Can the surface tension of a droplet above a hydrophobic surface be calculated only by knowing the contact angle with the surface?
The answer is yes, but you need more information. The following paper Contact Angle Measurements from the Contact Diameter of Sessile Drops by Means of a Modified Axisymmetric Drop Shape Analysis by Skinner Rottenberg and Neumann JCIS, vol 130, p 25, 1989 lays out the theory. You can find other related papers by checking who has cited this paper. Also I have a Mathematica demonstration that you can view and download from http://demonstrations.wolfram.com/ConfigurationOfASessileDrop/
The mathematica code for computing the shape is available from the Wolfram site. The essential idea is that if you know the contact angle, the radius of curvature at the apex of the drop, and surface tension, the shape of the drop can be computed from the Young Laplace equation. Thus if you measure the shape of the drop and the contact angle you can determine the surface tension of the liquid by constructing an objective function that minimizes the error between the shape of the measured drop and the shape from the theoretical computation, as shown in the Mathematica demonstration.
Yes you can. There is a relationship between surface curvature of the droplet and surface tension. But this is a bit complicated. you can use another method. You can use different liquids of known tension to find the surface tension of the solid, then by using contact angle and solid surface tension you can find the surface tension of any liquid on that solid by Young Equation.
its easier to do a pendant drop experiment where you look at the shape of a drop of liquid in air and essentially compare the horizontal and vertical radii of curvature, there are image J software algorithms available free of the internet I expect.
The correct answer is no. Contact angle and surface tension are independent variables! With ONLY a value for contact angle, say 110 on paraffin wax for water, there is not way to deduce the surface tension without any other information.
You might be interested in reading : An efficient method for the determination of interfacial tensions from drop profiles James W. Jennings, N. R. Pallas
Langmuir 04/2002; 4(4). DOI:10.1021/la00082a030
Dear Hadi Alqahtani,
NO. Multiple experimental problems exist concerning CA measurements. E.g. you are not able to measure the equilibrium CA, nearly all surfaces leads to non-axisymmetric droplets. And why do you want to perform a measurement on a tri-phase interface to obtain the interfacial tension liquid vapour. If you have a dosing system with a needle you can perform quite easily pendent drop experiments and evaluate the data with ADSA.
Best regards
Michael Schmitt
Reading attentively your question, it appears quite clear that you are thinking of deriving surface tension values of a liquid ONLY by their measured contact angle on a solid surface. You specify that the drop is Hydrophobicc, i.e. you suppose a very low level of interfacial interactions, at least.
However, as already stated by Prof Pallas, it is not possible to use only contact angles to derive surface tension values. As stated in other anwers, the best way is to go back using the Laplace equation, solved by fitting the theoretical profile to (experimentally) measured coordinates on the drop profile. As in this case the axisymmetry of the drop must be assured, you may choose to work in the "pendant drop" configuration, or using a support assuring its axial symmetry ( for example a tiny sharp-edge cup).
You can find both the methodology and the computer programs in the already suggested references as well in other papers I can supply.
Best wishes
Alberto Passerone
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