Microfluidics and Nanofluidics

, Volume 17, Issue 2, pp 375–391 | Cite as

On the background design for microscale background-oriented schlieren measurements of microfluidic mixing

Research Paper

Abstract

Using microfluidic mixing as the benchmark, we assess the influences of the background designs in the accuracy of the microscale background-oriented schlieren measurements in this study. Three parameters are considered, they are as follows: pattern configuration (random dot, random grid, and grid), dot diameter, and area fraction of dot coverage. A photomask covered with the defined pattern is placed on top of the microchannel to serve as the background. When miscible fluids with different refractive indices are mixed in a T-microchannel, light deflects and there are pattern shifts on the acquired image. After a calibration process is carried out to obtain the relationship between the pattern shift and gradient of mass fraction, we are able to evaluate the performance of each background design based on its corresponding uncertainty. Except for the grid configuration, we find that the lowest error level is achieved with a dot diameter of 6 μm, which corresponds to a dot-image diameter of 2.8 pixels. Because a sparse distribution leads to vacant interrogation windows, the optimal random-dot design has the highest area fraction of 0.178 (0.196 for the design value). In contrast, the random-grid design with too many dots becomes comparable to the grid design and has difficulties during the cross-correlation analysis. As a result, the best random-grid background has an area fraction of 0.098. For the grid design, on the other hand, accurate results can be obtained when there is only one dot in each interrogation window. Hence, a dot diameter of 16 μm leads to the lowest uncertainty for the grid design. Once these backgrounds are optimized, we prove that all three configurations are able to deliver satisfactory results for the reconstruction of a concentration field in a T-microchannel and an instantaneous profile of concentration gradient in a microfluidic oscillator.

Keywords

Microscale background-oriented schlieren Optimization of pattern design Mixing Mass transport 

List of symbols

DI

Size of interrogation window, pixel

da

Effect of geometric lens aberrations on dot-image diameter dt, μm

dp

Diameter of dot pattern, μm

dr

Pixel size, μm pixel−1

ds

Diffraction-limited dot diameter, μm

dt

Dot-image diameter, μm

i

Index notion

M

Magnification

m

Number of dots in the 4 × 4 matrix

N

Number of data points

NA

Numerical aperture

NI

Average number of dots per interrogation window

Nx

Number of rows in the evaluation zone

Ny

Number of columns in the evaluation zone

n

Refractive index

Re

Reynolds number

w

Mass fraction of ethanol in water

x

Streamwise coordinate, μm

y

Cross-stream coordinate, μm

Δypx

Displacement of pattern on the image plane, pixel

z

Coordinate parallel to the optical axis of the μBOS system, μm

Δz

Thickness of inhomogeneous medium/microchannel depth, μm

ZD

Distance between dot pattern and region of refraction gradients, μm

Symbols

φ

Area fraction of dots

λ

Wavelength of incident light

σ

Uncertainty

Subscripts

air

Air

ref

Reference

opt

Optimal

i

Index notion

j

Index notion

min

Minimum

num

Numerical simulation

w

Mass fraction

y

Cross-stream coordinate

Δy

Image displacement in the y-direction

w/∂y

y-component of gradient of mass fraction

total

Total

References

  1. Adrian RJ (1984) Scattering particle characteristics and their effect on pulsed laser measurements of fluid flow: speckle velocimetry vs particle image velocimetry. Appl Opt 23:1690–1691CrossRefGoogle Scholar
  2. Adrian RJ (1986) Multi-point optical measurements of simultaneous vectors in unsteady flow—a review. Int J Heat Fluid Flow 7:127–145CrossRefGoogle Scholar
  3. Adrian RJ (1997) Dynamic ranges of velocity and spatial resolution of particle image velocimetry. Measurement Sci Technol 8:1393–1398CrossRefGoogle Scholar
  4. Adrian RJ, Westerweel J (2011) Particle image velocimetry. Cambridge University Press, New YorkGoogle Scholar
  5. Atcheson B, Heidrich W, Ihrke I (2009) An evaluation of optical flow algorithms for background oriented schlieren imaging. Exp Fluids 46:467–476CrossRefGoogle Scholar
  6. Aubin J, Ferrando M, Jiricny V (2010) Current methods for characterising mixing and flow in microchannels. Chem Eng Sci 65:2065–2093CrossRefGoogle Scholar
  7. Bencs P, Szilard SZ, Bordas R, Thevenin D, Zahringer K (2012) Influence of background pattern on the temperature field measured by background oriented schlieren. In: 15th International Symposium on Flow Visualization. Minsk, BelarusGoogle Scholar
  8. Celik IB, Ghia U, Roache PJ, Freitas CJ, Coleman H, Raad PE (2008) Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J Fluids Eng 130:078001CrossRefGoogle Scholar
  9. CFD-ACE + V2008 User Manual (2008) ESI CFD, Huntsville, ALGoogle Scholar
  10. Chan KLA, Gulati S, Edel JB, de Mello AJ, Kazarian SG (2009) Chemical imaging of microfluidic flows using ATR-FTIR spectroscopy. Lab Chip 9:2909–2913CrossRefGoogle Scholar
  11. Dalziel SB, Hughes GO, Sutherland BR (2000) Whole-field density measurements by ‘synthetic schlieren’. Exp Fluids 28:322–335CrossRefGoogle Scholar
  12. Eckstein A, Vlachos PP (2009) Digital particle image velocimetry (DPIV) robust phase correlation. Measurement Sci Technol 20:055401CrossRefGoogle Scholar
  13. Gojani AB, Obayashi S (2012) Assessment of some experimental and image analysis factors for background-oriented schlieren measurements. Appl Opt 51:7554–7559CrossRefGoogle Scholar
  14. Goldhahn E, Seume J (2007) The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field. Exp Fluids 43:241–249CrossRefGoogle Scholar
  15. Gui L, Merzkirch W, Fei R (2000) A digital mask technique for reducing the bias error of the correlation-based PIV interrogation algorithm. Exp Fluids 29:30–35CrossRefGoogle Scholar
  16. Hargather MJ, Settles GS (2010) Natural-background-oriented schlieren imaging. Exp Fluids 48:59–68CrossRefGoogle Scholar
  17. Hartberger JE (2011) Background-oriented schlieren pattern optimization. Department of Aeronautics and Astronautics, Air Force Institute of Technology. Master thesisGoogle Scholar
  18. Keane RD, Adrian RJ (1990) Optimization of particle image velocimeters. I. Double pulsed systems. Measurement Sci Technol 1:1202–1215CrossRefGoogle Scholar
  19. Keane RD, Adrian RJ (1992) Theory of cross-correlation analysis of PIV images. Appl Sci Res 49:191–215CrossRefGoogle Scholar
  20. Lima R, Wada S, Tsubota KI, Yamaguchi T (2006) Confocal micro-PIV measurements of three-dimensional profiles of cell suspension flow in a square microchannel. Measurement Sci Technol 17:797–808CrossRefGoogle Scholar
  21. Matsunaga T, Lee H-J, Nishino K (2013) An approach for accurate simulation of liquid mixing in a T-shaped micromixer. Lab Chip 13:1515–1521CrossRefGoogle Scholar
  22. Meier G (2002) Computerized background-oriented schlieren. Exp Fluids 33:181–187CrossRefGoogle Scholar
  23. Melling A (1997) Tracer particles and seeding for particle image velocimetry. Measurement Sci Technol 8:1406–1416CrossRefGoogle Scholar
  24. Merzkirch W (1974) Flow visualization. Academic Press, New YorkMATHGoogle Scholar
  25. Nguyen N-T, Wu Z (2005) Micromixers—a review. J Micromech Microeng 15:R1–R16CrossRefGoogle Scholar
  26. Raffel M, Richard H, Meier GEA (2000) On the applicability of background oriented optical tomography for large scale aerodynamic investigations. Exp Fluids 28:477–481CrossRefGoogle Scholar
  27. Raffel M, Willert C, Wereley ST, Kompenhans J (2007) Particle image velocimetry: a practial guide, 2nd edn. Springer, HeidelbergGoogle Scholar
  28. Richard H, Raffel M (2001) Principle and applications of the background oriented schlieren (BOS) method. Measurement Sci Technol 12:1576–1585CrossRefGoogle Scholar
  29. Ryerson WG, Schwenk K (2012) A simple, inexpensive system for digital particle image velocimetry (DPIV) in biomechanics. J Exp Zool Part A: Ecol Genet Physiol 317:127–140CrossRefGoogle Scholar
  30. Samarage CR, Carberry J, Hourigan K, Fouras A (2012) Optimisation of temporal averaging processes in PIV. Exp Fluids 52:617–631CrossRefGoogle Scholar
  31. Schröder A, Over B, Geisler R, Bulit A, Schwane R, Kompenhans J (2009) Measurements of density fields in micro nozzle plumes in vacuum by using an enhanced tomographic Background Oriented Schlieren (BOS) technique. In: 9th International Symposium on Measurement Technology and Intelligent Instruments. Saint-Petersburg, RussiaGoogle Scholar
  32. Scott TA (1946) Refractive index of ethanol-water mixtures and density and refractive index of ethanol-water-ethyl ether mixtures. J Phys Chem 50:406–412CrossRefGoogle Scholar
  33. Sun C-l, Hsian T-H (2012) Microscale background-oriented schlieren for flow visualization and quantitative analysis in a microfluidic oscillator. In: 15th International Symposium on Flow Visualization. Minsk, BelarusGoogle Scholar
  34. Sun C-l, Hsiao T-H (2013) Quantitative analysis of microfluidic mixing using microscale schlieren technique. Microfluid Nanofluid 15:253–265CrossRefGoogle Scholar
  35. Sun C-L, Sun C-Y (2011) Effective mixing in a microfluidic oscillator using an impinging jet on a concave surface. Microsyst Technol 17:911–922CrossRefGoogle Scholar
  36. Taylor JR (1997) An introduction to error analysis, 2nd edn. University Science Books, Sausalito, CAGoogle Scholar
  37. Tung K-Y, Yang J-T (2008) Analysis of a chaotic micromixer by novel methods of particle tracking and FRET. Microfluid Nanofluid 6:749–759CrossRefGoogle Scholar
  38. Tyn MT, Calus WF (1975) Temperature and concentration dependence of mutual diffusion coefficients of some binary liquid systems. J Chem Eng Data 20:310–316CrossRefGoogle Scholar
  39. Venkatakrishnan L, Meier GEA (2004) Density measurements using the background oriented schlieren technique. Exp Fluids 37:237–247CrossRefGoogle Scholar
  40. Vest CM (1974) Formation of images from projections: Radon and Abel transforms. J Opt Soc Am 64:1215–1218MathSciNetCrossRefGoogle Scholar
  41. Westerweel J (2000) Theoretical analysis of the measurement precision in particle image velocimetry. Exp Fluids 29:S003–S012CrossRefGoogle Scholar
  42. Westerweel J (2008) On velocity gradients in PIV interrogation. Exp Fluids 44:831–842CrossRefGoogle Scholar
  43. Willert CE, Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10:181–193CrossRefGoogle Scholar
  44. Yevtikhiyeva OA, Skornyakova NM, Udalov AV (2009) An investigation of the error of the background schlieren method. Measurement Tech 52:1300–1305CrossRefGoogle Scholar
  45. Yick KY, Stocker R, Peacock T (2007) Microscale synthetic schlieren. Exp Fluids 42:41–48CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Taiwan UniversityTaipeiTaiwan
  2. 2.Department of Mechanical EngineeringNational Taiwan University of Science and TechnologyTaipeiTaiwan

Personalised recommendations