Questions tagged [diffusion]

Diffusion is the net movement (spreading out) of molecules or atoms down a concentration gradient: from a region of high concentration to a region of low concentration.

Filter by
Sorted by
Tagged with
1 vote
1 answer
32 views

Relation between time it take to diffuse and temperature

I was reading Reif's Statistical physics. In problem 7 in chapter 2, It says "Consider a thin copper wire stretched out along the $x$-axis. A few of the copper atoms, located near $x=0$, are ...
0 votes
0 answers
16 views

3D information from shadows

I was holding a 1 inch diameter pipe recently on a sunny morning. I noticed that the turning the pole at various orientations changed the shadow on the ground. The closer portion of the pipe to the ...
  • 2,155
2 votes
1 answer
21 views

Relation between the diffusion coefficients

My course is giving me a strange relation I have difficulties to understand. In the context of thermodynamics and evolution, we define: The mass diffusion flux: (Newton's law) $$J_{M_d} = -D\frac{dc}{...
1 vote
0 answers
37 views

Simulating diffusion for particles undergoing Brownian motion

I am trying to do a computer simulation as part of a research project of the diffusion of a few particles undergoing brownian motion along a two-dimensional canvas. I am having some holes in my ...
  • 127
3 votes
0 answers
30 views

Do pressure gradients affect diffusion speed for gases dissolved in liquids (scuba offgassing question)

This question comes from a scuba forum where we are discussing the technical scuba technique of breathing 100% O2 during stops at shallow depths to speed up the offgassing of nitrogen (N2) from body ...
  • 31
0 votes
0 answers
33 views

Where can I find/derive these equations?

I am currently investigating the behavior of the smoke and I will need to account for the velocity of the smoke as soon as the flame is smothered. There is also the behavior where the smoke expands in ...
3 votes
2 answers
291 views

Generalized random walk process: Fokker-Planck equation

The diffusion equation $$ \frac{\partial p(x,t)}{\partial t} = D \frac{\partial^2 p(x,t)}{\partial x^2} $$ can be derived from a simple random walk on a line. For example, if the probability of ...
  • 2,698
0 votes
1 answer
30 views

Understanding the Markovian and Gaussian approximations in Brownian motion

I am trying to understand in the original derivation of Brownain diffusion, where does the assumption of Markovian and Gaussian nature factor in. In Albert Einstein's original work on Brownian motion ...
  • 2,698
0 votes
0 answers
24 views

Diffusion of gas mixtures through a membrane

Suppose we have a mixture of gases $k = 1,2 \ldots$ in a large volume with constant pressure and temperature (via external pressure and temperature control). We immerse a small volume separated via a ...
  • 621
0 votes
0 answers
12 views

Where does the negative sign in the Cahn-Hillard model of diffusion come from?

In the Cahn-Hillard model of diffusion, motion of a particle field phi is defined by the diffusion of a potential mu For electrodynamics, phi can be thought of as charge, M as the conductivity of the ...
  • 33
0 votes
0 answers
38 views

Diffusion Equation vs. Gradient Flow

I am trying to understand the connection between the 'common' diffusion equation and the evolution equation of the concentration as a gradient flow of the free energy. So let's simply assume an ideal ...
  • 101
0 votes
2 answers
37 views

What is the entropy associated with a diffusion process?

Is it possible to calculate entropy from the solution of a diffusion equation(with natural boundary conditions) by using the formula of Shanon entropy? Could anyone help me to understand the entropic ...
  • 49
3 votes
2 answers
491 views

Is diffusion a nonequlibrium process?

We know that the diffusion equation can be viewed as the continuum limit of a discreet unbiased random walk. My question is the following: Is diffusion (or an unbiased random walk) a non-equilibrium ...
  • 49
0 votes
1 answer
31 views

Is it possible to define concepts like free energy in the diffusion process?

How does the idea of free energy (which we derive from the canonical partition function) fit in the domain of non-equilibrium processes like diffusion?
  • 49
1 vote
0 answers
73 views

Henry's Law - When scuba diving, why is breathing pure $\rm O_2$ not the same as going to outer space?

In Short I had a discussion with my dive instructor the other day. He said that for "decompression dives" you can cut down decompression time to 1/3 if you switch to pure $\rm O_2$ at 6m. ...
1 vote
1 answer
57 views

Doubts about how to apply Fick's law to gas

According to Fick's law the flux of gas through a membrane depends on the concentration gradient and then on the pressure gradient: $$\Delta P = P_a - P_b$$ where $P_a$ is the pressure of container $A$...
  • 51
0 votes
0 answers
15 views

Interdifussion (binary diffusion) of Gases Boundary Condition Question

I was trying to solve this 1D unsteady state diffusion problem of two gases being mixed in a finite length of a tube over time (each end is blocked and impermeable). $$ \frac{\partial{C}}{\partial{t}}...
  • 1
0 votes
0 answers
14 views

Estimate diffusion coefficient from 2D projections of 3D trajectories?

Given the projections x(t) y(t) of the trajectories of several particles moving in 3D in a water solution, is there a way to estimate the diffusion coefficient of the 3D diffusion, if we assume it ...
0 votes
1 answer
35 views

How should I set the boundary condition of a diffuse equation in a potential well?

I want to solve the initial value problem of a particle diffusing in a well on a disk. Paticle density$\rho(\vec{r},t)$satisfy the following equation: $$ \partial\rho/\partial t=\nabla\cdot(\nabla V(r)...
0 votes
0 answers
36 views

Can mass transfer occur without a concentration difference? (analogous to the question, can energy transfer occur without a temperature difference?)

The driving force for diffusion of mass is a concentration gradient. However, mass can be transported both in a diffusive and a convective (due to the flow of a fluid) way. By definition, the combined ...
1 vote
1 answer
161 views

Random walk in finite VERSUS infinite space: Probability density functions and their interpretation

I am studying the probability density function of a random walk in a confined geometry (2D-BOX). I am also comparing this probability density function to its equivalent in infinite two-dimensional ...
1 vote
1 answer
42 views

Properties of random-walk in infinite and finite two-dimensional space: probability of two particles being in the same location at time t

I have been told that one of the property of the continuous-time random walk in two dimensions is that: $$\int_{Z} \, G(z, t | p_1) \, G(z, t | p_2) \,dz = \,G(p_1,p_2,2t)$$ where ...
1 vote
1 answer
62 views

How can NO charge carriers exist in the depletion region?

I learned that no charge carriers exist in the depletion region of a PN junction due to the balance between the diffusion current and the drift current due to the electric field created by charged ...
0 votes
1 answer
56 views

Singularities/infinities of continuity equation in polar coordinate

I encountered a bit of a difficulty in solving the continuity equation for polar coordinates. For a "fluid" or density of particles moving radially outwards with constant velocity, its flux ...
0 votes
0 answers
40 views

Probability distribution of particle diffusion system with a source and absorbing boundaries

Consider a simple 1D particle diffusion process described by the SDE $dx=\sigma dW$, where $dW$ is a Wiener process. The forward Fokker-Planck equation can then be written as $$ \frac{\partial P(x,t)}{...
  • 127
0 votes
3 answers
45 views

If the inclination of a cloud of oxygen in outer space is to diffuse, then how do nebulae form?

If a cruise ship-size object in outer space were surrounded by a spherical cloud of oxygen, and there were no other bodies exerting significant gravitational force in the vicinity, would the cloud of ...
  • 101
0 votes
0 answers
56 views

What is the mathematical derivation for no diffusion term in the mass continuity equation of the Navier-Stokes/Euler equations?

In this post the fact that the mass continuity equation in a mixture of gases has no diffusion term, i.e., $$\frac{\partial\rho}{\partial t}+\nabla\cdot(\rho\vec{v})=0$$ has been discussed. ...
  • 699
0 votes
0 answers
14 views

What resources are you aware of and can recommend me to study and model spectral diffusion?

I am looking for textbooks, papers, etc. that cover this topic in some detail and would allow me to develop a simple model to use in my BSc thesis. I'm having a hard time finding the resources I need. ...
1 vote
0 answers
29 views

Brownian motion and multi-scale stochastic processes

The Stokes-Einstein equation for the diffusion coefficient of small colloidal particles in suspension is canonically derived under the assumption that the primary motion of the particle is ...
  • 2,913
1 vote
2 answers
19 views

Differences in interactions of light with different mediums

I am trying to figure out this problem, I apologize in advance if the question is silly. If i am correct sunsets are red because red light doesnt get diffounded as much as blue light, which eventually ...
1 vote
0 answers
40 views

How can I model convection in a simple and effective way?

I have a project in which we're trying to model heating of a room. We are modelling the room in 3D. The room has realistic walls, windows and a door, which will loose heat through them. To balance the ...
  • 11
0 votes
0 answers
16 views

Physical Interpretation of Large-Time Decay Estimates of Solutions to Navier-Stokes

It is well known (see for example Hoff-Zumbrun (1995)) that solutions to the compressible Navier-Stokes equation converge in $L^p$ spaces to the heat kernel. Formally, to keep things simple, we can ...
3 votes
1 answer
106 views

An intuitive reason for the fourth derivative in the beam equation?

The appearance of the second derivative (or Laplacian in higher dimensions) in the diffusion equation ($u_t=u_{xx}$) and the wave equation ($u_{tt}=u_{xx}$) seems intuitive to me. The quantity simply ...
  • 298
0 votes
2 answers
41 views

What differentiates an alloy from diffusion at an interface?

For the thin film deposition of some metal A onto another metal B, I understand it is possible for a bit of metal a to diffuse into grain boundaries of metal B. How are these diffused atoms of metal A ...
  • 135
0 votes
0 answers
36 views

In a forward biased P_N junction, "Why does the diffusion current increase while the density difference between the carriers on both sides decreases?"

In forward bias of a P_N junction the density of minority carries increases while the density of majorities doesn't change considerably. So compared with equilibrium the difference of densities ...
1 vote
1 answer
151 views

Poisson-Nearst-Planck equations with normal distribution as initial condition

I am having a hard time trying to think of this model: Imagine you have a normal distribution of +q charges in 2D $$\rho(r,t=0)=\rho_0 e^{-\frac{r^2}{\sigma_0^2}} $$ where $\sigma_0$ is the width of ...
  • 11
0 votes
2 answers
75 views

How does dye move in water?

My understanding is that dye moves through water primarily through diffusion. The introduction to these lecture notes seems to confirm: If you we put a drop of red dye in water, it will slowly ...
0 votes
0 answers
21 views

Diffusion of a quantity down the gradient of another one?

This might be a stupid question. Let's look at the diffusion equation for, say, the temperature: $$ \frac{\partial T}{\partial t}=\nabla\cdot(D\nabla T). $$ It's simple, the temperature diffuses down ...
0 votes
0 answers
19 views

Diffusion rate of two mixed gases

From my previous post Dependancy of molar mass, i came to know that rate of diffusion depends on molar mass of gas only. Here is a particular problem. In a container under standard condition, a fixed ...
  • 749
0 votes
1 answer
28 views

Heat transfer vs calorimetry equation

I'm trying to understand the difference between the equations $$Q=mc\Delta T$$ and, $$\frac{dQ}{dt}=\frac{-\kappa\alpha\Delta T}{l}$$ Suppose, we have two metal rods at $T_1$ and $T_2$ temperature, ...
  • 453
0 votes
0 answers
36 views

A question concerning gas diffusion

We are discussing the one dimension diffusion in a tube. To simplify the analysis, we isolate two adjacent thin layers sharing a same surface, in which gas concentration could be assumed as even ...
  • 65
0 votes
0 answers
63 views

Threaded Ring Polymer - Scaling approach to Diffusion

A monodisperse melt of linear chains is mixed with ring polymers, when a linear chain threads through the opening of a ring, that rings movement becomes confined along the backbone of the chain. (A ...
0 votes
0 answers
59 views

Non-linear Diffusion Equation

I'm currently trying to solve the equation $$ \frac{\partial C}{\partial t}= \frac{\partial}{\partial x}\left(\frac{D}{C}\frac{\partial C}{\partial x}\right), $$ where D is a constant and $C \equiv C(...
0 votes
0 answers
52 views

Conservative form of the vector diffusion equation

For some reason I am unable to find a source on the internet about this. I think I have an answer, but I want to be doubly sure about this. All I could find (here), is that for an incompressible fluid,...
2 votes
2 answers
84 views

Diffusion in an interval with zeroed boundaries

I am attempting to solve the diffusion equation $$\left( \partial / \partial t - D (\partial/\partial x)^2 \right) p = J$$ where $p$ is the probability density, $J$ is a source, and $D$ is the ...
  • 23.1k
0 votes
1 answer
106 views

Displacement root mean square for diffusion and random walks

For 1D random walks we have $$x_{rms}=\sqrt{\frac{l^{2}}{\tau } t}\tag{23}$$ (in this lecture) as well as for 2D case we have $$r_{rms}=\sqrt{\frac{l^{2}}{\tau } t}\tag{19}$$, where $l$ is length of ...
0 votes
0 answers
21 views

Is my book's method of using Graham's law of effusion correct?

Problem: Let the container which contains NH3 gas be A, and which contains HCl gas is B. If both the stopcocks are opened at the same time, then determine the distance from container A at which white ...
0 votes
0 answers
14 views

Is there a way to calculate the so-called 'diffusion velocity' of neutrons?

I am conducting some deterministic multigroup pulsed-neutron die away simulations where the neutron diffusion equation is being solved via finite difference methods and would like a way of verifying ...
0 votes
2 answers
71 views

Diffusion to capture on the surface of a cylinder wall

Hi all, is it correct to use equation 10.3.4 on the above textbook for the flux of particles onto a surface of the cylinder wall (radius a, length L)? If yes, then the rate of collisions of particles ...
  • 1
0 votes
1 answer
51 views

Diffusion from bulk to cylinder wall

If D is the diffusion constant of particles, C is concentration, R is the radius, diffusion to disk-like adsorber is 4DRC, and hemisphere is 2piDRC. So what is the diffusion equation to a cylinder ...
  • 1

1
2 3 4 5
11