Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in concentration.
The concept of diffusion is widely used in many fields, including physics (particle diffusion), chemistry, biology, sociology, economics, and finance (diffusion of people, ideas, and price values). The central idea of diffusion, however, is common to all of these: a substance or collection undergoing diffusion spreads out from a point or location at which there is a higher concentration of that substance or collection.
A gradient is the change in the value of a quantity, for example, concentration, pressure, or temperature with the change in another variable, usually distance. A change in concentration over a distance is called a concentration gradient, a change in pressure over a distance is called a pressure gradient, and a change in temperature over a distance is called a temperature gradient.
The word diffusion derives from the Latin word, diffundere, which means "to spread out."
A distinguishing feature of diffusion is that it depends on particle random walk, and results in mixing or mass transport without requiring directed bulk motion. Bulk motion, or bulk flow, is the characteristic of advection. The term convection is used to describe the combination of both transport phenomena.
If a diffusion process can be described by Fick's laws, it's called a normal diffusion (or Fickian diffusion); Otherwise, it's called an anomalous diffusion (or non-Fickian diffusion).
When talking about the extent of diffusion, two length scales are used in two different scenarios:
Brownian motion of an impulsive point source (for example, one single spray of perfume)—the square root of the mean squared displacement from this point. In Fickian diffusion, this is
2
n
D
t
{\displaystyle {\sqrt {2nDt}}}
, where
n
{\displaystyle n}
is the dimension of this Brownian motion;
Constant concentration source in one dimension—the diffusion length. In Fickian diffusion, this is
I am trying to solve a problem from Thorne and Blandford: Modern classical physics, chapter 3, problem 21: Neutron diffusion in nuclear reactor.
I am struggling with how the equation, from which this should be calculated, should look like. I watched some videos where they did the derivation a...
Suppose there is a cylindrical (pellet) sample in the oxygen atmosphere as shown on the photo attached. Oxygen diffuses from the outside to the sample interior everywhere on the outer surface of the sample. From the photo, it can be seen that diffusion profile of oxygen is measured in the axial...
Apologies if this question may come off as simple to some of you and/or its posted in the wrong thread (i'm not sure if its better on the chemistry or physics forum) but i was curious, i'm currently doing neuron work and it involves the diffusion of K+ and Na+ ions one part that made me ask this...
Suppose there is a non-stationary diffusion process in 2D rectangular plane. Component diffuses from the outside through all four faces of the plane.
When I think about the simulations of the non-stationary diffusion in Matlab for example (finite difference numerical solution), I remember how...
I have a discussion with a colleague of mine.
We have a thin cuboid sample whose two dimensions are similar to each other and are both much bigger than the sample thickness. I'm doing an experiment in which the diffusion of some species is induced and its diffusion profile is measured in one of...
TL;DR Summary: Solve heat equation in a disc using fourier transforms
Carbon dioxide dissolves in the blood plasma but is not absorbed by red blood cells. As the blood returns to an alveolus, assume that it is well-mixed so that the concentration of dissolved CO2 is uniform across a...
Hello all:
Read a book long time ago about some metals and vanadium was mentioned that it , the book read that you can not contain vanadium in normal container because it will diffuse from that container is that correct
Because I start seeing on social media Instagram for example people...
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I want to model the thermal behaviour of a moving heat transfer fluid in 1D, with convective exchanges with the walls. I have obtained the following equation (1 on the figure). I have performed a second order spatial discretization with decentred schemes at the extremities (y = 0 and H)...
In the textbook: Electrochemical Systems by Newman and Alyea, 3rd edition, chapter 11.9: Moderately Dilute Solutions, equation for the mole flux of the component ##i## is given by: $$ N_i = - \frac {u_i c_i} {z_i F} \nabla \bar\mu_i\ + c_i v \tag {1}$$
where ##u_i## is the ionic mobility...
I am reading the following article on Kirkendall effect leading to the Formation of a hollow binary alloy nanosphere: a kinetic montecarlo study. I am unable to understand or find in references the reasoning to obtain equation (1):
I (mechanical engineer) have researched this question but can't get to an answer.
The equilibrium condition for confined particle diffusion of a solute in a solvent is reached when the solute spatial density is uniform (= zero density gradient), and entropy is max.
But per Boltzmann, when...
U=U(x,t)
Ut=DUxx; 0<=x<=L, t>0
U(x,0)=0 0<x<=L
U(0,t)=a(t); t>0 *a(t) is known function*
(dU/dx)=0 for x=L
I have looked into many ways but not one is usable for diffusion equation with this boundary conditions.
When an n-type material comes in contact with a p-type material to form pn-junction, electrons with the highest energy in the conduction band will diffuse to the p-side to reach equilibrium so the entire band structure on n-side will shift down relative to p-side as described in the following...
I was reading posts this morning on another forum and came across a question that made me start thinking about physics. Since I've always tried to satisfy my curiosity through reading and trying to learn new things, or trying to remember the things that I've forgotten years ago, I went to...
Hi, a thought just occurred to me.
We all learned in school that oxygen diffuses from the air in the alveoli into the blood, and carbon dioxide diffuses from the blood into the air to be breathed out. But they never mention nitrogen, argon or any of the other gases in the air! Does something...
The code I have for solving the diffusion equation on the spherical domain. The solution seems to differ drastically depending on the refinement of the mesh which obviously shouldn't be the case. I have checked and double checked my derivation and code and I can't seem to find an error. One...
I recently found three old vintage diffusion pumps left over by the previous lab owners:
1. Veeco EP 2A
2. Veeco EP 2A-1
3. Edwards Speedivac F203
Is there a possibility that these pumps have PCB based oil inside? I do not have access to PCB oil testing at the moment. Also any further...
Say there is a gas made up of two gas molecules: Molecule A and Molecule B.
Molecule A has a mass: ma and mole fraction: na.
Molecule B has a mass: mb and mole fraction: nb.
The gas is at thermal equilibrium and has a constant temperature throughout itself (T) everywhere. It is placed in a...
recently I'm looking for diffusion coefﬁcient of gases in liquids. I have read "THE PROPERTIES OF
GASES AND LIQUIDS" from Bruce E. Poling. but in this book it isn't directly mention what is diffusion coefﬁcient of gases in liquids. can we using liquid-liquid models for gas-liquid models?
Einstein famously derived his relation between the diffusion constant of Brownian motion, particle mobility in a disippative medium, and temperature by considering Brownian motion in a harmonic oscillator potential. The result, $D = \mu k_BT$, is derived assuming that the mobility $\mu$ is...
I've tried to show b) by using the sine Fourier series on ##[0,2a]##, to get ##g_k = \Sigma_{n=0}^{2a} \sqrt\frac{2}{a} Sin(q_k x)##
Therefore ##\sqrt\frac{2}{a} = \frac{1}{a} \int_0^{2a} Sin(q_kx)g_k dx##
These are equal therefore it is an orthonomal basis.
I'm not sure if this is correct so...
Hi everyone,
I am trying to solve the 1 dimensional diffusion equation over an interval of 0 < x < L subject to the boundary conditions that C = kt at x = 0 and C = 0 at x = L. k is a constant. The diffusion equation is
\frac{dC}{dt}=D\frac{d^2C}{dx^2}
I am using the Laplace transform method...
I want to compare diffusion of a tracer gas with a low exposure limit (e.g. isoflurane) to the advection of air by a ventilation system. When will diffusion exceed advection? I can't make sense of diffusion constant to compare transfer rates or velocities.
At room temperature the diffusion...
<Mentor moved to Physics>
My teacher talks about turbulence (2D and 3D), but I don't quite understand this. How is the turbulence different in the two buckets, and why does my teacher talk about turbulence but not diffusion? Is not diffusion the reason why the dye spreads in the water? I have...
To choose random walk on a graph, it seems natural to to assume that the walker jumps using each possible edge with the same probability (1/degree) - such GRW (generic random walk) maximizes entropy locally (for each step).
Discretizing continuous space and taking infinitesimal limit we get...
Suppose you have a non-uniformly doped piece of semiconductor (without an applied bias) such that the acceptor dopant concentration Na(x) decreases from left to right (as x increases). In this case, the equilibrium hole distribution p(x) will not be uniform since then there would be a net drift...
How a high mobility of particles over surface cause to aggregation, the professor in the class said that "high mobility causes to local equilibration and thus to a compact aggregation".. which I didn't understand..! What does he mean about local equilibration and how all connect to each other?!
I'm trying to compute a 2D Heat diffusion parabolic PDE:
$$
\frac{\partial u}{\partial t} = \alpha \{ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \}
$$
by the ADI method. I am actually trying to go over the example in this youtube video. The video is in another...
I assumed p(r,t) as p(r,t) = R(r)T(t) as Separation of Variables method. I got the expression of T(t) as
T(t) = C1eC2t
and got a non-linear differential equation in R(r) as
d2R/dr2 + (2/r)dR/dr - (C/D)R = 0
(I assumed r to be the radial distance in spherical coordinates)
Now I'm not getting...
How do the pm2.5 (particles of 2.5 microns or less) diffuse compared to gas. I noticed when i turned on my air purifier at night and turned it off at daytime. The pm2.5 particles levels go back to high after 2 hours even when my doors and windows are closed. Do pm2.5 particles pass through...
Hi,
I understand the underlying concept of changing variables in PDEs (so that we can reduce it to a simpler form), however, I am just not completely clear on the mathematics of it so I have a quick question about it.
For example, if we have the transmission line equation \frac{\partial...
Greetings,
I realized that I don't understand a fundamental fact of common Li-ion batteries.
During the charging process, electrons are forcefully extracted from the cathode and pushed into the anode. Charge balance then yields a flow of positive Li ions from the cathode to the anode (through...
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I'm trying to workout the time for an element to diffuse at set distance in microns.
I have the distance, the diffusion coefficient, just unsure which equation I actually use.
X= sqrt DT or the other one x= sqrt 2DT.
I can't seem to figure out when you use one and not the...
Suppose I have an initial condition function ##f(x,t_0 )##, which is everywhere twice differentiable w.r.t. the variable ##x##, but the third or some higher derivative doesn't exist at some point ##x\in\mathbb{R}##.
Then, if I evolve that function with the diffusion equation...
The IPCC report strongly encouraged not only trying to get our carbon dioxide emissions down to fight climate change, but to go into negative emissions so as to draw the carbon dioxide out of the air (since it's too high as it is). Wouldn't that help to fight ocean acidification too?
Because...
Hello,
I am currently working through an introductory textbook on plasma physics, and I have encountered two topics that I separately understand but seem to be at odds with one another. In a quasi neutral plasma in steady state, the following relation must hold, $$\Gamma_i = \Gamma_e.$$ In...
Problem:
We wish to find the temperature and the diffusion coefficient of water by measuring the velocity of pollen grains in the medium, due to brownian motion and other forces.
Attempt:
We have a video clip and are using the program Tracker to measure the position of the pollen grains over...
So the normal diffusion equation looks like
\frac{\partial c}{\partial t} = k\frac{\partial}{\partial x}\left(\frac{\partial c}{\partial x}\right)
I know how to get explicit and implicit solutions to this equation using finite differences. However, I am trying to do the same for an equation of...
I'm trying to solve the diffusion equation in spherical co-ordinates with spherical symmetry. I have included the PDE in question and the scheme I'm using and although it works, it diverges which I don't understand as Crank-Nicholson should be unconditionally stable for the diffusion. The code...
Trying to determine diffusion rate of a gas emitted from a body of water. I believe Fick's first law may apply:
J = -D * (dc/dx)
where:
J = diffusion rate [mg/s×cm2]
D = diffusivity constant (can be looked up based on type of gas and local air temperature)
dc = change in concentration from...
Summary: I know that the diffusion of charged particles in a magnetic field is described as a diffusion tensor with 3 components: Diff parallel to the field, perpendicular and anti-symmetric diffusion. Is this last one that I do not understand.
Dear community,
I am PhD candidate in...
Hi,
A solution contains some ions (charged particles). We are only interested in my exemple to positive ions.
It is assumed that these ions acquired some mobility under a concentration gradient. Their direction is A to B.
Then these ions encounter/cross an electric field which is oriented from B...
From many sources (Internet, Landau & Lifshitz, etc.), it is claimed that the Schrödinger's equation is a wave equation. However I do not understand why for the following reasons:
It is Galilean invariant, unlike the wave equation which is Lorentz invariant. Note that the diffusion/heat...
Hello everyone,
I wish to know if someone could help me with the adjoint multigroup diffusion equation. In particular with the terms that make up the macroscopic removal cross section. Below, both the multigroup diffusion equation and its adjoint are shown, but I'm not sure about the latter. I...
Both the heat equation and the diffusion equation describe processes which are irreversible, because the equations have an odd time derivative. But how can these equations describe the real world when we know that all processes in nature are reversible, information is always conserved? But these...
Homework Statement
Hello, I am currently working on photon diffusion equation and trying to do it without using Monte Carlo technique.
Homework Equations
Starting equation integrated over t:
int(c*exp(-r^2/(4*D*c*t)-a*c*t)/(4*Pi*D*c*t)^(3/2), t = 0 .. infinity) (1)
Result...
Homework Statement
Hello, I have a problem with my data analysis from my lab. My goal is to find drift velocity of the electron and it's diffusion coefficient. The experiment looked like this: I've measured the time difference between signals on two gaseous detectors. The source of the signal...