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Droplet motion in one-component fluids on solid substrates with wettability gradients.

Xinpeng Xu1, Tiezheng Qian

  • 1Nano Science and Technology (NSNT) Program, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Droplets move towards more wettable surfaces due to wettability gradients, with migration speed depending on surface properties and droplet size. This study models droplet motion, evaporation, and heat transfer using dynamic van der Waals theory.

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Area of Science:

  • Fluid dynamics and interfacial phenomena
  • Soft matter physics
  • Surface science and nanotechnology

Background:

  • Droplet motion on solid substrates is crucial for fundamental research and applications in chemistry, biology, and industry.
  • Continuum descriptions of droplet behavior face challenges with hydrodynamic and thermal singularities near contact lines.
  • Existing models often require pre-defined evaporation rates, limiting comprehensive analysis.

Purpose of the Study:

  • To investigate the motion of an evaporating droplet on a solid substrate with a wettability gradient.
  • To model droplet dynamics, including phase transitions, capillary flows, and heat transfer, using a unified continuum approach.
  • To resolve hydrodynamic and thermal singularities near the contact line.

Main Methods:

  • Employed the dynamic van der Waals theory for hydrodynamic equations in the bulk fluid.
  • Utilized the phase field method (diffuse interface method) to automatically resolve singularities.
  • Incorporated boundary conditions at the fluid-solid interface to account for physical processes like evaporation, condensation, and velocity slip.

Main Results:

  • Droplets migrate towards regions of increasing wettability on substrates.
  • Migration velocity is proportional to wettability gradients, influenced by the slip length to droplet radius ratio.
  • The motion results from a balance between wettability-driven forces and viscous drag; temperature variations are accurately captured.

Conclusions:

  • The dynamic van der Waals theory provides a robust framework for modeling complex droplet behaviors, including evaporation and motion.
  • Wettability gradients are confirmed as a primary driver for droplet migration.
  • The findings offer a detailed understanding of fluid flow and phase transitions at moving contact lines, crucial for droplet-based device design.