Contact Angle

Author: Marco Brugnara (marco.brugnara at
History: 2004/07/08: First version
2005/07/21: Bug fixes and improved best fit precision
2005/09/29: Elliptical best fit option, calculation of the uncertainly, modifiable threshold level, minor bug fixes
2006/02/16: Variable number of points in profile selection; preference file; error propagation analysis; minor bug fixes
2006/03/14: Fixed bug with finding preference file
2006/12/07: Works with latest version of ImageJ
Source:Contained in Contact_Angle.jar, which can be opened using a ZIP utility
Installation: Download Contact_Angle.jar to the plugins folder, or subfolder, restart ImageJ, then run the plugin using the Contact Angle command.
Description: This plug-in calculates the contact angle of a drop on a flat surface using the sphere approximation (theta=2atan(2h/l) and the ellipse approximation. This code has been written by Marco Brugnara and ití»s based on the plug-in "Pointpicker".

The necessity to have a self-developed software comes by considering that commercial softwares do not provide a sufficient enough description of the methods used in their contact angle calculation. In fact people often perform contact angle measurements, by applying the sphere approximation, neglecting in this way the gravity effect, or by calculating the tangent of the profile without limit the drop volume. In our experience, confirmed by the Literature as well, the maximum volume, whose profile as a sphere shape, is about 3-5 microlitres; it depends on the contact angle as well. For bigger drops the other possible approaches are 2: to use some "correction factors", present in Literature, or to apply another model called ADSA, which in fact calculates the angle applying on the profile the Laplace equation. This last model works really well on profiles strongly modified by the gravity, instead it has some trouble by solving the equation if the drop has an almost spherical profile. It is important to underline that in many commercial packages coming with the devices, it is often present another approach called in general "tangent line" which calculates the tangent of a fitting curve of the drop profile near the triphase line. This approach is a least debatable, if the best-fit function is polynomial equation, chosen only for its low chi square, but without any physical meaning. Then way to analyze images can furnish precise results, which are however meaningless if the drop volume is too large: in fact the contact angle is not the geometrical angle if this last one is modified by other forces than surface tension. In fact if the shape depends significantly on the gravity force, the resulting angle is not a value of contact angle as defined in Theory, but just an angle depending on the gravity. It is a pity that who develops these programs, most of the times does not know the Literature.

In our plug-in the image analysis works offline; it means that an image database is required. After a picture is loaded, the drop profile is detected. It is important to remind that the program was written supposing the drop is upside down. The reason is that our images are obtained by a camera connected to a microscope and the final picture is reversed up/down.

A manual detection of the base line is required, by choosing the FIRST 2 points. For this reason the plug-in could fail if the triphase line is not a straight line.

In the PlugIn Preferences menu the user finds the option "boundary conditions" where one can include or exclude one or both of these points in the drop profile.

Other 3 points are then requested along the drop profile in order to identify a ROI.

In order to calculate to contact angle, four different options are possible:

  • a Manual points selection
  • a measurement by using a circle best-fit
  • a measurement by using an ellipse best-fit
  • an analysis by applying both bestfits
When the manual points selection is chosen, the user need to detect the profile manually placing some points along the drop edge. The circle and the ellipse passing trough the points are reckoned.

The best-fit analysis automatically detects the drop profile; for this reason a very well defined picture is required. The user has the possibility to modify the threshold in order to exclude the main part of the background. After these points are automatically collected a best fit procedure of a circle or an ellipse or both can be applied.

It is important to point out that an ellipse best-fit analysis poses itself between the circle best fit (which has a physical meaning) and an absolute best-bit function. Some times can happen that the drop is not perfectly symmetric, or that there is a slight effect of the gravity. In this case an almost-circle analysis can provide useful results.

Our plug-in is completely open source and in a constant developing and there are still many things to improve. For instance many error controls are not implemented yet, so if points are chosen in the wrong sequence, the user just obtains meaningless results.

A sample image is available.

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