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Unique nonconcentric semicircular arrays of nanoparticles via controlled gravitational force

Sanjoy Khawas1, Suman Bhattacharjee2, and Sunita Srivastava1,*

  • *Contact author: sunita.srivastava@iitb.ac.in
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Phys. Rev. E 114, 045506 – Published 27 October, 2026

DOI: https://doi.org/10.1103/kwts-ft26

Abstract

The dynamic behavior of the three-phase contact line (TPCL) during droplet evaporation plays a critical role in governing particle assembly processes, enabling spatially controlled deposition of nanomaterials at micro/nanoscales. This phenomenon utilizes evaporation-driven capillary and possible Marangoni flows arising from surface tension gradients to direct particle migration, resulting in pattern formation through TPCL pinning-depinning dynamics and solvent gradient effects. In this study, we report the formation of unique nonconcentric semicircular arrays of nanoparticle deposition on hydrophilic silicon substrates. This patterning is achieved by manipulating TPCL dynamics through gravity-induced asymmetric droplet deformation. A droplet placed on an inclined substrate adopts an asymmetric shape due to the competing effects of surface tension and gravity, producing spatially heterogeneous TPCL motion characterized by distinct pinning and depinning regimes. These events drive directional deposition of suspended particles, facilitating the self-organization of semicircular stripes. The physical features of the stripe patterns, such as density and spacing, are precisely tunable by adjusting the effective parallel gravitational force (Fg∥), which we control via substrate inclination (α) and droplet volume (V). A universal linear relationship between stripe density and Fg∥ is found, independent of the mode of force modulation. However, subtle changes in the structural morphology of the surface pattern have been observed, resulting in periodic semicircular patterns with varying radii of curvature, while the final structure is significantly influenced by the sample preparation-related memory effect. An assembly mechanism and an empirical relation based on the experimental results are provided to correlate stripe density with α and V, capturing the interplay between gravitational forces and TPCL kinetics.

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Phys. Rev. E 114, 045506– Published 27 October, 2026
  • Received 31 January 2026
  • Accepted 17 September 2026
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