Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Reaction Mechanisms: The Steady-State Approximation

Reaction Mechanisms: The Steady-State Approximation

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...

Multi-Step Reactions

Multi-Step Reactions

Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...

Reaction Mechanisms: Rate-limiting Step Approximation

Reaction Mechanisms: Rate-limiting Step Approximation

The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...

Boundary Conditions for Current Density

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.

The Integrated Rate Law: The Dependence of Concentration on Time

The Integrated Rate Law: The Dependence of Concentration on Time

While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...

Consecutive Reactions

Consecutive Reactions

Consecutive reactions involve a sequence where the product of a preceding reaction becomes the reactant for the subsequent one. In a simple scheme, A transforms into B, which further reacts to form C, with rate constants k1 and k2, respectively. This concept is evident in the radioactive decay series. Assuming an initial state with only A present, the conservation of matter leads to three coupled differential equations, determining the concentrations of A, B, and C over time.The rate of change...

You might also read

Related Articles

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

Sort by

Same author

A Review of the Australian MRI Linac Program: From Pie in the Sky to Research Milestone.

Journal of medical imaging and radiation oncology·2026

Same author

Protocol optimization for MRI studies in radiation oncology: III. MRI relaxometry.

Physics in medicine and biology·2026

Same author

Protocol optimization for quantitative MRI studies in radiation oncology: II. Diffusion MRI.

Physics in medicine and biology·2026

Same author

Protocol optimization for MRI studies in radiation oncology: I. Phantoms.

Physics in medicine and biology·2026

Same author

Band-selective excitation short transient <sup>1</sup>H PGSE NMR.

Progress in nuclear magnetic resonance spectroscopy·2026

Same author

Aggregation of Phosphates Enhances Enzyme Activity in Aqueous Solution.

Chemphyschem : a European journal of chemical physics and physical chemistry·2026

Search research articles

Related Experiment Video

Updated: Jul 10, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Exact solution for anisotropic diffusion-controlled reactions with partially reflecting conditions.

Sergey D Traytak¹, William S Price

¹Institute of Applied Mechanics, Russian Academy of Sciences, 32a Lenin Avenue, GSP-1, 119991 Moscow, Russia.

The Journal of Chemical Physics

|November 21, 2007

Summary

This study generalizes the Solc-Stockmayer model for anisotropic diffusion-controlled reactions. It provides an exact solution for partially reflecting surfaces, aiding in the validation of numerical simulations for complex chemical systems.

More Related Videos

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

Related Experiment Videos

Last Updated: Jul 10, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

Area of Science:

Physical Chemistry
Chemical Kinetics
Theoretical Chemistry

Background:

Diffusion-controlled reactions are fundamental in chemical processes.
Anisotropic reactivity complicates modeling due to directional dependencies.
Existing models may not fully capture complex surface interactions.

Purpose of the Study:

To generalize the Solc-Stockmayer model for chemically anisotropic reactants.
To incorporate partially reflecting conditions on reaction surfaces.
To provide an exact analytical solution for diffusion-controlled reactions with anisotropic reactivity.

Main Methods:

Generalization of the Solc-Stockmayer model.
Mathematical analysis of mixed boundary-value problems.
Derivation of exact solutions for reaction rate constants.

Main Results:

An exact solution was obtained for diffusion-controlled reactions with anisotropic reactants.
The solution accounts for partially reflecting conditions on the reaction surface.
The study determined solutions for various ratios of intrinsic rate constants.

Conclusions:

The derived exact solution offers a benchmark for numerical methods.
This work enhances the understanding of diffusion-controlled reactions in anisotropic systems.
The findings are applicable to real-world particle systems with varied reactivity.