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Related Concept Videos

Diffusion01:12

Diffusion

213.5K
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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Diffusion01:21

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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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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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Diffusion on Chromatography Columns01:07

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

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

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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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Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
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Related Experiment Video

Updated: Nov 29, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

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Exact solution to the first-passage problem for a particle with a dichotomous diffusion coefficient.

Koushik Goswami1, K L Sebastian1,2

  • 1Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, Karnataka, India.

Physical Review. E
|November 20, 2020
PubMed
Summary
This summary is machine-generated.

We derived exact survival probabilities for a diffusing particle in a confined 1D space with a randomly switching diffusion coefficient. This model is relevant for biological processes like protein-DNA interactions.

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Area of Science:

  • Statistical Physics
  • Biophysics
  • Chemical Kinetics

Background:

  • Understanding particle diffusion in complex environments is crucial for biological processes.
  • Many biological systems involve reactants searching for targets in heterogeneous media.
  • The diffusion coefficient can fluctuate randomly over time, mimicking environmental changes.

Purpose of the Study:

  • To analyze the first-passage time problem for a particle diffusing in one dimension with a time-dependent diffusion coefficient.
  • To derive exact analytical expressions for the survival probability.
  • To characterize the decay of survival probability using average and instantaneous rate constants.

Main Methods:

  • Analytical solution of the diffusion equation with a switching diffusion coefficient.
  • Calculation of survival probability as a function of time.
  • Characterization of decay using average rate constant (k) and instantaneous rate (r(t)).

Main Results:

  • Exact analytical expressions for survival probability were obtained.
  • Survival probability exhibits a multi-exponential decay.
  • The approach is generalizable to diffusion coefficients with 'n' different values.

Conclusions:

  • The derived model provides an exact analytical solution for diffusion in a heterogeneous environment.
  • The findings are applicable to biological search processes, such as protein-DNA target recognition.
  • The model offers a framework for studying diffusion with time-varying properties.