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Exit time of colloidal particles from falling drops.

Nishanth Murugan1, Anubhab Roy1

  • 1Indian Institute of Technology Madras, Department of Applied Mechanics, Chennai 600036, India.

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|January 21, 2026
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Summary

Convective transport in sedimenting drops significantly impacts colloidal particle exit times. Brownian dynamics simulations reveal how Péclet numbers, balancing flow and fluctuations, dictate particle escape, crucial for understanding colloidal dynamics.

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Area of Science:

  • Colloid and Interface Science
  • Fluid Dynamics
  • Computational Physics

Background:

  • Sedimenting drops create internal flow fields (Hadamard-Rybczynski flow).
  • Colloidal particles within these drops experience both convective transport and Brownian motion.
  • Understanding particle dynamics is key in fields like materials science and biophysics.

Purpose of the Study:

  • To investigate how convective transport within a sedimenting drop affects a colloidal particle's exit time.
  • To quantify the influence of the Péclet number on particle exit dynamics.
  • To model particle exit as a first-passage process.

Main Methods:

  • Brownian dynamics simulations were employed to compute particle exit times.
  • The Péclet number (Pe) was systematically varied to represent different balances of convection and diffusion.
  • The backward Kolmogorov equation was used for analytical and numerical modeling of the first-passage process.

Main Results:

  • Exit times are strongly dependent on the particle's starting position within the drop and the Péclet number.
  • Asymptotic solutions for low (Pe≪1) and high (Pe≫1) Péclet numbers were derived.
  • Numerical solutions provided a comprehensive mean exit time as a function of Pe.

Conclusions:

  • Convective transport within sedimenting drops is a critical factor governing colloidal particle exit times.
  • The Péclet number effectively characterizes the interplay between fluid flow and thermal fluctuations in determining particle escape.
  • This study provides a framework for predicting colloidal particle behavior in complex fluid environments.