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.

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Approximate the bilayer heat equation

If we consider a bilayer material the heat equation will be: $$\frac{\partial\Phi_0}{\partial t} -D_0 \frac{\partial^2\Phi_0}{\partial^2x}=q_0(x,t)$$ for $0<x<s$ $$\frac{\partial\Phi_1}{\partial ...
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Understand how diffusion film for LED lighting work

I'm reading the datasheet of a Diffusion film for LED lighting: Kimoto OptSaver L-series. As far as I understand here the "Total light transmittance" parameter states how much of the ...
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Why is the rate of diffusion of a gas dependent on the partial pressure of that gas, rather than the overall pressure gradient across the mixture?

I can intuitively understand that Brownian motion will gradually disperse gas molecules from an area of higher concentration to an area of lower concentration, until a uniform partial pressure is ...
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32 views

Co-ordinate transformation of diffusion and heat equation PDE for dimensionless $r$ (1D spherical case)

I'm trying to simulate the drying of a particle using the heat and diffusion equations for a 1D spherical case $$ Heat: \frac {\partial T}{\partial t} = \frac{\alpha}{r^2}\left[\frac{\partial}{\...
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Diffusion due to difference in partial pressure

I learnt about diffusion as the flow of component from a region of higher concentration to lower concentration. Fine, I understood this because for example , if we spray a perfume at one corner of an ...
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Diffusion time with a variable mean free path

If I have a population of particles diffusing outwards with mean free path $\lambda$, the time taken for them to reach an average displacement $R$ from the centre is $$ ct = \frac{R^2}{\lambda}, $$ ...
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Similarity in the solution for diffusion and Schrödinger equations [duplicate]

Both diffusion and Schrödinger equations are PDEs (first order in time and second order in space) with a different physical meaning. When solving a simple case of 1d diffusion with fixed boundary ...
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Intuition re. log scale versus linear scale

I have a dataset with the speed of movement of two sets of particles (the red, slower, and the blue, faster) as calculated by the diffusion constant. Below is a histogram, on the left on linear scale ...
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Is 1D diffusion equivalent to diffusion in symmetrical coordinates?

Say you are modelling heat diffusion from hot air into a sphere. The thermal conductivity is the same at all positions on the sphere. Using the 1D diffusion equation, the temperature of the sphere is ...
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What is the meaning of Thouless energy?

Wikipedia article says "a measure of the sensitivity of energy levels to a change in the boundary conditions of the system", which I don't really understand. Thouless energy is defined as $$...
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Force of tension of elastic band around a group of cylinders(atoms)

For my FYP we are building a model that represents interstitial diffusion, with a group of atoms and a smaller atom that will move between interstices all surrounded by an elastic band where the force ...
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Does diffusion happens for the photons from higher concentration to lower concentration

I understand that it is the random motion of the molecules that causes them to move from an area of high concentration to an area with a lower concentration and the diffusion will continue until the ...
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How fast do very small particles diffuse through still air?

I have been trying without success to find the rate at which small particles, on the order of $3\cdot10^{-10}\mathrm{g}$, diffuse in air at room temperature $-$ say 20 to 25 degrees C. The purpose of ...
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Can I simplify computational fluid dynamics using the average values in 9 squares on an excel spreadsheet?

I wrote an excel VBA program that shows how a dye diffuses through water by taking one spreadhsheet cell and getting the average dye concentration for this cell and 8 of its immediate neighbours and ...
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Why smoke particles go down? [closed]

Let's say in an apartment the upstairs neighbor smokes but the smoke goes down to the below neighbors. Is it a difference in temperature that causes the smoke to flow down instead of going up through ...
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Quantifying how fast gases reach equilibrium again when opening a window

When opening a window in a typical room with higher CO2 and lower O2 concentrations compared to the outside, how fast does it equilibrate again? Assuming no wind, just diffusion, the answer still ...
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Heat diffusion in an oven

I have this problem where I am preheating an oven to reach $n^\circ$. So lets say within the oven there's a heating element at the bottom, which in turn heats up the rest of the oven. Assuming that ...
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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....
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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 ...
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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.
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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 ...
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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 ...
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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) +\...
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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\...
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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,...
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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....
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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?) $...
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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 ...
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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|\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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28 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}\...
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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. ...
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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 ...
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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 ...
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121 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 ...
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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 ...
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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 ...
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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 $...
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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. ...
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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 ...

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