Microfluidics and Nanofluidics

, Volume 15, Issue 2, pp 253–265 | Cite as

Quantitative analysis of microfluidic mixing using microscale schlieren technique

  • Chen-li SunEmail author
  • Tzu-hsun Hsiao
Research Paper


In this study, we discuss the employment of microscale schlieren technique to facilitate measurement of inhomogeneities in a micromixer. By mixing dilute aqueous ethanol and water in a T-microchannel, calibration procedures are carried out to obtain the relation between the concentration gradients and grayscale readouts under various incident illuminations, concentrations of aqueous ethanol solution, and knife-edge cutoffs. We find that to broaden measuring range with minimal error, the luminous exitance should be tuned to have a reference background with an average grayscale readout of 121, and dilute aqueous ethanol solution with a mass fraction of 0.05 should be used along a 50 % cutoff. For concentration gradients greater than 6.8 × 10−3 or below −2.5 × 10−2 μm−1, the calibration curves show great linearity. Correspondingly, the discernable limit of our microscale schlieren system is 2.3 × 10−5 μm−1 for a positive refractive index gradient and −8.6 × 10−5 μm−1 for a negative refractive index gradient. Once the relation between concentration gradients and grayscale readouts is known, the concentration distribution in a microfluidic can be reconstructed by integrating its microscale schlieren image with appropriate boundary conditions. The results prove that the microscale schlieren technique is able to provide spatially resolved, noninvasive, full-field measurements. Since the microscale schlieren technique is directly linked to the measurement of a refractive index gradient, the present method can be easily extended to other scalar quantifications that are related to the variation of refractive index.


Microscale schlieren technique Mixing Mass transport Quantitative analysis 

List of symbols



Height of the source image in the plane of the knife-edge


Normalized concentration


Thickness of inhomogeneous medium/microchannel depth


Focal length of the reception objective


Grayscale readout of micro-schlieren image




Refractive index


Mass fraction of ethanol in water


Streamwise coordinate, μm


Cross-stream coordinate, μm


Coordinate parallel to the optical axis of the system





Degree of cutoff


Standard deviation





Positive/negative gradient











This work is supported by the National Science Council of Taiwan under grant number NSC 100-2221-E-011-113.

Supplementary material

Supplementary material 1 (MPG 832 kb)


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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

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