Liquid drops on vertical and inclined surfaces; II. A method for approximating drop shapes

Area of Science:

• Fluid dynamics
• Surface science
• Materials science

Background:

• Accurate prediction of liquid drop volume and shape is crucial in various scientific and industrial applications.
• Existing methods, like the spherical cap approximation, often lack precision, leading to significant errors in volume estimation (up to 75%).

Purpose of the Study:

• To introduce a new, more accurate method for approximating the shapes of liquid drops on vertical and inclined surfaces.
• To validate the proposed method against experimental data and literature values.
• To investigate the influence of various drop parameters on volume prediction and explore its utility in contact angle measurement.

Main Methods:

• Approximating the drop profile at any azimuthal angle using two circles with a common tangent at maximum height.
• Calculating drop volume by integrating these profiles over the base circumference.
• Expressing drop volume as a function of contact angles and the three-phase contact line.

Main Results:

• The proposed two-circle method demonstrates high accuracy in predicting liquid drop volumes, validated by data from Part I and independent literature sources.
• The method significantly outperforms the spherical cap approximation, mitigating substantial prediction errors.
• The geometry derived from the two-circle model can be effectively utilized for measuring contact angles from profile images.

Conclusions:

• The novel two-circle approximation provides a robust and accurate method for characterizing liquid drop shapes and volumes on diverse surfaces.
• This method offers a superior alternative to simplified models, enhancing precision in fluid behavior studies.
• The technique's dual capability in volume prediction and contact angle measurement makes it a valuable tool in surface science and fluid dynamics research.