1. Beyond Microfluidics: Measuring Nanoscale Fluid Dynamics Christopher Limbach University of Arizona Physics Department

2. Overview Motivation Atomic Force Microscopy Samples and Equipment Fluid Mechanics Experimental Results – Convolution Effects – Pipes vs. Screens Future Research and Applications

3. Motivation Development of AFM as a microflow probe Applications – Porous media characterization – Microfiltration Study of non-continuum behavior Biology Microfluidic gene sorter www.sinc.stonybrook.edu Bacterial flagellum http://coris.noaa.gov/

4. Atomic Force Microscopy nano.tm.agilent.com www.llnl.gov

5. Samples and Equipment Large Single Pipe Small Pipe Array Screen 50μm scan 50μm scan 20μm scan 10μm scan 20 μm Hole Micro-channel Plate Track-Etch MembraneLacey Carbon Film

6. Expectations (Continuum Fluid Mechanics) ScreenPipe Fox, McDonald & Pritchard “Poiseuille Flow Profile” (parabolic shape) “No-Slip” Condition

7. 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

8. Experimental Setup Sample

9. Single 20μm Hole 100μm x 100μm non-contact AFM image. 100μm x 100μm simulated image of cantilever/flow convolution.

10. Hole Array Image Data (Track Etch Membrane) 10 μm contact image Without airflow High imaging force 10 μm contact image With airflow High imaging force 10 μm non-contact image With airflow Low imaging force

11. Flow Profiles Is this a velocity profile? What happened to convolution effects? Height [nm] x [microns] 10 μm contact image With airflow

12. Poiseuille Flow? (Parabolic Profiles?) 1. Convolution effects decrease at small scales

13. Poiseuille Flow? (Parabolic Profiles?) 2. All observed profiles are parabolic -profile vertices aligned -data rescaled Data re-scaling y = ax 2 x’ = xa -1/2 y = x’ 2 Overlay of 14 non-contact flow profiles

14. Poiseuille Flow? (Parabolic Profiles?) Convolution with an idealized cantilever tip can reproduce parabolic flow profiles.

15. Flow Through Screens No airflow Airflow

16. 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

17. Acknowledgements Dr. Srinivas Manne Elaine Ulrich

18. Resonant Frequency Shifts Resonance shifts can detect the presence of different gases. GasAirNitrogenHelium Freq. [kHz] (±0.01) 308.62308.65309.19 Damped Harmonic Motion ω’=(ω 0 2 -(b/2m) 2 ) 1/2 (Halliday and Resnick)

19. Contact Flow Profile Data