The accuracy of the contact angle measurement is strongly dependent on the correct detection of the contact points. The usual strategy for detecting contact points is user intervention during one of the images in a series. The intervention normally takes the form of drawing a horizontal line or selecting the contact points on the screen. If a line is used, the intersections between this line and the detected drop profile reveal the contact points. However, since the positioning of the contact line or the selection of contact points is subjective, the performance of the measurement relies heavily on the user’s experience. To address this issue, we created an automatic contact point detection system that is not dependent on the operator’s experience. In practical measurements, depending on the solid surface and lighting conditions, the liquid drop can have a reflection or not. Thus, it’s necessary that the automatic contact point detection system work for both types of images. The automatic detection system follows the slope of the droplet profile and when the slope is 0 (no reflection) or changes from +ve to -ve OR -ve to +ve (with reflection) that point is the contact point.

Therefore, the contact points of a drop can be detected by checking the slope of the drop profile. To check the slope of the drop profile close to the contact point, a point of the drop profile close to the contact point needs to be identified first. In our system, this point (first point) is found by asking the user to provide an estimated position of the contact. The intersection point between the drop profile and this estimated contact line is then identified automatically. As the estimated position for the contact line does not need to be too accurate, subjectivity is not an issue. Using image analysis to detect the pixels of the drop profile, neighboring pixels slightly above the contact point are used to find the slope of the droplet profile. This is done with each pixel until the contact point is reached (the slope is 0, OR changes from +ve to -ve, OR -ve to +ve).

Once the contact points are detected, the contact angle is the angle between the tangent of the drop profile and the horizontal plane at the contact point. The tangent of the drop profile is tained by fitting first the drop profile points detected and by the image analysis with either the Young-Laplace or a second-order polynomial function (method chosen by the user). To then calculate the contact angle, the slope of the fitted curve is found by differentiation using the coordinates of contact points. The Young-Laplace fitting method finds a theoretical profile that best matches the drop profile exacted from the image and calculates the contact angle using this best matching profile. To calculate the drop profile using the Young-Laplace equation, the values of liquid density (∆ρ), gravity acceleration (g), liquid surface tension (γ), the total length of the drop profile (s), and the Laplace pressure difference (∆P) are needed. The values of ∆ρ and g are needed as the initial inputs. Initial guessed values for γ, s, and ∆P are set. An optimization algorithm is applied in the program to find the theoretical profile that best matches the drop profile exacted from the image by varying the three initial guess values. For the polynomial fitting method, a percentage of the detected drop profile is used to fit a second-order polynomial.