Experiments in Fluids

, 56:177 | Cite as

Shadow imaging in bubbly gas–liquid two-phase flow in porous structures

  • Marco Altheimer
  • Richard Häfeli
  • Carmen Wälchli
  • Philipp Rudolf von Rohr
Research Article


Shadow imaging is used for the investigation of bubbly gas–liquid two-phase flow in a porous structure. The porous structure is made of Somos\({^{\textregistered }}\) WaterShed XC 11122, a clear epoxy resin used in rapid prototyping. Optical access is provided by using an aqueous solution of sodium iodide and zinc iodide having the same refractive index as the structure material (\(n = 1.515\)). Nitrogen is injected into the continuous phase at volumetric transport fractions in the range of \(\dot{\varepsilon } = 2.4-4.1\,\%\) resulting in a hold-up of \(\varepsilon = 0.94-2.17\,\%\). The obtained images of overlapping bubble shadows are processed to measure the bubble dimensions. Therefore, a new processing sequence is developed to determine bubble dimensions from overlapping bubble shadows by ellipse fitting. The accuracy of the bubble detection and sizing routine is assessed processing synthetic images. It is shown that the developed technique is suitable for volumetric two-phase flow measurements. Important global quantities such as gas hold-up and total interfacial area can be measured with only one camera. Operation parameters for gas–liquid two-phase flows are determined to improve mass and heat transfer between the phases.


Particle Image Velocimetry Bubble Size Bubble Column Bubble Diameter Bubbly Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Roman symbols


Area (mm2)


Constant \(((\sqrt{\hbox {pix}}\,s){^{-1}})\)


Sum of algebraic distances (−)


Frequency threshold (Hz)


Function (−)


Length (mm)


Reynolds number (−)


Volume (mm3)


Coefficients (−)


Coefficients vector (−)


Major semi-axis (mm)


Minor semi-axis (mm)


Minor semi-axis (mm)


Diameter (mm)


Numerical eccentricity (−)


Height (mm)


Curvature (1/pix)


Number of drawings (−)


Refractive index (−)


Sample size (−)


Slip (−)


Perimeter length (pix)


Velocity (m/s)


Variables vector (−)


Positions (pix)


First-order derivatives (−)


Second-order derivatives (1/pix)

Greek letters


Relative error (%)


Porosity (−)


Hold-up (%)

\(\dot{\varepsilon }\)

Volumetric transport fraction (%)


Dynamic viscosity (kg/(m s))


Density (kg/m3)


Coefficient of variation (−)


Surface tension (mN/m)


Standard deviation (−)

Sub- and superscripts


Sauter mean


Major semi-axis














Arithmetic mean












Periodic unit





Black and white


Computer-aided design


Fast Fourier transform


Light-emitting diode


Particle image velocimetry


Polymethyl methacrylate


Particle tracking velocimetry


Periodic unit

\(\hbox {P} \& \hbox {ID}\)

Process and instrumentation diagram



We gratefully acknowledge financial support from the Swiss Confederation’s innovation promotion agency (CTI) in cooperation with DSM Nutritional Products.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Marco Altheimer
    • 1
  • Richard Häfeli
    • 1
  • Carmen Wälchli
    • 1
  • Philipp Rudolf von Rohr
    • 1
  1. 1.Institute of Process Engineering ETH ZürichZürichSwitzerland

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