Beyond Microfluidics: Measuring Nanoscale Fluid Dynamics

Christopher LimbachUniversity of Arizona Physics

Department

Overview

• Motivation• Atomic Force Microscopy• Samples and Equipment• Fluid Mechanics• Experimental Results– Convolution Effects– Pipes vs. Screens

• Future Research and Applications

Motivation• Development of AFM as a microflow probe • Applications– Porous media characterization– Microfiltration

• Study of non-continuum behavior• Biology

Microfluidic gene sorterwww.sinc.stonybrook.edu

Bacterial flagellumhttp://coris.noaa.gov/

Atomic Force Microscopy

nano.tm.agilent.com www.llnl.gov

Samples and Equipment

Large Single Pipe Small Pipe Array Screen50μm scan 50μm scan 20μm scan 10μm scan

20 μm Hole Micro-channel Plate Track-Etch Membrane Lacey Carbon Film

Expectations(Continuum Fluid Mechanics)

Screen Pipe

Fox, McDonald & Pritchard

“Poiseuille Flow Profile” (parabolic shape)

“No-Slip” Condition

Expectations(Molecular Flows)

• Rarified flows can be parameterized by the Knudsen number, Kn=λ/L

λ=mean free path

• No-slip condition breaks down

Pipe Flow Profiles

Experimental Setup

Sample

Single 20μm Hole

100μm x 100μm non-contact AFM image.

100μm x 100μm simulated imageof cantilever/flow convolution.

Hole Array Image Data(Track Etch Membrane)

10 μm contact image Without airflow

High imaging force

10 μm contact imageWith airflow

High imaging force

10 μm non-contact imageWith airflow

Low imaging force

Flow Profiles

Is this a velocity profile? What happened to convolution effects?

Hei

ght [

nm]

x [microns]

10 μm contact imageWith airflow

Poiseuille Flow?(Parabolic Profiles?)

1. Convolution effects decrease at small scales

Poiseuille Flow?(Parabolic Profiles?)

2. All observed profiles are parabolic

-profile vertices aligned-data rescaled

Data re-scaling y = ax2

x’ = xa-1/2

y = x’2

Overlay of 14 non-contact flow profiles

Poiseuille Flow?(Parabolic Profiles?)

• Convolution with an idealized cantilever tip can reproduce parabolic flow profiles.

Flow Through ScreensNo airflow Airflow

Conclusions and Future Efforts

• Micro-fluidic measurements are possible with the Atomic Force Microscope.

• Approaching direct profile measurement in Knudsen flow regime.– Mean free path ~ 0.1μm (room temperature)– Both continuum and Knudsen profiles are parabolic

• Higher Knudsen number needed– Experimental challenges

Acknowledgements

• Dr. Srinivas Manne• Elaine Ulrich

Resonant Frequency Shifts

• Resonance shifts can detect the presence of different gases.

Gas Air Nitrogen Helium

Freq. [kHz] (±0.01)

308.62 308.65 309.19

Damped Harmonic Motionω’=(ω0

2-(b/2m)2)1/2

(Halliday and Resnick)

Contact Flow Profile Data