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
0answers
22 views

How does cream or milk diffuse into a coffee cup? [duplicate]

So I was listening to a recent podcast on Google Podcasts by Math and Physics on Particle Physics. The guest for the podcast was Dr. Pekka Sinervo. At 07:30 he says "there are lots of phenomenons ...
0
votes
0answers
14 views

How to derive $V_1 Y_1 = -D_{12} \nabla Y_1$ in Fick's law

From Forman Williams' kinetic theory Diffusion velocity can be related to Binary diff. coeff. and gradient of mass fraction as below. $V_1 Y_1 = -D_{12} \nabla Y_1$ How can be this derived? In order ...
0
votes
1answer
40 views

Heat equation with inhomogenous Neumann boundary conditions

Solving second order inhomogenous PDE by separation of variables requires homogenization of the boundary conditions. Let's say we are looking at 1D heat equation. From intuition, if we have fixed ...
0
votes
0answers
3 views

Is there a model/method to calculate the length dependent diffusivity of amyoid fibrils or polymers?

I am working on amyloid assembly kinetics and want to calculate the diffusivity of the fibrils as a function of the length to estimate their Peclet number. Are there any techniques from polymer ...
0
votes
0answers
16 views

Current definition used in kinetic theory of gases

Is the term 'effusion' still used in kinetic theory of gases , as opposed to ' diffusion' to differentiate between the passage of a gas through a solid or membrane, as opposed to 'diffusion' of a gas ...
0
votes
1answer
37 views

Is there a diffusive current in the steady state?

Consider the diffusion equation, $\frac{\partial n(x,t)}{\partial t}=D\frac{\partial ^2n(x,t)}{\partial x^2}$, inside a box from $x=0$ to $x=L$ subject to the boundary conditions $n(x=0)=0$, $n(x=L)=1$...
1
vote
1answer
58 views

Fokker-Planck equation in $N$-dimensions: a doubt regarding the average velocity

Consider the Langevin equation in the overdamped regime, $$ 0 = -\gamma \dot{\mathbf{x}} -\nabla U(\mathbf{x}) +\boldsymbol{\eta}(t) \, $$ where $\boldsymbol{\eta}$ is the usual white-noise term, $U$...
0
votes
2answers
27 views

What is 'diffusion' in a stator/diffuser?

I understand what diffusion of mass or diffusion of heat means. I know that the conversion of the dynamic head of the flow into static pressure in a stator or diffuser is called 'diffusion'. But in ...
4
votes
1answer
76 views

Diffusion of Ink in Water

I am investigating the diffusion of ink in water. A drop of blue ink is dropped to the center of a round plate of radius $R$. Say the drop of ink has an initial radius of $r=r_0$ (the very edge of the ...
0
votes
0answers
19 views

Fluctuation for diffusion flux (Fick's law)

I am trying to write the formulation for fluctuation in diffusion flux (Fick's law): $$ \vec{j}= - \rho D\vec{\nabla} c $$ Then I describe fluctuation in concentration and density as the following: ...
0
votes
0answers
16 views

Random walks and the Doppler limit in laser cooling

I have a question about some conflicting definitions I have encountered regarding the diffusion coefficient in random walks of laser cooled atoms. I was wondering if someone here may be able to clear ...
1
vote
1answer
66 views

Trouble understanding exactly why core of sun does not mix with outer layers

I’ve had trouble understanding exactly why there is not more mixing of plasma at the core of the sun with the outer layers. I understand the difference between the radiative zone and the convective ...
0
votes
0answers
15 views

Why do we have different probability densities in the forward and backward Fokker-Planck equations?

For a system involving randomness, we can find a probability distribution $\rho$ that obeys the forward Fokker-Planck equation: \begin{align} \partial_t \rho + \nabla (\vec b \rho) &= D \nabla^2 \...
1
vote
0answers
45 views

What's the difference between anomalous diffusion and non-linear diffusion?

I'm doing some research on diffusion and I came across these two terms. What's the difference between them? Is there any? Is there any example of these phenomena in semiconductor physics? Thank you.
0
votes
0answers
27 views

Diffusion on a circle?

I've been trying to solve the diffusion equation on a circle. The problem I am running into is that because of the periodic boundary, the wavevector k (when you Fourier transform) gets quantized ...
0
votes
1answer
44 views

Solution of diffusion equation for 2 infinite slabs reactor

I have exercise where I have to calculate flux for reactor with 2 same infinite slabs of multiplying medium in vacuum. I have to calculate flux inside slabs and in the slot between them. I am ...
0
votes
0answers
17 views

Diffusion on the surface of a 2-sphere

I am dealing with diffusion problems currently. Specifically, diffusion on the surface of 2-sphere. But I am unable to find a good reference showing analytical results for mean-square displacement. I ...
1
vote
0answers
40 views

How can we interpret a system in which the probability distribution obeys the forward and the backward Fokker-Planck equation simultaneously?

For a system involving randomness, there is no longer a unique derivative and hence no longer a unique definition of velocity. But for the forward (Ito) derivative, we can find a probability ...
5
votes
0answers
130 views

Why is the Fokker-Planck equation only valid for the forward and backward velocities but not for the flux velocity?

I noticed that the Fokker-Planck equation is often only written for the forward velocity $\vec b$ and the backward velocity $\vec b^*$: \begin{align} \partial_t \rho + \nabla (\vec b \rho) &= D \...
2
votes
1answer
33 views

Is the continuity equation valid for a diffusion current?

On the one hand, we have the diffusion equation: \begin{align} \frac{\partial\rho}{\partial t}&=D \nabla^2 \rho \end{align} and on the other hand, we have Fick's first law: \begin{align} \vec J = ...
1
vote
0answers
17 views

Why is the continuity equation only valid for the flux velocity but not for the osmotic velocity?

The continuity equation $$ \partial_t \rho + \nabla (\vec v \rho) = 0 , $$ can be derived from the Fokker-Planck equations for the forward- and backward velocity ($b,b^\star)$: $$ \partial_t \...
2
votes
2answers
66 views

What's the meaning of a continuity equation with $\nabla^2 \rho$ on the right-hand side?

I stumbled upon a continuity equation with a $\nabla^2$ term on the right-hand side: $$ \partial_t \rho + \nabla (\vec b \rho) = D \nabla^2 \rho , $$ where $b$ denotes the forward velocity and $D$...
0
votes
0answers
59 views

Sethna's Derivation of the diffusion equation: number of terms of Taylor expansion

I found the general narrative of the following derivation of the diffusion equation in page 20 of this book made sense, but I have a question about one particular step. In (2.11), shown in the second ...
0
votes
1answer
37 views

How can laser diffusion be reduced?

So, a laser works by bouncing photons back and forth between two mirrors until they straighten each other out and exit a small hole, like this: The problem is that no matter how much the photons ...
0
votes
1answer
37 views

Change in Fermi level Produces Electric field

I was reading book On Semiconductor Physics By Donald Neamen,In page 176 He discussed semiconductor that is nonuniformly doped with donor impurity atoms.Now Here The doping concentration decreases as ...
1
vote
1answer
51 views

Two versions of Diffusion coefficient

I found two versions of the Diffusion coefficient, first: $$D=\frac{\pi \lambda }{8}\overline{c}$$ Where $ \overline{c}$ ist the particles mean thermal velocity and $\lambda$ the particles mean free ...
0
votes
0answers
36 views

Diffusion Fick's 1st law for non-isothermal ideal gas

I have some doubts regarding diffusion. Let's imagine two chambers, with infinite volume, connected by a capillary. Both chambers are filled with the same gas, but at different temperatures, thus ...
1
vote
0answers
90 views

Can we deduce that particles behave as Brownian motions if the collection obeys the Einstein model?

The density dynamics of a continuum of particles with the dynamics $$dx^i_s = d w^i_s,$$ where $dw^i_s$, $0 \leq s$, $i \in \mathcal{N}$ is a standard Brownian motion, are given by the diffusion PDE $$...
0
votes
0answers
48 views

Problem in derivation of Smoluchowski Equation

I am trying to derive Smoluchowski equation using Fokker Planck equation. I am following the book ''Non Equilibrium Statistical Mechanics'' by Robert Zwanzig. I am attaching a screenshot of a few ...
1
vote
2answers
97 views

Moisture diffusion in air

Moist air is less dense than dry air. Additionally hot air is less dense than cold air. If we have moist hot air packets above dry cold air packets. How can the mixture of these air layers be ...
0
votes
0answers
8 views

About the sign of the scattering length

Why do we say that a triplet has a positive scattering length while a singlet has a negative one?
0
votes
1answer
32 views

Diffusion of gas across a membrane

Two adiabatic cylinders are divided internally into two equal parts by a semi-permeable membrane. The membrane only lets hydrogen pass through it. The first cylinder has one half filled with hydrogen (...
1
vote
1answer
61 views

Diffusion equations and classical mechanics

In Wikipedia it is stated that the diffusion equation can be derived from the continuity equation. It is not clear to me how the classical mechanics affect the diffusion equation. For example, if the ...
4
votes
0answers
46 views

Fokker-Planck equation for 2D SDE

Consider the following two-dimensional SDE \begin{align*} \mathrm{d}\mathbf{X}(t) &= {\mathbf{f}(\mathbf{X}(t))}\mathrm{d}t+\mathrm{d}\mathbf{W}(t)\\ \end{align*} where $\mathbf{X}(t)=\begin{...
2
votes
1answer
46 views

Origin of terms in the Nernst-Planck equation

We know the Nernst Planck equation is $$ \frac{\partial c}{\partial t} = - \nabla \cdot J \quad | \quad J = -\left[ D \nabla c - u c + \frac{Dze}{k_\mathrm{B} T}c\left(\nabla \phi+\frac{\partial \...
4
votes
1answer
146 views

Molecular vs Eddy Diffusion

Let us assume that we have two boxes that are connected by a thin permeable barrier: If both boxes are non-convective and all motions are due to the brownian motion of atoms, then I assume that you ...
0
votes
0answers
30 views

Flow always increases diffusion flux

Reading Falkovich's Fluid Mechanics (Section 2.2.4 Mixing), I became stuck when tying to understand this piece of reasoning that is meant 'to show that incompressible flows can only increase the flux ...
0
votes
1answer
42 views

Eigenvalue corresponding to the stationary state

If $M$ denotes the transition matrix of a Markov chain, then the vector $x$ that satisfies $Mx=x$ is the stationary distribution or stationary state. However, this paper seems to use the term ...
0
votes
0answers
25 views

Diffusion coefficient of Yperine (sulfur mustard) in water

I'm currently working on a project and I need the diffusion coefficients of Yperine in water. I've searched online and I haven't found anything. If any of you have information about this (or diffusion ...
1
vote
1answer
39 views

What is Ambipolar Diffusion in a plasma?

I understood the mathematical derivation from the text book. But I am having hard time imagining the phenomenon physically. Can someone please explain it to me in layman's term (or in terms of some ...
0
votes
2answers
102 views

Feynman: 'The “average time until the next collision” is obtained in the usual way:'

In The Feynman Lectures on Physics Vol I 43-1 Feynman says The “average time until the next collision” is obtained in the usual way: \begin{equation*} \text{Average time until the next ...
0
votes
1answer
17 views

Dirichlet/Neuman conditions for the concentration of oxygen at the interface air-water

I'd like to compute (with a simulation) the variation of the concentration $c$ ($kg/m^3$) of oxygen in water with a simple diffusion equation : $$\partial_t c = D\nabla^2 c $$ $$c(z=0)=c_0 $$ $$c(...
0
votes
0answers
16 views

Calculating the mutual diffusion coefficient of two spheres

I have several trajectories of two spheres and I'm trying to obtain the mutual diffusion coefficient of the two spheres as a function of their separation. I'm wondering if there is a nice way to do ...
0
votes
0answers
15 views

Nuclear Fission- One-group diffusion equation - Compute arbitrary constants

Nuclear Fission. In the one-group neutron diffusion equation it is possible to find an expression for the neutron flux for a specified geometry. For example, for an infinite slab the neutron flux can ...
0
votes
1answer
35 views

Diffusion of perfume according to fick's law

Fick's first law relates the diffusive flux to the concentration under the assumption of steady state. It postulates that the flux goes from regions of high concentration to regions of low ...
2
votes
1answer
106 views

How to derive the backward Fokker-Planck equation from a forward Fokker-Planck equation (with state-dependent diffusion coefficient)?

I am interested in a system with state-dependent diffusion coefficients. This paper by Lau and Lubensky derives the correct Forward FPE in this case: $$\partial_tP(x,t) = \frac{\partial}{\partial x} ...
0
votes
0answers
4 views

Is there any way to measure or calculate the diffuse reflection of a polymeric fibre?

I want to estimate the diffuse reflection of a polymer fibre. Is there any equation, for example, can be used to determine this value?
0
votes
0answers
23 views

Exponent of Lewis number in coupled heat-mass transfer problem

I am writing a small model of the coupling of heat and mass transfers in the nose and mouth. By solving the heat and mass balance equations, Lewis number expression appears that allows for coupling ...
0
votes
0answers
17 views

Gas Transport Problem

I have a question that I thought would be a very simple effusion calculation that sent me down a massive rabbit hole after I tried to look it up in Landau's Physical Kinetics and so now I'm coming to ...
2
votes
1answer
89 views

Derivation of heat equation

What are the main physical laws to derive the following heat equation: $$u_t -\Delta u=f(t,x)?$$ I'm wondering about the interpretation of the Laplacian $\Delta$ and its role in heat process.

1
2 3 4 5
8