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Diffusion01:12

Diffusion

231.8K
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...
231.8K
Diffusion01:21

Diffusion

7.3K
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...
7.3K
Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

1.8K
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...
1.8K
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

32.2K
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...
32.2K
Diffusion on Chromatography Columns01:07

Diffusion on Chromatography Columns

1.6K
In column chromatography, when an analyte is introduced as a narrow band at the top of the column, the solutes begin to separate and broaden, developing a Gaussian profile. This broadening occurs due to various factors, such as longitudinal diffusion.
Longitudinal diffusion occurs when the solute molecules in the mobile phase diffuse from the more concentrated center of the chromatographic band to the more dilute regions on either side, both towards and against the flow direction. This...
1.6K
Protein Diffusion in the Membrane01:24

Protein Diffusion in the Membrane

6.3K
Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
6.3K

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Related Experiment Video

Updated: Apr 10, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
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The Diffusion of Passive Tracers in Laminar Shear Flow

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Smoluchowski diffusion equation for active Brownian swimmers.

Francisco J Sevilla1, Mario Sandoval2

  • 1Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, México D.F., Mexico.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2015
PubMed
Summary

This study analyzes active Brownian swimmers in 2D, revealing how their movement and position distribution evolve over time. Key findings detail the mean-square displacement and kurtosis, offering insights into non-equilibrium dynamics.

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Area of Science:

  • Statistical Physics
  • Soft Matter Physics
  • Complex Systems

Background:

  • Active Brownian swimmers are self-propelled particles exhibiting complex dynamics.
  • Understanding their diffusion is crucial for fields like biophysics and materials science.
  • Non-equilibrium statistical mechanics governs the behavior of such systems.

Purpose of the Study:

  • To analytically solve the Smoluchowski equation for active Brownian swimmers in 2D.
  • To characterize the out-of-equilibrium evolution of particle position distributions.
  • To investigate the effects of passive translational and active rotational fluctuations.

Main Methods:

  • Derivation of the Smoluchowski equation from a Langevin-like model.
  • Analytical solution in the long-time regime for arbitrary Péclet numbers.
  • Validation through Brownian dynamics simulations.

Main Results:

  • Explicit expressions for mean-square displacement and kurtosis derived.
  • Exact time dependence of mean-square displacement confirmed by simulations.
  • Kurtosis analysis reveals deviations from Gaussian behavior at short and long times.

Conclusions:

  • The study provides a comprehensive analytical framework for active Brownian swimmer diffusion.
  • Non-equilibrium properties, including deviations from Gaussian statistics, are quantified.
  • Results offer precise predictions for experimental validation.