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


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.


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

List of symbols


Size of interrogation window, pixel


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


Diameter of dot pattern, μm


Pixel size, μm pixel−1


Diffraction-limited dot diameter, μm


Dot-image diameter, μm


Index notion




Number of dots in the 4 × 4 matrix


Number of data points


Numerical aperture


Average number of dots per interrogation window


Number of rows in the evaluation zone


Number of columns in the evaluation zone


Refractive index


Reynolds number


Mass fraction of ethanol in water


Streamwise coordinate, μm


Cross-stream coordinate, μm


Displacement of pattern on the image plane, pixel


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


Thickness of inhomogeneous medium/microchannel depth, μm


Distance between dot pattern and region of refraction gradients, μm



Area fraction of dots


Wavelength of incident light











Index notion


Index notion




Numerical simulation


Mass fraction


Cross-stream coordinate


Image displacement in the y-direction


y-component of gradient of mass fraction




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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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