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Colloids and Suspensions01:17

Colloids and Suspensions

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Children at play often make suspensions such as mixtures of mud and water, flour and water, or a suspension of solid pigments in water known as tempera paint. These suspensions are heterogeneous mixtures composed of relatively large particles visible to the naked eye or seen with a magnifying glass. They are cloudy, and the suspended particles settle out after mixing. The suspended particles in a suspension settle out after some time of mixing. The separation of particles from a suspension is...
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Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

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Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
When administered orally, drugs establish a substantial concentration gradient between the gastrointestinal (GI) lumen and the bloodstream, expediting...
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Laminar Flow01:27

Laminar Flow

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Laminar flow represents a smooth, orderly fluid motion where particles move along parallel paths, resulting in minimal mixing between layers. Streamlined particle paths characterize this flow regime and occur under conditions where viscous forces dominate over inertial forces. The distinction between laminar, transitional, and turbulent flow is primarily determined by the Reynolds number, a dimensionless quantity calculated as:
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Accelerating Fluids01:17

Accelerating Fluids

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When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
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Reynolds Transport Theorem01:24

Reynolds Transport Theorem

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The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
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Theories of Dissolution: Diffusion Layer Model01:15

Theories of Dissolution: Diffusion Layer Model

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Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
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Related Experiment Video

Updated: Dec 26, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

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Loopy Lévy flights enhance tracer diffusion in active suspensions.

Kiyoshi Kanazawa1,2, Tomohiko G Sano3,4, Andrea Cairoli5,6,7

  • 1Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba, Japan. kiyoshi@sk.tsukuba.ac.jp.

Nature
|March 20, 2020
PubMed
Summary

Active systems exhibit enhanced diffusion and non-Gaussian statistics, deviating from Brownian motion. A new theory explains this tracer motion, predicting a tunable Lévy flight regime crucial for understanding active matter dynamics.

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Last Updated: Dec 26, 2025

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Area of Science:

  • Physics
  • Chemistry
  • Biology
  • Active Matter Physics
  • Statistical Mechanics

Background:

  • Brownian motion models diffusion in equilibrium systems.
  • Real-world systems are often out of equilibrium due to active processes.
  • Tracer diffusion in active media shows enhanced diffusion and non-Gaussian statistics, unlike Brownian motion.

Purpose of the Study:

  • Develop a comprehensive theory for tracer diffusion in active media.
  • Explain the emergence of enhanced diffusion and non-Gaussian statistics from microscopic dynamics.
  • Model hydrodynamic interactions between tracers and active swimmers.

Main Methods:

  • Developed a theoretical framework to model hydrodynamic interactions.
  • Utilized a non-Markovian colored Poisson process to describe tracer motion.
  • Analyzed tracer displacements and diffusion coefficients.

Main Results:

  • The tracer follows a non-Markovian colored Poisson process, explaining empirical observations.
  • Predicted a long-lived Lévy flight regime with tunable power-law exponents.
  • Demonstrated that swimmer density influences the duration of the Lévy flight regime.

Conclusions:

  • The developed theory provides a comprehensive explanation for tracer diffusion in active media.
  • The findings have implications for understanding active system thermodynamics and biological processes like foraging.
  • The framework can guide the design of artificial nanoscale machines and analyze particle interactions.