Micrometer and Nanometer Spatial Resolution with µpiv

Transcription

1 Micrometer and Nanometer Spatial Resolution with µpiv Steve Wereley Associate Professor of Mechanical Engineering Birck Nanotechnology Center Purdue University (USA)

2 Experiments in Fluids Top 1* *according to Web of Science on Sept 23, Title: DIGITAL PARTICLE IMAGE VELOCIMETRY Author(s): WILLERT CE, GHARIB M Source: EXPERIMENTS IN FLUIDS 1 (4): Cited References: 27 Times Cited: Title: A particle image velocimetry system for microfluidics Author(s): Santiago JG, Wereley ST, Meinhart CD, Beebe DJ, Adrian RJ Source: EXPERIMENTS IN FLUIDS 25 (4): SEP 1998 Cited References: 1 Times Cited: Title: PIV measurements of a microchannel flow Author(s): Meinhart CD, Wereley ST, Santiago JG Source: EXPERIMENTS IN FLUIDS 27 (5): OCT 1999 Cited References: 1 Times Cited: Title: The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings Author(s): Westerweel J, Dabiri D, Gharib M Source: EXPERIMENTS IN FLUIDS 23 (1): 2-28 MAY 1997 Cited References: 11 Times Cited: Title: EFFECT OF RESOLUTION ON THE SPEED AND ACCURACY OF PARTICLE IMAGE VELOCIMETRY INTERROGATION Author(s): PRASAD AK, ADRIAN RJ, LANDRETH CC, OFFUTT PW Source: EXPERIMENTS IN FLUIDS 13 (2-3): JUN 1992 Cited References: 9 Times Cited: Title: Low cost, high resolution DPIV for measurement of turbulent fluid flow Author(s): Fincham AM, Spedding GR Source: EXPERIMENTS IN FLUIDS 23 (6): DEC 1997 Cited References: 31 Times Cited: Title: STEREOSCOPIC PARTICLE IMAGE VELOCIMETRY APPLIED TO LIQUID FLOWS Author(s): PRASAD AK, ADRIAN RJ Source: EXPERIMENTS IN FLUIDS 15 (1): 49-6 JUN 1993 Cited References: 15 Times Cited: Title: Iterative multigrid approach in PIV image processing with discrete window offset Author(s): SCARANO F, RIETHMULLER ML Source: EXPERIMENTS IN FLUIDS 26 (6): Cited References: 22 Times Cited: 135

3 Papers Citing Santiago (1998) or Meinhart (1999) Figure 1 from Wereley and Meinhart, Annual Reviews of Fluid Mechanics, 21 (Web of Science data as of November 28).

4 Micro Particle Image Velocimetry (μpiv) Santiago, Wereley, Meinhart, Beebe, Adrian, Exp. Fluids, 1998 US Patents 6,653,651 and 7,57,198--Licensed to TSI, Inc. MCROFLUIDIC DEVICE Micro Device CCD CAMERA Flow in Flow out MICROSCOPE BEAM EXPANDER Nd:YAG LASER Micro-Fluidics Lab Purdue University Micro-PIV Measurement Nd:YAG Laser Focal Plane Beam Expander λ=532 nm Micro-PIV image pair λ = 61 nm Flood Illumination Microscope Epi-fluorescent Prism / Filter Cube Glass cover CCD Camera (128x124 pixels)

5 Differences between μpiv and conventional PIV Brownian motion of nm-scale tracers ε B = s 2 1/ 2 Δx = 1 u 2D Δ t where D = κt 3πμd p Typically minimal optical access Volume illumination and wavelength filtering low particle concentrations Miniscule signal reflected from tracer particles Rayleigh scattering range (d p λ) A 1 nm particle scatters 1 6 times more light than a 1 nm particle

6 Where we started Santiago, Wereley, Meinhart, Beebee, and Adrian, A particle image velocimetry system for microfluidics, Exp. Fluids, 1998

7 Correlation Analysis for μpiv (steady flow) AB ( ) ( ) ( ) R s AX B X s dx = Three techniques involve the same operations 1. Acquire image fields ensemble average 2. Correlate image fields ensemble average 3. Determining velocity vector from peak in correlation ensemble average Operations (2) and (3) are nonlinear and don t commute.

8 Correlation of Ensemble-Averaged Image Fields Image Sequence Image A (t = t ) Image B (t = t Δt ) Correlation R AB Peak Search 1 A 1 B 1 2 A 2 B 2 3 A 3 B 3 N A N B N (Ensemble Ave.) < A > < B > R < <A> R A <B> B >

9 Ensemble-Averaged Velocity Fields Image Sequence Image A (t = t ) Image B (t = t Δt ) Correlation R AB Peak Search A 1 B 1 A 2 B 2 A 3 B 3 R A 1B1 R A 2B2 R A 3B3 N A N B N R A N BN (Ensemble Ave.)

10 Ensemble-Averaged Correlation Function Image Sequence Image A (t = t ) Image B (t = t Δt ) Correlation R AB Peak Search 1 A 1 B 1 R A 1B1 2 3 A 2 B 2 A 3 B 3 R A 2B2 R A 3B3 N A N B N R A N BN (Ensemble Ave.) < R A B >

11 Ensemble-Averaged Particle-Image Correlation Functions 3 x 1 4 R A1 B 1 R A2 B 2 R A3 B x x R AN B N <R AB > x

12 Performance of 3 correlation methods Meinhart, et al., JFE, 2 Valid measurement is one which differs by less than 1% from the long-time averaged and smoothed vector field

13 Assessing Accuracy of μpiv Measure a Known Flow Top View V(y,z) z x 3 μm Measurement Area y x Side View 3 μm V(y,z)

14 Microchannel Flow (x-z plane) wall-normal spatial resolution < 1um 3 1 mm/s Spanwise Position (μm) (µm) Streamwise Position (µm)

15 Streamwise Profile (x-z plane) C.D. Meinhart, S.T. Wereley, and J.G. Santiago, PIV Measurements of a Microchannel Flow, Exp. Fluids, Vol. 27, No. 5, , (1999). 8 p (µ ) Spanwise Position (μm) z Velocity (mm/s) 2% FS error

16 Tracer Particle Diffusion Based on Brownian motion of tracers broadening correlation peak Einstein (195) developed formula for diffusion coefficient 2 s = 2DΔt where kt D = 3πμ d p 2 2Δtk T s = 3πd μ T p ( ) No Diffusion Diffusion (autocorrelation) (cross correlation)

17 Particle Imaging Fundamentals Adrian and Yao, 1983; Olsen and Adrian, 2 Calculate the particle image size d e in the object plane: For light sheet PIV: e = p s d M d d where M is magnification, d p is particle diameter, and d s is spot size of imaging system For volume illumination (micro-piv): e = p s z d M d d d d z = zmda x z ( )

18 Relating Temperature to Peak Area Change Olsen and Adrian, Δ s = de 8M β DΔt β where β 2 = 3.67 is fit parameter for matching Gaussian to Airy function π ( 2 2 ) 2 2 Δ A= Δs, c Δ s, a = 2πM β DΔt 4 where Δs autocorrelation peak diameter ( Δt=), a and Δs, c is the cross-correlation peak diameter T 3d p ΔA =Δ A = C ( ) 2 μ T 2M kδt Δt

19 T μ ( T) Temperature Measurement Results 3d p =Δ A = C 2 2M kδt Measure correlation peak areas at e -1 level Use calibration to get constant of proportionality Original result within ±3º C over significant temp range (2-5 C) Recent results approx ±1.5º C over larger range (2-8 C) ΔA Δt PIV Temp. [C] Thermocouple Temp. [C] Hohreiter, Chung, Olsen, Wereley, MST 22 Chamarthy, Garimella, Wereley, Exp. Fluids 29

20 Assess hydrodynamic size of particle Gorti, Shang, Wereley and Lee, Langmuir, 28 Kumar, Gorti, Shang, Lee, Yip, and Wereley, J. Fluids Eng, 28 Use as biodetector for any number of substances Linear for small number of analytes per particle Sensitivity of about 1 virus per particle Frictional Resistance (x1-9 Ns/m) ξ =.275n R 2 = nm particle with 1 M13 viruses attached Purdue Microfluidics Laboratory Number 25 Years of of viruses PIV, DLR per particle Göttingen, 29

21 Single Pixel Evaluation (SPE) Westerweel, Geelhoed, Lindken, 24 With modern cameras and computers we can increase the sample number almost without bound We can decrease the correlation region size to its smallest possible value->one pixel k tot k q p tot ( i(, i, j; jm; mn, n, )) f ( i, j) f ( gi,( ji) gm(, ij mn, ) j n) Φ = spavg spe k k k k kk= 1 j= 1 i= 1

22 Some Results (Westerweel, et al.) Infinitely thin shear layer (simulated) Flow in a nearly rectangular channel (experimental) Spatial resolution reported smaller than d p

23 Beating the Diffraction Limit Experimental Parameters Optics M = 2x, NA =.4, λ ~.5 um Particle size d p =.5 um Pixel size d pix ~ 3 nm Diffraction spot size d diff ~ 1.3 um Working well below the diffraction limit! Ultimate limit, M=1x, pixel size ~ 6 nm Wereley and Meinhart, 25

24 What have I left out? Nearly everything short talk In recent years we ve seen developed: 3D systems 3 hole mask Diffraction pattern Stereo Astigmatism-based Time-resolved systems Evanescent wave PIV Confocal PIV Important work on theory of µpiv: Depth of correlation Particle visibility And I m still leaving a ton out