<p>Dust accumulation and wind effects can form structure-like obstacles on exposed surfaces, making it challenging to remove dust using rolling water droplets, as the droplets encounter obstacles of varying sizes during their motion. Controlling droplet motion over dusty surfaces becomes vital for efficient self-cleaning process. In this study, droplet motions including rolling, wobbling, tumbling over obstacles, and breaking off are investigated through a scaling-based estimate rather than a general predictive framework for all possible droplet–obstacle interactions. Numerical simulations and experimental observations are also provided within frame of parameters incorporated. Hydrophobic sample surfaces were created by dip-coating with functionalized nanoscale silica particles, which in turn results in a wetting state characterized by a contact angle of ~ 152.1° ± 0.9°, contact angle hysteresis of ~ 1.5° ± 0.9°, and a roughness parameter of ~ 1.62. The rolling droplet exhibits wobbling, and its dynamic motion alters both the mass center and contact angle hysteresis of droplet incorporated in the present study. This variation modifies the griping and interfacial friction forces acting on the droplet, effects that become more pronounced for larger droplets. The experimental conditions were designed to illustrate both tumbling and non-tumbling behavior of droplets as they rolled over obstacles. The inherited spin of the droplet has minimal influence on the jump length and contact time of droplet on hydrophobic surface. Droplets undergo break off for relatively large inertia (Weber number <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\:\ge\:\)</EquationSource></InlineEquation> 10), which becomes more pronounced when the obstacle height exceeds one-quarter of the droplet diameter; however, the proposed breakup criterion and newborn-droplet size estimate are valid within the tested range of droplet volumes, obstacle geometries, inclination angles, and surface properties considered in the present study. The radius of the newborn droplets varies inversely with Weber number such that <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(\:{R}_{newborn}\sim\frac{{R}_{d}}{{We}^{1/3}}\)</EquationSource></InlineEquation> for the cases considered in the present study. The newborn droplets reduce droplet kinetic energy by an amount of <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(\:{E}_{loss}=\mu\:{R}_{d}{U}_{T}^{2}\sqrt{\frac{\rho\:{R}_{d}^{3}}{\gamma\:}}\)</EquationSource></InlineEquation> while influencing the oblique impact dynamics of the tumbled droplet within the investigated parameters range. Although the present study provides useful information on droplet tumble characteristics and breakoff in relation to self-cleaning applications, we acknowledge that the number of newborn droplets, the detailed breakup morphology, and the transferability of the results to other surface chemistries or real outdoor dusty environments remain outside the fully validated scope of the present work.</p>

Dynamics of water droplet tumble over obstacles on hydrophobic surfaces

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2026年6月29日

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Bekir Sami Yilbas,
Ghassan Hassan,
Hussain Al-Qahtani,
Fadel Abdelrahman,
Abba Abdulhamid Abubakar,
Abdullah Al-Sharafi,
Mohamed A.S. Hegazy

摘要

Dust accumulation and wind effects can form structure-like obstacles on exposed surfaces, making it challenging to remove dust using rolling water droplets, as the droplets encounter obstacles of varying sizes during their motion. Controlling droplet motion over dusty surfaces becomes vital for efficient self-cleaning process. In this study, droplet motions including rolling, wobbling, tumbling over obstacles, and breaking off are investigated through a scaling-based estimate rather than a general predictive framework for all possible droplet–obstacle interactions. Numerical simulations and experimental observations are also provided within frame of parameters incorporated. Hydrophobic sample surfaces were created by dip-coating with functionalized nanoscale silica particles, which in turn results in a wetting state characterized by a contact angle of ~ 152.1° ± 0.9°, contact angle hysteresis of ~ 1.5° ± 0.9°, and a roughness parameter of ~ 1.62. The rolling droplet exhibits wobbling, and its dynamic motion alters both the mass center and contact angle hysteresis of droplet incorporated in the present study. This variation modifies the griping and interfacial friction forces acting on the droplet, effects that become more pronounced for larger droplets. The experimental conditions were designed to illustrate both tumbling and non-tumbling behavior of droplets as they rolled over obstacles. The inherited spin of the droplet has minimal influence on the jump length and contact time of droplet on hydrophobic surface. Droplets undergo break off for relatively large inertia (Weber number \(\:\ge\:\) 10), which becomes more pronounced when the obstacle height exceeds one-quarter of the droplet diameter; however, the proposed breakup criterion and newborn-droplet size estimate are valid within the tested range of droplet volumes, obstacle geometries, inclination angles, and surface properties considered in the present study. The radius of the newborn droplets varies inversely with Weber number such that \(\:{R}_{newborn}\sim\frac{{R}_{d}}{{We}^{1/3}}\) for the cases considered in the present study. The newborn droplets reduce droplet kinetic energy by an amount of \(\:{E}_{loss}=\mu\:{R}_{d}{U}_{T}^{2}\sqrt{\frac{\rho\:{R}_{d}^{3}}{\gamma\:}}\) while influencing the oblique impact dynamics of the tumbled droplet within the investigated parameters range. Although the present study provides useful information on droplet tumble characteristics and breakoff in relation to self-cleaning applications, we acknowledge that the number of newborn droplets, the detailed breakup morphology, and the transferability of the results to other surface chemistries or real outdoor dusty environments remain outside the fully validated scope of the present work.