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Related Concept Videos

Diffusion01:12

Diffusion

Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
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Fast reactions occurring in times shorter than the time needed to mix reactants pose a unique challenge for investigation. In a liquid-phase continuous-flow system, reactants A and B are swiftly pushed into the mixing chamber, where mixing occurs within 1 ms. The reaction mixture then flows through an observation tube, and one measures light absorption to determine species concentrations at various points of the tube. This method is most appropriate when relatively large volumes of reactants...
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Updated: Jun 14, 2026

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

Distribution in flowing reaction-diffusion systems.

Atsushi Kamimura1, Hans J Herrmann, Nobuyasu Ito

  • 1Computational Physics for Engineering Materials, IfB, ETH Zürich, Schafmattstrasse 6, CH-8093 Zürich, Switzerland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Reacting systems under flow exhibit power-law density profiles. Reactant concentrations decay in space, with decay rates depending on dimensionality and reaction type, offering insights into diffusion processes.

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Area of Science:

  • Chemical kinetics
  • Statistical physics
  • Reaction-diffusion systems

Background:

  • Power-law distributions are observed in various natural phenomena, including chemical reactions.
  • Understanding reactant density profiles under flow is crucial for predicting reaction outcomes.
  • Previous studies have explored diffusion-influenced reactions, but flow effects require further investigation.

Purpose of the Study:

  • To investigate the density profiles of reacting systems A+B-->C+D and 2A-->2C under flow in two and three dimensions.
  • To determine the spatial decay rates of reactant concentrations.
  • To explain the observed decay patterns based on segregation and diffusion behaviors.

Main Methods:

  • Theoretical analysis of reaction-diffusion systems with fixed reactant densities at boundaries.
  • Mathematical modeling of spatial concentration decay under flow conditions.
  • Dimensional analysis to compare two- and three-dimensional systems.

Main Results:

  • A power-law distribution was identified in the density profiles of both reaction systems.
  • For A+B --> C+D, reactant concentrations decay as x-1/2 (2D) and x-3/4 (3D).
  • For 2A --> 2C, the decay in 2D is described by log(x)/x, with a logarithmic divergence of the diffusion constant.

Conclusions:

  • Reactant segregation in isotropic cases explains the A+B decay.
  • Marginal behavior of two-dimensional diffusion accounts for the 2A decay.
  • The study reveals unique diffusion characteristics in two-dimensional systems under flow.