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Relating Angular And Linear Quantities - I01:09

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If the rotational definitions are compared with the definitions of linear kinematic variables from motion along a straight line and motion in two and three dimensions, we can observe a mapping of the linear variables to the rotational ones.
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In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
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Principle of Linear Impulse and Momentum for a System of Particles01:21

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In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
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Updated: Jan 3, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Linear and angular motion of self-diffusiophoretic Janus particles.

Jérôme Burelbach1, Holger Stark1

  • 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.

Physical Review. E
|November 28, 2019
PubMed
Summary
This summary is machine-generated.

Self-diffusiophoretic Janus particles (JPs) exhibit active motion driven by anisotropic surface reactivity. Their velocity arises from coupled electrochemical forces and fluid flow, with interactions depending on solute concentration.

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Area of Science:

  • Colloid and Interface Science
  • Soft Matter Physics
  • Chemical Physics

Background:

  • Janus particles (JPs) are engineered micro- or nanoparticles with distinct surface properties.
  • Self-diffusiophoresis describes particle motion driven by self-generated chemical gradients.
  • Understanding JP motion is crucial for designing active soft matter systems.

Purpose of the Study:

  • To theoretically investigate the active motion of self-diffusiophoretic Janus particles (JPs).
  • To elucidate the relationship between electrochemical forces, fluid flow, and particle velocity.
  • To explore conditions for active linear and rotational motion, and inter-particle interactions.

Main Methods:

  • Application of Onsager-Casimir reciprocal relations for theoretical analysis.
  • Model calculations for half-capped JPs catalyzing surface reactions.
  • Reduction of solute continuity equations to Poisson equations for electrochemical fields.

Main Results:

  • Anisotropic surface reactivity alone drives active linear motion in JPs.
  • Active rotation requires non-axisymmetric JPs.
  • Linear velocity correlates with solute friction coefficients or hydrodynamic radii.
  • Far-field interactions necessitate specific solute interactions and interfacial solute excess.

Conclusions:

  • The study provides a theoretical framework for active JP motion beyond boundary-layer approximations.
  • It unifies diffusio- and electrophoretic contributions to active movement.
  • The findings offer insights into controlling and predicting the behavior of active colloidal systems.