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Young-Laplace fit

The Young-Laplace fit is a method for determining the contact angle in drop shape analysis. The drop shape is analysed based on the shape of an ideal sessile drop, the surface curvature of which results only from the force equilibrium between surface tension and weight.


According to the Young-Laplace equation, with a curved liquid surface, there is a relationship between the radii of curvature r1 and r2, the surface tension σ and the Laplace pressure p:

With a sessile drop under the effect of gravity, the curvature is affected by the hydrostatic pressure resulting from the weight of the liquid. At the same time, the radii of curvature of the surface change as a function of height. With the Young-Laplace fit, parameters of an equation system which models the shape of the sessile drop are determined by means of numerical analysis. The point of intersection of the modelled contour with the baseline (three-phase point) is determined in order to measure the contact angle.


In the case of a symmetrical, undistorted drop on a level, smooth surface, the Young-Lapace fit gives the best correspondence between the theoretical drop shape and the real drop shape. In addition, the surface tension of the liquid can be calculated if the scale of the video image of the drop and the density of the liquid are known.


As the shape of the drop deviates from the elliptical form for large contact angles and volumes, in these cases the Young-Laplace fit is preferred to the conic section method. The Young-Laplace fit is not suitable for asymmetrical drops (e.g. when measuring the dynamic contact angle) or for samples which are not level (e.g. for measurements on a tilting table).


The Young-Laplace fit is also used to calculate the surface tension of a liquid or the interfacial tension of a two-phase system using a pendant drop and, finally, for interfacial tension measurements with a spinning drop tensiometer.

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