Novel framework for PDMS membrane characterization: Droplet induced indentation and machine learning classification

Abstract

We present a novel approach for determining the Young's Modulus of PDMS membranes by analyzing the bulge depth induced by a sessile droplet. The combined effects of Laplace pressure and droplet weight produce a measurable indentation. Statistical analysis revealed significant variations in bulge depth across PDMS compositions (10:1, 15:1, 20:1 elastomer-to-curing-agent ratio). To establish a correlation between Young’s Modulus and membrane deformation, droplet size, shape, and contact angles, we developed analytical models based on three strain assumptions: zero tangential strain, equal radial and tangential strain, and plane strain. While all models captured the trend of increasing stiffness with higher elastomer content, the zero tangential strain approach demonstrated the highest accuracy. This model estimated Young's Modulus for PDMS membranes as follows: (a) 10:1 ratio: $E=2.51\pm 0.14\mathrm{MPa}$, (b) 15:1 ratio: $E=1.14\pm 0.24\mathrm{MPa}$, and (c) 20:1 ratio: $E=0.97\pm 0.16\mathrm{MPa}$. These estimates align with reported values, confirming that for thin membranes (20–110 µm), the zero tangential strain model best describes deformation behavior. Additionally, machine learning algorithms—including Logistic Regression, SVM, Gradient Boosting, and Random Forest—achieved high classification accuracy $(\ge 0.96$) in distinguishing membrane composition based on droplet shape, contact angle, and membrane deformation. This study presents a valuable framework for characterizing thin PDMS membrane mechanics, with significant implications for microfluidic device design.