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
0 votes
3 answers
42 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 ...
user avatar
0 votes
0 answers
41 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. ...
user avatar
  • 699
0 votes
0 answers
11 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
23 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 ...
user avatar
  • 2,863
1 vote
2 answers
18 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 ...
user avatar
1 vote
0 answers
37 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 ...
user avatar
  • 11
0 votes
0 answers
14 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 ...
user avatar
3 votes
1 answer
53 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 ...
user avatar
  • 163
0 votes
2 answers
35 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 ...
user avatar
  • 135
0 votes
0 answers
30 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 ...
user avatar
1 vote
1 answer
140 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 ...
user avatar
  • 11
0 votes
2 answers
43 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 ...
user avatar
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 ...
user avatar
0 votes
0 answers
15 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 ...
user avatar
  • 585
0 votes
1 answer
27 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, ...
user avatar
  • 417
0 votes
0 answers
26 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 ...
user avatar
  • 65
0 votes
0 answers
61 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 ...
user avatar
0 votes
0 answers
54 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(...
user avatar
0 votes
0 answers
41 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,...
user avatar
2 votes
1 answer
58 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 ...
user avatar
  • 22.9k
0 votes
1 answer
73 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 ...
user avatar
0 votes
0 answers
17 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 ...
user avatar
0 votes
0 answers
13 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 ...
user avatar
0 votes
2 answers
56 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 ...
user avatar
  • 1
0 votes
1 answer
44 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 ...
user avatar
  • 1
0 votes
0 answers
40 views

What's the difference between Debye length and electrons diffusion length in a n-type semiconductor?

I was reading a book about semiconductor physics and I came across this doubt about the diffusion of majority carriers. The problem was that of a (compensated) n-type doped sample where some radiation ...
user avatar
2 votes
1 answer
172 views

How can we represent thermal energy and heat diffusion in the Lagrangian?

My question has two parts. But let's first introduce the problem: In Lagrangian mechanics, a central part is the Lagrangian $$ \mathcal L\left(t, q,\dot{q}\right) = T\left(t, q,\dot{q}\right) - V\left(...
user avatar
9 votes
2 answers
1k views

Inverting the heat equation

I have a wire that stretches from $x=0$ to $\infty$. The temperature at $x=0$ is given by the unknown function $f(t)$ for $t$ from $-\infty$ to now ($t=0$). I can measure the temperature of the wire ...
user avatar
  • 325
0 votes
1 answer
18 views

FEM for propation of light through optical tissue / boundary conditions

FEM has been used extensively to model the diffusion of light through scattering material. (See for example: NIRFAST software. While I find it easy to understand the formulation of the diffusion ...
user avatar
0 votes
2 answers
126 views

How to modify single phase fluid/solid coupled PDEs to account for a phase change?

I have two PDEs that model both fluid and solid temperature change due to fluid flow through a packed bed. Schematic and equations here (where the f and s subscripts are for the fluid and solid ...
user avatar
9 votes
2 answers
364 views

Is the Navier-Stokes equation valid in $d=2$ spatial dimensions?

In this article, the authors study the time behaviour of the velocity-velocity correlation function of a particle in a gas. If the gas is immersed in $d$ spatial dimensions, they find that $$ C(t)=\...
user avatar
  • 2,895
0 votes
0 answers
15 views

1D flow equation with source inside the medium

How do I set up and solve a 1D flow problem which looks like this - i.e There is a source of water injecting directly into the medium at a point $a$ distance away from the origin. The source is time-...
user avatar
0 votes
0 answers
25 views

Diffusion on a manifold

I am trying to read this paper (which can also be found here). This paper makes the following claim about diffusion on a manifold Quantitatively, diffusion from an initial position $x$ to a final ...
user avatar
0 votes
1 answer
19 views

Feasibility of the Diffusion Equation to Model Electric Charges in a Conductor

Background: Given that equilibrium solutions of charges in a spherical shell formed from a conductor satisfy the Poisson problem $\nabla^2 \Phi = - \frac{\rho}{\epsilon_0}$ as a corollary of the ...
user avatar
  • 133
1 vote
2 answers
127 views

Mass diffusion from a point source in spherical coordinates

Is an analytical solution for the mass diffusion from a point source in spherical coordinates even possible? I posted what I thought was a valid solution here but the plot doesn't align with my ...
user avatar
0 votes
0 answers
92 views

How to calculate convection between a hot and a cold area through a circular hole?

Consider the below problem: where we have two half infinite worlds with $T_2 < T_1$ and a circular hole with the diameter of $D$ in an infinite isolating wall. There is no ...
user avatar
  • 323
0 votes
2 answers
59 views

Groundwater flow with external forcing

I want to solve the diffusion equation in porous media with some external forcing at the origin. The regular diffusion equation- $$ \frac{\partial h}{\partial t}=D\nabla^2h $$ But I want to solve for ...
user avatar
0 votes
1 answer
71 views

Asymmetric Random walk with a pause [closed]

In the non-equilibrium statistical mechanics framework, there are two basic paradigms for defining the dynamics of the system: the Langevin and Fokker-Planck equations for diffusion processes and the ...
user avatar
2 votes
2 answers
67 views

Interpreting distance in random walk

I've recently started reading about the random walk, from different sources across the internet, and there is this small detail that I'm not being able to wrap my head around. Suppose we have, a ...
user avatar
0 votes
2 answers
45 views

'Convective' Fourier number

I'm working with a numerical solution to a 1D advection-diffusion equation for a multiphase problem, with convective exchange between the gas and solid phase. A non-dimensional parameter which comes ...
user avatar
  • 1
0 votes
0 answers
16 views

Fick's law for charge distribution in conductor

I am working on a project in electrodynamics. One part of the procect is to calculate how a charge distribution in a conductor would "smear out" over time. Another person in the group ...
user avatar
1 vote
2 answers
95 views

What does it mean for a degree of freedom to come to thermal equilibrium?

I'm learning about diffusion speeds of particles in aqueous solution and the fundamental concept is thermal energy. The notes I'm working from say that "every degree of freedom comes to thermal ...
user avatar
0 votes
1 answer
44 views

How to formulate a PDE for diffusion between two different materials?

Suppose I have two (connected) materials with different diffusion coefficients for which I am modelling diffusion. Consider the one dimensional case. I am not sure what conditions to impose at the ...
user avatar
  • 103
2 votes
1 answer
80 views

How can mass diffuse out of a lagrangian control volume when it always tracks the same mass?

I am trying to understand how mass conservation in fluid flow works and how it relates to lagrangian and eulerian control volumes. The way I understand eulerian control volumes is that they are ...
user avatar
4 votes
0 answers
45 views

Why is thermal conductivity of a gas higher than one would think from diffusion coefficient

When we study kinetic theory of gases we find relationships between the processes of diffusion, heat conduction and viscosity, and collisions in the gas. In particular the diffusion coefficient is ...
user avatar
22 votes
7 answers
4k views

Does diffusion cause the bottle to move to the left?

There is a solution of solute and water inside the bottle, placed on a smooth horizontal surface with no friction, with the density of the solute greater than the density of the water, and the ...
user avatar
  • 333
1 vote
0 answers
43 views

How to get marginalized Fokker-Planck equation for the time-dependent Gaussian velocity distribution?

I have come across the term "Marginalized Fokker-Planck equation! ", which I have never heard of and could not find any resource online. The equation reads as following $$ \frac{\partial}{\...
user avatar
  • 31
2 votes
0 answers
26 views

How "Mean free passage time" depend on the temperature? [closed]

The mean free passage time in the Kramer's potential escape problem is given by $$ \tau_{MFPT} = \frac{2\pi \gamma} {\omega_{min} \omega_{max}} exp^{\beta({U_{max} - U_{min}})} = \frac{2\pi \gamma} {\...
user avatar
  • 31
0 votes
1 answer
42 views

Negative diffusion, or force that changes particle velocity distribution

Here is my problem: I am studying the dynamics of particles with a 1D "random" force. This "random" force is expressed as a Fourier series (sum of cosines) with a random initial ...
user avatar
  • 1
0 votes
1 answer
156 views

Random Diffusion - Variance of the distribution

In most of the textbooks, I have read, for a random diffusion, it is given that the random displacements are chosen from a normal distribution with zero mean, and variance $$\sigma^2 = \frac{2k_BT\...
user avatar

1
2 3 4 5
10