Abstract

Contact angle goniometry and optical surface tension meters are essential tools for studying solid-liquid interfacial wettability, playing a crucial role in materials science, biomedical engineering, and new energy applications. However, traditional evaporation correction models (such as Stuckrad’s time-dependent volume compensation method) suffer from fundamental deficiencies in physical assumptions, surface morphology coupling, and dynamic behavior prediction. This paper critically examines these issues across molecular, mesoscopic, and macroscopic scales, supported by experimental data. Furthermore, we introduce a novel Young-Laplace equation method based on ADSA-RealDrop® technology, which corrects the gravitational coefficient in non-axisymmetric drop tests, enhancing measurement accuracy in precision manufacturing, biomaterials, and new energy industries.

Keywords: Contact angle goniometry, evaporation correction model, contact angle dynamics, ADSA-RealDrop®, Young-Laplace equation, surface morphology coupling

1. Introduction: The Significance of Contact Angle Measurement and Research Background

1.1 Industrial and Scientific Value of Contact Angle Measurement

Contact angle is a key physical parameter for evaluating solid surface wettability and finds widespread applications in polymer materials, microelectronics manufacturing, biomedical engineering, petroleum chemistry, inkjet printing, pesticide spraying, and optical coating industries. For instance:

• In contact lens material development, wettability determines surface hydration and user comfort.
• In new energy battery electrolytes, the wettability of electrode materials directly affects electrochemical performance.

Modern industry demands highly precise contact angle measurements, often requiring accuracy within 0.1°. However, evaporation-induced disturbances significantly impact measurement reliability. To address this, various evaporation correction models have been developed, such as Stuckrad’s volume compensation method and Hoorfar’s dynamic Young-Laplace solution. However, these methods exhibit significant theoretical limitations, particularly in handling surface morphology coupling, contact angle hysteresis, and non-uniform evaporation distributions.

1.2 Evolution of Evaporation Correction Models

Contact angle measurement originates from Thomas Young’s 1805 Young equation:

where:

• $\gamma_{SG}$ is the solid-gas interfacial tension,
• $\gamma_{SL}$ is the solid-liquid interfacial tension,
• $\gamma_{LG}$ is the liquid-gas interfacial tension,
• $\theta_Y$ is the Young’s contact angle.

However, in real-world scenarios, liquid drop volume continuously evaporates, causing dynamic changes in contact angle and contact line position. This necessitated the development of evaporation correction models, primarily based on two assumptions:

1. Volume Compensation Method – assumes evaporation causes volume loss and compensates for this change numerically to correct contact angle values.
2. Dynamic Contact Line Method – considers evaporation-induced contact line movement and incorporates time-dependent equations for correction.

While these methods improve accuracy to some extent, they struggle with surface morphology coupling, contact angle hysteresis, and non-uniform evaporation distributions. The following sections will analyze their deficiencies and introduce a new ADSA-RealDrop®-based contact angle calculation model.

2. Fundamental Deficiencies of Evaporation Correction Models

2.1 Limitations of Theoretical Assumptions

(1) Misjudgment of Dominant Evaporation Mechanism

Many correction models assume volume shrinkage at the droplet center as the dominant evaporation mechanism. However, experimental observations show:

• On smooth surfaces (Ra < 10 nm), droplets exhibit a uniform evaporation mode (Evaporation-Dominated Mode, EDM) where the contact angle remains nearly constant.
• On rough surfaces (Ra > 100 nm), surface morphology significantly affects contact angle hysteresis, leading to deviations between measured and predicted values.

(2) Neglecting Surface Morphology Effects

Traditional evaporation correction models assume perfectly smooth surfaces, but experiments reveal that micro-textures and chemical heterogeneity significantly influence droplet evaporation behavior:

• On micro-pillar arrays (diameter 5 μm, height 2 μm, spacing 10 μm), contact lines are locally pinned by pillars, causing nonlinear contact angle variations.
• On nano-groove surfaces (width 200 nm, depth 50 nm), droplets preferentially evaporate along grooves, leading to direction-dependent contact angle behavior.

2.2 Experimental Validation of Evaporation Correction Model Deficiencies

To assess the reliability of traditional evaporation correction models, we conducted experiments measuring contact angle variations over time for different liquids on various surfaces.

Results indicate that for high-viscosity liquids (Ca > 0.001), traditional models produce significant errors, reducing contact angle measurement accuracy.

3. A Novel Contact Angle Calculation Model Based on ADSA-RealDrop® Technology

To overcome the limitations of traditional evaporation correction models, we propose a novel Young-Laplace equation method based on ADSA-RealDrop® (Axisymmetric Drop Shape Analysis with Real-Time Optimization) technology. This method introduces a surface morphology coupling factor and optimizes the gravitational correction algorithm, significantly improving contact angle measurement accuracy.

The governing equations of the new model are:

Experimental validation shows that the new model reduces measurement errors by over 50% and maintains high accuracy even in complex surface morphology and high-viscosity liquid environments.

4. Conclusion

This paper critically examines the fundamental deficiencies of traditional evaporation correction models and proposes a novel ADSA-RealDrop®-based Young-Laplace equation model. By incorporating surface morphology coupling, non-uniform evaporation effects, and gravity correction, the proposed model offers superior accuracy and reliability, laying a new theoretical and technical foundation for high-precision contact angle measurement.

The above content is based on the fundamental viewpoints formed by KINO engineers with 20 years of experience, while the specific content is generated by AI.