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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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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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 ...
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56 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 ...
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69 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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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 ...
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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 $\...
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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 ...
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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 ...
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2answers
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $n(x=0)=0$, $n(x=L)=1$...
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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, $U$...
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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 ...
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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 ...
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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: ...
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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 ...
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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 ...
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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 \...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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 \...
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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 = ...
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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 \...
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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 $D$...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $$...
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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 ...
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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 ...

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