Table of Contents
What is a reaction-diffusion equation?
Reaction-diffusion equations describe the behaviour of a large range of chemical systems where diffusion of material competes with the production of that material by some form of chemical reaction. Many other kinds of systems are described by the same type of relation.
How does reaction-diffusion work?
Abstract. The reaction-diffusion system is naturally used in chemistry to represent substances reacting and diffusing over the spatial domain. Its solution illustrates the underlying process of a chemical reaction and displays diverse spatial patterns of the substances.
What is diffusion in statistics?
In probability theory and statistics, a diffusion process is a solution to a stochastic differential equation. It is a continuous-time Markov process with almost surely continuous sample paths. Brownian motion, reflected Brownian motion and Ornstein–Uhlenbeck processes are examples of diffusion processes.
What is reaction-diffusion model?
The reaction-diffusion model describes the emergence of periodic patterns such as spots, stripes, and maze on the surface of animal coat through chemical interaction among cells [34]; see Figure 6.5. In the reaction-diffusion model, two hypothetical chemicals, called morphogens (activator and inhibitor) are considered.
How do you measure rate of diffusion?
In this experiment, diffusion rates are determined by measuring the increase in salt concentrations in the cell chamber over a fixed time period. If the salt concentrations (dependent variable) are plotted against the time they were measured (independent variable), the slope of the resulting line is the diffusion rate.
What is net diffusion?
Net diffusion is when the flow of solute particle moving in one direction is bigger than the flow of solute particles moving in the opposite direction.
How do you write the first law of diffusion?
Writing the first law in a modern mathematical form: where for species i, Ni is the molar flux (mol m -2 s -1 ), Di is the diffusion coefficient (m 2 s -1 ), and ci is the concentration (mol m -3 ).
How to compute diffusion coefficient?
To compute for diffusion coefficient, three essential parameters are needed and these parameters are Constant (BA), Boltzmann’s Constant (KB) and Temperature (T). The formula for calculating diffusion coefficient:
What is the simplest description of diffusion?
The simplest description of diffusion is given by Fick’s laws, which were developed by Adolf Fick in the 19th century: The molar flux due to diffusion is proportional to the concentration gradient.
How do you find the mass flux of a diffusion system?
The diffusive mass flux of each species is, in turn, expressed based on the gradients of the mole or mass fractions, using multi-component diffusion coefficients D ik. These are symmetric, so that an n-component system requires n(n-1)/2 independent coefficients to parameterize the rate of diffusion of its components.