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Diffusion01:12

Diffusion

221.8K
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...
221.8K
Diffusion01:21

Diffusion

6.5K
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...
6.5K
Coefficient of Variation01:10

Coefficient of Variation

8.7K
The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or...
8.7K
Coefficient of Correlation01:12

Coefficient of Correlation

8.7K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
8.7K
Confidence Coefficient01:24

Confidence Coefficient

10.7K
The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
10.7K
Thermodynamics: Activity Coefficient01:24

Thermodynamics: Activity Coefficient

3.0K
Activity is the measure of the effective concentration of the species in solution. It can be expressed as the product of the molar concentration of the species and its activity coefficient. The activity coefficient is a dimensionless quantity and depends on the total ionic strength of the solution.
The activity coefficient is a measure of the deviation from ideal behavior. When the ionic strength of the solution is minimal, the activity coefficient of an ionic species is close to unity, making...
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Related Experiment Video

Updated: Feb 12, 2026

Measuring Diffusion Coefficients via Two-photon Fluorescence Recovery After Photobleaching
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Measuring Diffusion Coefficients via Two-photon Fluorescence Recovery After Photobleaching

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Effective diffusion coefficient including the Marangoni effect.

Hiroyuki Kitahata1, Natsuhiko Yoshinaga2

  • 1Department of Physics, Chiba University, Chiba 263-8522, Japan.

The Journal of Chemical Physics
|April 9, 2018
PubMed
Summary
This summary is machine-generated.

Marangoni convection, driven by surface-active molecules, enhances diffusion by transporting molecules away from their source. This study analytically derives the effective diffusion coefficient, confirming experimental observations.

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Area of Science:

  • Fluid dynamics
  • Surface science
  • Physical chemistry

Background:

  • Surface-active molecules at interfaces can induce fluid flow.
  • Concentration gradients drive Marangoni convection.
  • Enhanced diffusion is crucial in various chemical and physical processes.

Purpose of the Study:

  • To analytically determine the effective diffusion coefficient in the presence of Marangoni convection.
  • To understand how convective flow influences molecular transport.
  • To validate theoretical findings with experimental and numerical data.

Main Methods:

  • Analytical derivation of the effective diffusion coefficient.
  • Modeling of Marangoni convection rolls.
  • Comparison with numerical simulations and experimental measurements.

Main Results:

  • A spatial gradient of surface-active molecules induces Marangoni convection.
  • Convective flow significantly enhances the effective diffusion of molecules.
  • The derived effective diffusion coefficient aligns with numerical and experimental results.

Conclusions:

  • Marangoni convection provides a mechanism for enhanced molecular transport.
  • The analytical model accurately predicts the effective diffusion coefficient.
  • This work offers insights into diffusion processes in systems with surface-driven flows.