Pendant Drop Tensiometry: A Machine Learning Approach

TL;DR

This paper presents a deep learning method for pendant drop tensiometry that significantly improves the speed and accuracy of surface tension measurements compared to traditional shape fitting techniques.

Contribution

It introduces a neural network-based approach to efficiently determine surface tension from droplet shapes, outperforming existing methods in speed and precision.

Findings

Deep neural networks can accurately determine surface tension from droplet shapes.

The machine learning approach is faster and more precise than traditional shape fitting methods.

Optimized training sets improve the sensitivity and reliability of the neural network.

Abstract

Modern pendant drop tensiometry relies on numerical solution of the Young-Laplace equation and allow to determine the surface tension from a single picture of a pendant drop with high precision. Most of these techniques solve the Young-Laplace equation many times over to find the material parameters that provide a fit to a supplied image of a real droplet. Here we introduce a machine learning approach to solve this problem in a computationally more efficient way. We train a deep neural network to determine the surface tension of a given droplet shape using a large training set of numerically generated droplet shapes. We show that the deep learning approach is superior to the current state of the art shape fitting approach in speed and precision, in particular if shapes in the training set reflect the sensitivity of the droplet shape with respect to surface tension. In order to derive such an optimized training set we clarify the role of the Worthington number as quality indicator in conventional shape fitting and in the machine learning approach. Our approach demonstrates the capabilities of deep neural networks in the material parameter determination from rheological deformation experiments in general.