What is Diffusion: Definition and 476 Discussions

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



2


D
t




{\displaystyle 2{\sqrt {Dt}}}
.

View More On Wikipedia.org
  1. S

    Heat (or diffusion) equation in semi infinite region

    Homework Statement Homework Equations \[ \frac{{\partial c\left( {x,t} \right)}}{{\partial t}} = D\frac{{\partial ^2 c\left( {x,t} \right)}}{{\partial ^2 x}} \] The Attempt at a Solution First of all, I am not sure how to translate the given data to exact mathematical...
  2. R

    Diffusion across a cell membrane?

    Hi, I'm looking for information on blood and neuron cells. Specifically I need to know how the membrane transport mechanism in blood and neuron cells work? I am aware of concepts such as active diffusion, facilitated diffusion, and simple diffusion. The task is to look at the membrane...
  3. M

    Understanding Diffusion: Steady State and Boundary Conditions Explained

    Something has been bothering me recently regarding a diffusion problem. Consider a source of particles in a box, diffusing outwards. Set the boundary conditions so that the density is zero at the edge of the box. We can solve this problem in "steady state" and we find essentially a parabolic...
  4. H

    Heat diffusion equation solutions for semi-infinite slab

    Homework Statement http://img42.imageshack.us/img42/1082/clipboard01lx.jpg Homework Equations (see solution) The Attempt at a Solution I literary just spent 5 hours trying to apply those boundary conditions, trying exponentials, sines, cosines, hyperbolic function etc... I...
  5. M

    Calculating the Diffusion Coefficient of a TiAlN Alloy Coating

    Homework Statement Constant for the diffusion of hydrogen through steel is D(steal) = 4 x 10^5 cm²/s. They try to improve steel tanks for hydrogen storage by applying the coating based on TiAlN alloys. What is the diffusion coefficient Dp of such coating, if the permeability of hydrogen is...
  6. M

    Calculating Diffusion Coefficient for TiAlN Alloy Coating

    Homework Statement Constant for the diffusion of hydrogen through steel is D(steal) = 4 x 10^5 cm²/s. They try to improve steel tanks for hydrogen storage by applying the coating based on TiAlN alloys. What is the diffusion coefficient Dp of such coating, if the permeability of hydrogen is...
  7. O

    Diffusion equation with variable dissipation

    Homework Statement Solve the equation U{t}=kU{xx}+cU Hint:use an integrating factor Homework Equations The Attempt at a Solution
  8. L

    Diffusion Limited Aggregation Matlab Problem

    Homework Statement Hello, I have this project due for next Friday. I need help. Its on diffusion limited aggregation. A topic which is unfamiliar to me. I know exactly how to do the problem, but I don't know how to code it correctly. Basically I allow a seed particle to be in a location in a...
  9. P

    Neglecting brownian diffusion

    I am going to run an experiment where I have a laminar flow of water with a dye solvent. It is necessary that the velocity of the dye particles is mostly in the horisontal directions. Naturally particles will diffuse but my questions is how I can ascertain that this is kept below some...
  10. L

    Solving 2D Heat Diffusion Eqn w/ Finite Difference Method

    I have to write a FD expilicit method, for temp dist on 2D plane. I am trying to mod the 1D solver to 2D solver, the code below is a 1D solver. Any possible suggestions how it can be done? I initially, derived u(i,j+1) for 2D for in that derivation i,j corresponds to x,y... where as in 1D...
  11. X

    Why is Diffusion Called a Second Rank Tensor Variable?

    Hi all: Does anyone explain why we call diffusion as the second rank tensor variable? I understand Based on the tensor definition, we know tensor expresses the relationship between input vector and output vector. How about diffusion? what is its input vector? what is its output vector? thanks...
  12. O

    Solving the 1D Diffusion Equation: Boundary Conditions & Eigenvalues

    Technically speaking, this is not a homework problem; it is something extra that I want to explore using data from my biomedical engineering class. We recently finished a lab involving testing the design of a micromixer; now comes the analysis of the data. No where in the lab are we instructed...
  13. L

    Diffusion Limited Aggregation

    1. Hello, I got this project to show DLA on matlab. I have to write up the pseudocode, which is basically just a code explaining the bare bones of the solution. It contains no coding. I'm just wondering if I have enough information or if I'm running low. Its the first time I heard of DLA so I'm...
  14. L

    MATLAB Diffusion Limited Aggregation Matlab

    Hello, I got this project to show DLA on matlab. I have to write up the pseudocode, which is basically just a code explaining the bare bones of the solution. It contains no coding. I'm just wondering if I have enough information or if I'm running low. Its the first time I heard of DLA so I'm not...
  15. S

    How Does Solubility Influence Diffusion Rates?

    Hello everyone, I got some questions about diffusion. My note says that diffusion is affected by 1. Solubilty of solute- What do they mean by this. Does solubility increase or decrease the rate. Since water is the major liquid found inside the body. Are they referring to solubilty in...
  16. A

    Physics Physicist with background in diffusion, simulationwhat after PhD?

    Hi there, as the title already suggests, I'm currently a phd student focusing on molecular simulation of diffusion phenomena. I took this position, because I'm very interested in the application and development of simulation methods in general. However, for my taste there is simply way to...
  17. S

    Fourier method for non-uniform heat diffusion

    Homework Statement The Fourier method specifies that change of heat energy of = heat out from left boundary - heat in from right boundary segment in time Δt If vars such as c,p.. are constant in the equation, and T(-L,L) = T_a, does the the aforementioned Fourier method...
  18. S

    Heat diffusion with arrhenius source

    Homework Statement a material occupies -L < x < L and has uniform ambient temperature T_a. A chemical reaction begins within the body leading to the 1-d heat equation: pc \frac {\partial{T}}{\partial{t}} = k \frac {\partial^2{T}}{\partial{x^2}} + pQAe^\frac{-E}{RT} with BC and IC T(+/-...
  19. S

    Heat diffusion with source

    Homework Statement a material occupies -L < x < L and has uniform ambient temperature T_a. A chemical reaction begins within the body leading to the 1-d heat equation: pc \frac {\partial{T}}{\partial{t}} = k \frac {\partial^2{T}}{\partial{x^2}} + pQAe^\frac{-E}{RT} with BC and IC T(+/-...
  20. J

    Why is the diffusion coefficient in Fick's law squared?

    Hi there, I'm trying to wrap my head around Fick's first law of diffusion (for one dimension): J_{x} = -D \frac{\partial \phi}{\partial x} I understand that \phi is the concentration in units amount/volume and that x is position on the gradient in units length. What I don't understand...
  21. T

    Diffusion problem with concentration

    Homework Statement Show that concentration of a substance obeys the diffusion equation if the rate at which substance leaves a region is proportional to the concentration gradient. Homework Equations Diffusion equation: \nabla2\phi = (1/a) (d(phi)/dt) where Phi is a function of r, t...
  22. M

    General Biology - Simple/Facilitated Diffusion & Active Transport

    Homework Statement (Last one!) I think I filled out this table correctly, I just want someone to check over it for me, if you would :) Oxygen enters cells by simple diffusion, glucose enters most cells by carrier assisted (facilitated) diffusion, the sodium/potassium pump removes sodium...
  23. M

    General Biology - Faciliated Diffusion

    Homework Statement Explain why facilitated diffusion, unlike simple diffusion, is both specific and saturable. (Short essay, 4 points) Homework Equations -------------------------- The Attempt at a Solution Is this a good beginning to an answer? I feel like I can never...
  24. I

    Diffusion Equation with source term

    I have been asked to solve a diffusion equation with a source term using finite differences method. I need to numerically integrate the following equation either in MATLAB or C++. The equation is dT/dt = d2T/dx2 + S(x) The form of S(x) is some function given by a Gaussian profile...
  25. X

    Spin magnetic moment diffusion length in NMR

    Hi all: I am confused about how far spin magnetic moment goes during a finite diffusion time (such as 100 ms). As we know, due to T2 relaxation mechanism in NMR, spin 1 and spin 2 can exchange magnetic moment but no energy transfer during this exchanging process due to dipole-dipole...
  26. G

    Diffusion equation, semi-infinite solution

    help w/ diffusion equation on semi-infinite domain 0<x<infinity Woo! First post! And I'm trying out/learning the latex code which is really neato! Okay, so... please help! I'm trying to solve \frac{\partial^{2}T}{\partial x^{2}} + \frac{1}{x}\frac{\partial T}{\partial x} =...
  27. M

    Lattice Diffusion : Techniques & Procedure

    Hello, I would like to know how the lattice diffusion is done & why is it temperature dependent? I have tried googling Lattice diffusion several times, but I couldn't find any complete online reading/video... Your contributions will be highly appreciated.
  28. C

    Solving Diffusion Problem with Crank Nicholson Method

    Hi I am trying to solve the following diffusion problem using crank Nicholson method, but having trouble on how to proceed with the tridiagonal matrix and boundary conditions. dy/dt = k* d^2y/dx^2 K = increases with x My initial condition is y(x,0)=0; Boundary conditions are...
  29. C

    Diffusion Coefficient for gases at different temperatures

    Does anyone know figures for Diffusivity (diffusion coefficients) for two gases at different temperatures. Such as air - Hydrogen or air-methane. For example the diffusivity of hydrogen into air when the hydrogen is at 300C and the air at 100C. Please don't point me to Fick's laws...
  30. K

    Exploring Diffusion Paths: A Student's Project

    Hi! I'm a student and I have a project to do. It's about the diffusion's path. My problem is that I can't find a definiction of diffusion path. Could anybody be able to tell my where to look, or what is that?
  31. C

    What is the Diffusion Tensor for Isotropic Media?

    Does anyone know how to write the diffusion tensor (coefficient) for a isotropic media? It should be a matrix but I can't find it in the literature. Maybe you guys know it or can help. Jackson doesn't have it. Cheers
  32. J

    Fourier transform, diffusion equation

    Homework Statement The Attempt at a Solution I'm really at a loss on this question, which is why i have achieved so little on it so far. I think i more or less understand what a Fourier transform does (transpose amplitude vs time to amplitude vs frequency, ie the Fourier transform...
  33. S

    Reaction diffusion problem concentric spheres

    Hello, I am trying to (numerically) solve the following reaction-diffusion equation for the probability density of the a pair, \rho (\vec{r}_1,\vec{r}_2): \dot{\rho} (\vec{r}_1,\vec{r}_2,t) = D_1 \nabla^2_1 \rho (\vec{r}_1,\vec{r}_2,t) + D_2 \nabla^2_2 \rho (\vec{r}_1,\vec{r}_2,t) - k...
  34. D

    Solution to diffusion equation - different input

    Hi, I have seen the solution to the diffusion equation written as C=(N/sqrt(4PiDt))exp(-x^2/4Dt). Hoever, as I understand it, this is for an instant input of N material. I want to express the concentration of substance at a point x away from the source for an arbitrary input signal. Is there...
  35. C

    Thermionic emission and diffusion theory

    What is the main physical difference behind these two theories? 1) I understand that the thermionic emission theory is applied in metal-semiconductor contacts and heterostructures where the energy band off-sets are large. Whereas the diffusion theory is applied in a simple homojunction, of...
  36. S

    Discover Steady-State Concentration for Diffusion in a 1D Trap with U(x) = ax^2

    N particles diffuse in one dimension in the potential U(x) = ax^2, with a > 0. Find steady-state concentration, c0(x). No idea how to solve this. Any equations?
  37. S

    Protein Diffusion: How Could This Happen?

    Homework Statement You release a billion protein molecules at position x=0 in the middle of a narrow capillary test tube. The molecues' diffusion constant is 10^-6 cm^2s^-1. An electric field pulls the molecules to the right (larger x) with a drift velocity of 1 micrometer per second...
  38. E

    Solving Diffusion Equations: F'(t) / [1 - F(t)] = p + q F(t)

    The diff. eq. F'(t) / [1 - F(t)] = p + q F(t) or F'(t) = [p + q F(t)][1 - F(t)] has the solution F(t) = [1 - exp(-bt)]/[1 + a exp(-bt)] where a = q / p and b = p + q. How can I write the system of equations with the solution {F1(t), F2(t)} = { [1 - exp(-b*t)]/[1 + a exp(-b*t)] , [1 -...
  39. S

    Diffusion Equation by Method of Images

    Homework Statement I need help in solving a problem I was assigned from Numerical Methods for Physics, 2nd Ed., by Garcia. We are asked to create a solution, by hand, for the diffusion equation, using the method of images. In particular, we have a 1-dimensional bar, centered at x = 0, of...
  40. T

    The difference between the Heat and Diffusion equation ?

    the difference between the Heat and Diffusion equation ?! Please: What is the difference between the Heat and Diffusion equation ?! thank you.
  41. B

    PDE: a traveling wave solution to the diffusion equation

    Homework Statement Consider a traveling wave u(x,t) =f(x - at) where f is a given function of one variable. (a) If it is a solution of the wave equation, show that the speed must be a = \pm c (unless f is a linear function). (b) If it is a solution of the diffusion equation, find f and show...
  42. L

    Diffusion Equation/Change of Variable

    Homework Statement Apologies if this doesn't come through properly. The question states Use a change of time variable to show that the equation c(\tau) \frac{\partial u}{\partial \tau} = \frac{\partial^2 u}{\partial x^2} can be reduced to the diffusion equation. The...
  43. S

    Diffusion vs. Size: Exploring Eq. 4.14

    Homework Statement Eq. 4.14: \zeta = 6 \pi \eta R (Stokes formula) 2. The attempt at a solution In my plot, collagen, hemoglobin and lactoglobulin give a straight line, while ribonuclease is a bit above the others. I don't know which diffusion law I'm supposed to use...
  44. S

    Solving Diffusion Problem Homework Statement

    Homework Statement 2. The attempt at a solution a) The steady state concentration is the concentration when t --> infitine, right? How can I find that when I don't know c(x, 0)?
  45. S

    Diffusion Ques: Unintuitive Concentration Change Over Time?

    If the gas particles in a box are uniformly distributed in the y and z directions, and linearly distributed in the x direction, is it true that the concentration won't change with time, according to the diffusion equation? I find this very unintuitive.
  46. K

    Calculating Diffusion Constant for Phosphatidylcholine in Water

    Phosphatidylcholine is a lipid that can be found in egg yolk. When phosphatidylcholine is mixed with water it will form micelles – spherical particles. Molecular weight (Mw) for the particles is 97*000 g/mole Density for the particles is 1.018 g/cm3 The temperature is 25°C a) What is the...
  47. A

    Age Diffusion Theory and Fourier Transforms

    I am attempting to solve a second order differential, but I am have never done anything like this. I was told that it was a good Idea to think about Fourier transforms. \frac{d^{2}q}{dx^{2}}=\frac{dq}{dt} Boundary Conditions: q(+/-\infty,t)=0 q(x,0)=S_{0}\delta(x) Apparently the final...
  48. W

    A Simple Question about Diffusion and ion speed

    Greetings, I'm trying to get an intuitive understanding about a process involving an ion mobility that (I'm told) has D = 9.3 x 10-5 cm2/s. I'm assuming that D is a diffusion coefficient. I'd like to know approximately how long it takes for the ion to travel about 10 cm. Would this be...
  49. A

    Diffusion and Drift Current

    Homework Statement http://img223.imagevenue.com/img.php?image=79777_Untitled_122_69lo.jpg So for this setup i understand that the light generates EHP in the semiconductor and creates a concentration gradient which causes the electrons and holes to diffuse to the other side, so if the light is...
  50. S

    Diffusion of flavour in a fishing bait

    Hi this is my first post and so I hope it will be good one for you physicists to solve for me! In angling anglers use small round balls called boilies.Say for instance you make 2 round boilies of 14mm in diameter.When these are prepared they are boilied in water to make a tough skin.They will...
Back
Top