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Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
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Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is...
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In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
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Related Experiment Video

Updated: Sep 18, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Particle dynamics in biconical cavities: First-passage, direct-transit, and looping time distributions.

Alexander M Berezhkovskii1, Leonardo Dagdug2, Sergey M Bezrukov1

  • 1Section of Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20819, USA.

The Journal of Chemical Physics
|June 25, 2025
PubMed
Summary

Particle dynamics in biconical cavities show identical first-passage times but different transit and looping times. The mean direct-transit time differs significantly between entropy potential wells and barriers.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Particle diffusion in tubes with changing entropy potentials was previously studied.
  • Biconical cavities present unique structures influencing particle motion via entropy potentials.

Purpose of the Study:

  • Investigate particle dynamics in biconical cavities with entropy potential wells and barriers.
  • Derive analytical expressions for first-passage, direct-transit, and looping times.
  • Compare time distributions between expanding-narrowing and narrowing-expanding cavities.

Main Methods:

  • Analysis of particle dynamics in biconical geometries.
  • Derivation of analytical expressions for time-dependent distributions.
  • Mathematical modeling of entropy potential effects on particle transport.

Main Results:

  • First-passage time distributions are identical for both cavity types.
  • Direct-transit and looping time distributions differ significantly.
  • Mean direct-transit time in expanding-narrowing cavities (well) saturates, while in narrowing-expanding cavities (barrier) it diverges.

Conclusions:

  • Biconical cavities exhibit distinct particle transport behaviors based on entropy potential shape.
  • The geometry of entropy potential (well vs. barrier) critically impacts particle transit and looping dynamics.
  • Findings are relevant to micro- and nanoscale systems in technology and biology.