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
0answers
19 views

Is it possible to calculate how far vapor particles go?

Is it possible to calculate how far vapor particles go? I'm curious about vape pens and how far their smell goes. I thought if I think about it in terms of particles maybe I can come up with something....
1
vote
0answers
11 views

Measuring and modelling mass-loss from confined gas phase due to diffusion

I am trying to model substance losses from an enclosed higher-concentration gas phase (uncompressed CO2-enriched air) that circulates through an arrangement of containers and tubes. My intention is ...
1
vote
1answer
13 views

Energy Density of radiation and Flux

How can I prove the relation: $$\epsilon=\frac{3}{4}\frac{Q}{c}\tau$$ where: $\epsilon$ is the energy density of radiation, $Q$ is the flux and $\tau$ is the optical thickness.
0
votes
2answers
42 views

Question about application of Fick's Law

I'm reading the book "An Introduction to thermal physics" by D. Schroeder and in section 1.7 about Diffusion he presents Fick's Law for 1 dimension: $$J_{x}=-D\frac{dn}{dx}$$ where n is the ...
1
vote
0answers
23 views

Movement of a biological cell in water-Probability of collision?

Firstly, I apologize, as I am a systems biology scientist, so quite naïve when it comes to physics and mathematics. There is a chance that my question is deemed as very simple, but help would be ...
1
vote
0answers
21 views

Smoluchowski diffusion equation for 2D diffusion

I am trying to solve the Smoluchowski diffusion equation, for 50 particles in the x/y plane. I have derived the equations $$ X(t+\delta t) = X(t) +\sqrt{2D\delta t}\phi_x \\ Y(t+\delta t) = Y(t) +\...
1
vote
0answers
30 views

How to derive Fick's law of diffusion from kinetic theory?

I'm studying diffusion limits of kinetic equations and trying to figure out how one may (at least formally) derive Fick's law of diffusion (and hence the diffusion equation), i.e. \begin{align} \nabla\...
2
votes
0answers
47 views

Understanding $D \partial^2 P(x,v,t)/\partial x^2$ as a type of collision term

Using conservation of particles in a control volume in phase space (in one dimension with no sources of particles or external forces), one can derive the formal transport equation $$ \partial_t P(x,v,...
3
votes
2answers
73 views

Existence of atoms - Einstein or Smoluchowski

When Einstein's seminal work on Brownian motion is discussed, Smoluchowski's name often comes up as having derived more or less the same results as Einstein, but from the perspective of kinetic theory....
0
votes
1answer
13 views

Diffusion in porous media - interface flow

i have been working on a problem lately where i think i m missing some basic understanding: I consider the diffusion of a macromolecule in porous media, which i see as Brownian motion through the ...
4
votes
1answer
59 views

Does diffusion do work?

Imagine I drop a sugar cube of 2 cubic centimeter into a cup of distilled water and then wait for the sugar molecule to break apart and dissolves into the soon to be solution. Is there any work done ...
1
vote
1answer
35 views

Fick's law should contain a factor 2, but it doesn't. Why?

Consider the above system. We will drive the Fick's law from it. Let $\sigma(x,y)$ be the concentration inside the box centered at $(x,y)$. Then, (using some physical argument which I will skip in ...
0
votes
1answer
53 views

Free diffusion with a one absorbing boundary and one “re-loading” boundary

If we are considering free diffusion of a particle which is heavily damped then the evolution of its position $x$ can be expressed by a Langevin equation: $\dot{x} = A\cdot\eta (t)$ where $A$ is ...
0
votes
1answer
52 views

What is potential in Fick's law

I am asked to find the potential in Fick's Law of Diffusion. As I don't speak English very well, I have no idea what that potential is. The only thing I know is that Fick’s law applies to the ...
0
votes
1answer
25 views

How does phase coherence length depend on elastic collisions?

In the context of electron transport, it is stated in many references that the elastic scattering does not destroy phase coherence, but inelastic scattering is the source of the phase loss of ...
5
votes
1answer
170 views

Proving that the diffusion equation is not time-reversible

The diffusion equation (in appropriate units) is $$ \frac{\partial\rho}{\partial t}(\mathbf r,t)=\nabla^2\rho(\mathbf r,t). $$ By time-reversibility, I mean that there exists a function (bijection?) $...
2
votes
1answer
71 views

Diffusion heat on an egg

Let suppose that I have a egg at $T=20ºC$ and I assume it's almost an sphere of radius $R$, let's call it surface $S$. I put the egg inside a bath with water at $T_w=100ºC$. I want to know the ...
1
vote
1answer
29 views

Implication of velocity of Wiener's process on diffusive flux

We know that Wiener process $\omega(t)$ characterized by the probability distributions: $$p(\omega_0,t_0) = \frac{1}{\sqrt{4\pi Dt}}\exp\left(-\frac{\omega_0^{2}}{4D t_0}\right)$$ $$p(\omega_1,t_1|\...
1
vote
1answer
29 views

Cases for reasoning about mass transfer

I'm doing some simulations of a 1D system with diffusion. One boundary has a no-flux boundary condition, while the other boundary has a prescribed-flux boundary condition with a specified mass ...
5
votes
2answers
506 views

Why doesn't the Diffusion Equation with an initial condition of $u = x$ lead to an even distribution?

Diffusion equation, or Fick's second law states $$\frac{\partial u}{\partial t} = D\frac{\partial^2 u}{\partial^2 x} $$ where $u$ is the concentration of the molecules. My question is, say if we have ...
0
votes
0answers
27 views

Why are linear diffusion graphs limited to a max and min value. Graph shown in link

This is the graph https://prnt.sc/vpwcz6 I have tried various things to understand why the limits are the way they are for the specific metals. I tried to check if the limit is their melting point but ...
1
vote
2answers
56 views

How can I use the Navier-Stokes equation to model the diffusion of a gas with the data I gathered?

I am currently a senior high school student taking IB and I chose to write an extended essay in physics. The essay is about the diffusion of a gas with the research questions: "How does the ...
1
vote
0answers
33 views

Does membrane permeability affect the equilibrium reached by two different concentrations of equally charged ions?

I'm asking this question to aid understanding of the formation of membrane potential in a cell from electrochemical gradients of ions e.g. why the membrane potential is skewed towards the equilibrium ...
1
vote
1answer
26 views

Drift velocity in advection-diffusion equation

The advection-diffusion equation is given by $$\partial_{t}\rho=-\nabla\cdot\left(\rho\mathbf{v}_{drift}\right)+\nabla\cdot\left(D\nabla\rho\right)\equiv-\nabla\cdot\left(\rho\mathbf{v}_{current}\...
0
votes
1answer
39 views

Solution of the 2D stationary diffusion equation

I'm trying to find the solution to the 2D stationary diffusion equation $$-D\nabla^2P(\vec{\rho_2})=\delta(\vec{\rho_1}-\vec{\rho_2})$$ where $\vec{\rho}=(x,y)$ and $D$ is the diffusion coefficient. ...
1
vote
1answer
29 views

Meaning of Fokker-Planck with non-differentiable and/or infinite potential

The Fokker-Planck equation for a diffusing particle in the potential $V$ is $$\partial_t p = -\nabla\cdot (p \nabla V) + D \Delta p.\tag{1}$$ In the literature, one often sees this formulation used ...
2
votes
1answer
103 views

Diffusion and dispersion relation

I'm looking at some dispersion relations for some complex systems and realised I actually don't have a clear understanding of what physics I can get from a dispersion relation from equations that ...
1
vote
1answer
58 views

Why is the diffusion length defined for minority charge carriers only?

As far as I could infer from the solar cell literature, when talk is about the "diffusion length", only the minority carriers are concerned. Is there a diffusion length defined for majority ...
24
votes
4answers
5k views

Is there any way for a gas to pass through a solid metal?

Let's say that we have a gaseous or liquidus compound (I don't know if elements or compounds make a difference, take this as a thought experiment), and we have a tungsten or steel block that's 5cm (or ...
0
votes
0answers
12 views

On the continuity of the normal component of the diffusion flux

Is the normal component of diffusion flux is always continuous? I know the continuity at any surface would mean the amount of fluid that is entering through the surface is the same amount that is ...
0
votes
0answers
48 views

Is the diffusion of wave packets in time according to Schrödinger due to the uncertainty principle?

I hope this isn't too much of a 'why' question. Let's imagine we measure at time $t=0$ the momentum of a free non-relativistic particle with positive mass in 1D. What we find is a certain momentum $...
0
votes
0answers
35 views

Brownian motion and the heat equation

Einstein showed that the Brownian motion provides a solution to the heat equation. As written here, the relation between the brownian motion and the heat equation can be shown by the taylor series. ...
0
votes
0answers
20 views

Peak splitting in one-component reaction–diffusion equations

I am studying a one-component reaction–diffusion equation: $$ \partial_t u(x,t) = D \partial^2_x u(x,t) + R\left(u(x,t)\right)$$ Looking at systems that exhibit a peak solution (solitary localized ...
-3
votes
1answer
46 views

Why atmospheric pressure exist related?

My Question is That? There are a variety of gases that are in our atmosphere. They all together create an atmospheric pressure. why this pressure exist I mean look at outside the earth there is ...
0
votes
0answers
91 views

Root Mean Square Displacement of Diffusion and Radial Diffusion Function

I read, that for normal diffusion the root mean square displacement $\sqrt{\langle x^2(t)\rangle}$ (for particles at the origin) can be interpreted as the mean distance the particles have with respect ...
3
votes
3answers
124 views

Why diffusion happens?

The reason we smell fragrance from a far distance is due to the diffusion of its molecules. But which force causes this diffusion? Which forces cause the material to propagate from higher density to ...
3
votes
0answers
29 views

Diffusion of a particle between two immiscible liquids

I am trying to find a model, or construct my own to describe the diffusion of a particle between layers of immiscible fluids with different densities. The particle size is much larger than the sizes ...
0
votes
0answers
33 views

Can one model fluid flow only by using the convection–diffusion equation?

Modeling fluid flow in a coil seems very complicated, especially for turbulent flow. Having Navier-Stokes equations seems to be the right way to go, but I was wondering... can one use the convection-...
2
votes
1answer
38 views

Formula for flux of electrons in 1D from carrier density profile

This content was taken from https://ecee.colorado.edu/~bart/book/contents.htm. In that they derive the diffusion current expression from this particular carrier density profile. Their derivation is as ...
0
votes
1answer
33 views

Corrected Diffusivity in Draken's equation

In the article I have been reading, we introduce the term "corrected diffusivity". Diffusion alone and the rest of the article is pretty much clear, but I can't quite grasp the physical ...
0
votes
0answers
8 views

Diffusion-limited aggregation and the particles mobility

How a high mobility of particles over surface cause to aggregation, the professor in the class said that "high mobility causes to local equilibrium and thus to a compact aggregation".. which ...
4
votes
1answer
167 views

Advection-diffusion with periodic boundary conditions

Context: Consider the advection-diffusion equation with periodic boundary conditions (PBC) over a flat square domain $L \times L$. The scalar density $\rho $ is transported by a prescribed field $\...
-1
votes
1answer
59 views

Solution of the 1D diffusion equation

This equation is related to a similar question I have asked before here-Diffusion profile for localised release. I am trying to solve this equation numerically in MATLAB. I have approximated the ...
0
votes
1answer
20 views

Diffusion profile for localised release

I am trying to solve the 1-D diffusion equation in a tube of finite length that extends from $-L\leq x \leq L$. I have assumed that the radius is much smaller than the length of the tube so that we ...
0
votes
2answers
57 views

Heat equation with a source and homogenous boundary and initial conditions

I am trying to solve the following: $$\frac{\partial^2u}{\partial x^2}-3\frac{\partial u}{\partial t}=-9$$ $$u(0,t)=0=u(\pi,t)$$ $$u(x,0)=0$$ So solving the homogenous case first by separation of ...
2
votes
3answers
219 views

Why would tennis balls filled with sulfur hexafluoride explode?

An answer at Chemistry.SE tells the following anecdote: Another fill gas to avoid is sulfur hexafluoride. A tennis ball manufacturer once decided to fill tennis balls with sulfur hexafluoride, ...
0
votes
1answer
65 views

Why the rate of effusion of a gas through an orifice is inversely proportional to the square root of the absolute temperature?

The net rate of effusion of a gas through orifice is given by the following equation: $$ r = \frac {\Delta P A}{\sqrt {2 π R T M}}$$ Rest being constant, the rate of effusion is inversely proportional ...
2
votes
1answer
76 views

Analogous structure of Diffusion and Schrödinger equation and definition of flux?

I came across some analogous structure of diffusion and the quantum mechanical particle (Schrödinger eq.). I have seen that there have been similar questions asked, but the (probablitily flux and the ...
0
votes
0answers
15 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
93 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 ...

1
2 3 4 5
9