Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Chemical Equilibria: Systematic Approach to Equilibrium Calculations01:21

Chemical Equilibria: Systematic Approach to Equilibrium Calculations

1.8K
Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
The first step is to identify all the chemical reactions involved, The...
1.8K
Dynamic Equilibrium02:20

Dynamic Equilibrium

63.6K
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
63.6K
The Thermodynamics of Mixing01:28

The Thermodynamics of Mixing

169
Mixing is a fascinating phenomenon in thermodynamics, particularly when considering the Gibbs energy of a mixture at constant temperature and pressure. This energy, denoted as G, tends to decrease during spontaneous mixing processes, offering insights into the composition changes that occur.Imagine two ideal gases, initially separated in different containers, with amounts nA and nB, respectively, both at a temperature T and pressure p. The chemical potentials of these gases have their 'pure'...
169
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

12
The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
12
The Equilibrium Constant03:10

The Equilibrium Constant

46.6K
Consider the oxidation of sulfur dioxide:
46.6K
Homogeneous Equilibria for Gaseous Reactions02:15

Homogeneous Equilibria for Gaseous Reactions

26.7K
Homogeneous Equilibria for Gaseous Reactions
For gas-phase reactions, the equilibrium constant may be expressed in terms of either the molar concentrations (Kc) or partial pressures (Kp) of the reactants and products. A relation between these two K values may be simply derived from the ideal gas equation and the definition of molarity. According to the ideal gas equation:
26.7K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A Spatiotemporal Physics-Motivated State-Space Model of Lake Temperature Profiles.

Environmental science & technology·2026
Same author

Stochastic model for mixing interface evolution through three-dimensional fracture networks.

Physical review. E·2025
Same author

Parameters Driving Anomalous Transport in Colloids: Dimensional Analysis.

Langmuir : the ACS journal of surfaces and colloids·2025
Same author

Experimental Confirmation of the Interception History Paradigm for Colloid (Micro and Nanoparticle) Transport in Porous Media.

Environmental science & technology·2025
Same author

Interception History Drives Colloid Transport Variance in Porous Media.

Environmental science & technology·2025
Same author

Statistical-physical method for simulating the transport of microplastic-antibiotic compound pollutants in typical bay area.

Environmental pollution (Barking, Essex : 1987)·2024

Related Experiment Video

Updated: May 6, 2026

Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup
09:56

Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup

Published on: October 7, 2025

762

Mixing-Driven Equilibrium Reactions in Multidimensional Fractional Advection Dispersion Systems.

Diogo Bolster1, David A Benson, Mm Meerschaert

  • 1Environmental Fluid Dynamics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, IN, USA.

Physica A
|November 14, 2013
PubMed
Summary

Anomalous dispersion significantly alters reaction rates compared to classical diffusion models. This study reveals how superdiffusion impacts reaction locations and mixing dynamics, offering new insights into chemical reaction systems.

Keywords:
Fractional DispersionMultiple DimensionsReactions

More Related Videos

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

9.9K
Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
10:12

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

Published on: June 12, 2015

8.7K

Related Experiment Videos

Last Updated: May 6, 2026

Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup
09:56

Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup

Published on: October 7, 2025

762
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

9.9K
Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
10:12

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

Published on: June 12, 2015

8.7K

Area of Science:

  • Chemical kinetics
  • Transport phenomena
  • Mathematical modeling

Background:

  • Classical diffusion models (Fickian) assume local interactions.
  • Bimolecular equilibrium reactions are fundamental in chemical systems.
  • Understanding anomalous transport is crucial for complex reaction dynamics.

Purpose of the Study:

  • To investigate the impact of anomalous dispersion on mixing-driven bimolecular reactions.
  • To analyze how superdiffusive, nonlocal transport affects reaction rates and locations.
  • To compute the asymptotic scaling of the scalar dissipation rate.

Main Methods:

  • Utilizing a multidimensional space fractional dispersion equation to model transport.
  • Analyzing instantaneous, mixing-driven, bimolecular equilibrium reactions.
  • Deriving analytical solutions for the scalar dissipation rate's asymptotic behavior.

Main Results:

  • Anomalous dispersion leads to significant deviations in reaction location and magnitude compared to Fickian diffusion.
  • Regions with zero reaction rates in Fickian models exhibit maximum reaction rates under anomalous dispersion.
  • The scalar dissipation rate scales asymptotically as t^-(d+α)/α, where d is spatial dimensions and α is the fractional exponent.

Conclusions:

  • Superdiffusion fundamentally alters reaction dynamics in chemical systems.
  • The fractional dispersion model provides a more accurate representation of reaction-diffusion processes in certain complex environments.
  • Analytical insights into scalar dissipation rate scaling offer predictive capabilities for mixing processes.