1. Advantageous features of microfluidic devices in BioMEMS applications

Equations: To solve the flow velocity profile for a fluid that is incompressible, Newtonian, isotropic, with viscosity that does not depend on temperature. Arbitrary constant cross section (flow in x-direction):

Circular constant cross section

2-2. Flow speed profile for a rectangular channel

Microchannel resistance

For a rectangular microchannel:

High aspect ratio rectangular microchannel:

For a circular microchannel (pipe):

Hagen-Poiseuille Equation (1838)

Shear stress

Tensor:

For a Newtonian fluid:

For rectilinear flow (along x axis):

Force acting on bottom surface (x-z):

The force acts along x

z

y

x

ux

Fx

For a rectangular channel:

Taking the derivative and rearranging:

Force acting on the bottom surface of a rectangular microchannel

Flow through porous media

Darcy’s Law (1855)

2-3. The complementary error function

Ci

t D

2Ci

x 2Ficke’s 2nd Law of Diffusion

Ficke’s 1st Law of Diffusion

Ji DCi

x

D kT

6RH

Stokes-Einstein relationship

x 2 2Dt

2-4. Forces at contact point

2-5. The role of surface charges in electroosmosis

2-6. Positive and negative dielectrophoresis

)()(

2Re2

23rEF

mp

mp

m R

2-7. Electrowetting

2-8. Acoustophoresis

2-9. The phenomenon of acoustic streaming

The building materials

The “historical” materials: Silicon and glass

The advent of plastics

A new kid on the block: PDMS

Other polymers: Mylar, biodegradable polymers

Hydrogel devices

Paper

2-D stacking and bonding

Inlets: the “Macro-to-Micro Interface” problem

Microchannel wall coatings

Fabrication of microfluidic channels

2-10. “Shrinky-Dinks” Microfluidics

2-11. Biodegradable microfluidics

2-12. Paper microfluidics

2-12. Cell-seeded ECM-hydrogel microchannels

2-13. Alginate microfluidics

2-14. Fabrication of biocompatible PEG hydrogel microchannels

2-15. Paper microfluidics

2-16. Laminar flow patterns created in laser-cut paper microchannels

2-17. Microfluidics outreach

2-18. Fabrication of complex multilevel microfluidics

2-19. Alignment of microfabricated parts

2-20. Nano-adhesive plasma-deposited coatings

2-21. Room-temperature bonding of PDMS to plastics using silanes

2-22. Modular microfluidics

2-23. 96-well plate incorporating embedded microchannels

2-24. Vacuum manifold for world-to-chip interface

2-25. A chip-to-chip nanoliter dispenser

2-26. Grafting of PDMS channels

2-27. Spontaneous migration of Pluronic to the PDMS surface.

2-28. Measuring flow rate with bending fiber

2-29. Common setup for manipulation of droplets by electrowetting

2-30. Generation of droplets in microchannels.

2-31. High-throughput droplet microfluidics

2-32. Microvalve-actuated control of individual droplets

2-33. Microdroplets separated by air carrier

2-34. Pressure and response times typical of actuators used in microvalves and micropumps

2-35. Electrokinetic valving

2-36. Flow “Field-Effect Transistor”

2-37. Microvalving strategies used in centrifugal microfluidics

2-38. Flap microvalve

2-39. PDMS pinch microvalves by Quake

2-40. PDMS “doormat” microvalves

2-41. Metering of nanoliter volumes with PDMS “doormat” microvalves

2-42. PDMS microvalves implemented in the sidewall

2-43. PDMS “curtain” microvalves

2-44. PDMS “plunger” microvalve

2-45. Latching microvalves

2-46. Microvalve based on thermal expansion of PEG

2-47. Braille-actuated microvalves

2-48. Smart-polymer microvalves

2-49. Sacrificial membranes for single-use microvalves

2-50. Capillary burst microvalve

2-51. Tangential microchannels for switching flows

2-52. The SlipChip

2-53. Microfluidic resistors using inflatable elements

2-54. Microfluidic resistors using microvalves

2-55. Binary multiplexer with “anti-contamination” layout

2-56. Combinatorial operation of a binary multiplexer

2-57. Combinatorial multiplexer

2-58. Multiplexer with quaternary valves

2-59. Capillary pump

2-60. Surface tension-driven passive micropump

2-61. A PDMS vacuum pump

2-62. Gas permeation micropump

2-63. Peristaltic micropumps constructed with “doormat” PDMS microvalves

2-64. PDMS peristaltic micropump featuring circularly-symmetric microvalves

2-65. Serpentine-channel micropumps

2-66. Compact PDMS peristaltic pump actuated by a single pneumatic channel

2-67. Micropump powered by a piezoelectric actuator

2-68. Microfluidic flow gauge fabricated by stop-flow lithography

2-69. Microfluidic flow comparator

2-70. The “Butterfly effect”

2-71. The Dertinger gradient generator

2-72. “Universal” gradient generator

2-73. Microfluidic gradient generators for arbitrary gradients using electrical-circuit analogs

2-74. Dilution generator based on ratiometric distribution of flow resistance

2-75. Gradient generator based on transport through microtunnels

2-76. Linear dilution-generator microfluidic device

2-77. Stacked-flow gradient generator

2-78. Gradient generator using microfluidic “jets”

2-79. Microjets in a closed microchamber

2-80. A diffusive gradient generator using microjets

2-81. Microfluidic pen

2-82. Local delivery of fluids onto cells using a two-phase system

2-83. Gradient generator based on diffusion through nitrocellulose paper

2-84. Gradient generator based on transport through a thin polyester membrane

2-85. Gradient generator made in agarose

2-86. Gradient generator based on diffusion across a hydrogel slab

2-87. Agarose-filled microchannels as gradient generators

2-88. ECM gel-filled microchannels as gradient generators

2-89. Gradient generator incorporating collagen gels as diffusional barriers

2-90. Combinatorial micromixer

2-91. Homogeneization by pulsatile flow

2-92. Shear superposition micromixer

2-93. Microfluidic homogeneizer with complex 3D architecture

2-94. Folded-over serpentine mixer

2-95. A passive micromixer that induces fluid rotation.

2-96. Microfluidic homogeneizer with 3D “F” splitter-recombiners

2-97. A criss-crossing 3D micromixer

2-98. Microfluidic homogeneizer based on Tesla mixer

2-99. Homogeneization directed by surface topology

2-100. Homogeneizer enhanced by a circulation-disturbance barrier

2-101. Homogeneization induced by surface charge patterns

2-102. Bubble-based on-off millisecond homogeneizer

2-103. Automated combinatorial mixer based on microvalves

2-104. Metering of nanoliter-scale volumes in a micromixer using microvalves

2-105. Dynamic micromixer with tunable microtopographies

2-106. On/Off Chaotic Micromixer

2-107. Spatiotemporal mixing using an On/Off chaotic micromixer

2-108. Microstructured membranes and microvalves for trapping fluids and for substrate patterning

2-109. Vortex-type micromixer

2-90. Cells under laminar flow