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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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what's the difference between viscous flow and diffusion

For a one-componet gas flow in a channel. There are a pressure i.e density difference between two ends of the channel. There will be a mass flux. My question is how to describe this flux? it's a ...
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The influence of a temperature gradient on the growth of dendrites in a solid liquid interface

Not sure if this is the correct place to ask... My book states that, for a Solid Liquid interface in which the liquid has an increasing positive temperature gradient (increasing temperatures in ...
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Why and how do holes in the valence band of the p-type material of a p-n junction diffuse through to the valence band of the n-type material

tl;dr -- See the question title I quote from this Wikipedia article on the depletion region: By definition, the N-type semiconductor has an excess of free electrons (in the conduction band) ...
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Why don't we use Leibniz integral rule when solving Diffusion equation using the Fourier transform?

My question concerns the solution to the diffusion equation: $$\frac{\partial{p(x,t)}}{\partial{t}}=D\frac{\partial^2{p(x,t)}}{\partial{x}^2}~.\tag{1}\label{1}$$ I have a question about the solution ...
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What formula can serve as an approximate estimate of the time taken for the smell of a perfume to reach somebody?

I am in an attempt to calculate the time required for the smell of a bottle of perfume to reach a person's nose $10$m away. Real life experience tells me that it takes several seconds. I tried to work ...
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Diffusion equation in sphere with boundary conditions [on hold]

I have the diffusion equation in a sphere of radius R given by: $\frac{\partial U(r,t)}{\partial t} = D[\frac{\partial^2 U(r,t)}{\partial r^2} + \frac{2}{r}\frac{\partial U(r,t)}{\partial r}]$ $D$ ...
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46 views

Classification of 2D time dependent diffusion equation

I was trying to classify the following PDE: $$\frac{\partial{u}}{\partial{t}}=\frac{\partial^2{u}}{\partial{x^2}}+\frac{\partial^2{u}}{\partial{y^2}}$$ where $u = u(x,y,t)$. I was originally using ...
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25 views

Rand-walk/Brownian-motion on 2D lattice [closed]

I started to learn stochastic processes this year. Only had two classes, but I already have some problem. We learned about Einstein's and Langevin's description of Brownian-motion and now I need to ...
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62 views

Diffusion equation Lagrangian: what is the conjugate field?

Morse and Feshbach state without elaboration that the diffusion equation for temperature or concentration $\psi$ and its "conjugate" $\psi^*$ (quotation marks theirs) has Lagrangian density: $$L=-\...
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Diffusion stopping current?

In the forward bias when electrons enter the p-type region of the semiconductor, the charge concentration is increased, and since the movement of electrons is faster than the movement of holes, it ...
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on diffusion process in semiconductor devices

Consider a PN junction. Say that the P and the N sides are just brought into contact and the diffusion process has started. We say that as the diffusion occurs, the charge carriers leave behind ...
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How to fit mean squared displacement data from nanoparticle tracking analysis?

I am trying to independently analyze raw nanoparticle tracking analysis (NTA) data, but my diffusion coefficients calculated directly from x and y pixel values only moderately correlate with reported ...
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Commutation of differential operators with boundary conditions

First post ever. Let's see how this goes... My question concerns the commutation of differential operators in the presence of boundary conditions. If it is of any help, this is relevant to me in the ...
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“Regularization” of the stationnary solution for diffusion in spherical coordinates

In spherical coordinates $(r,\theta,\phi)$, the stationnary diffusion equation is a Laplace equation $\Delta f =0$. The solution in a radial symmetry : $f=f_{\infty}-r_0/r$ where $f_{\infty}$ and $r_0$...
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How long for released dye to uniformly saturate the oceans?

Suppose a supertanker filled with purple dye breaks open at a particular point in the middle of the Pacific Ocean and spills an enormous volume of purple dye into the ocean all at once. Imagine that ...
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Diffusion 2D on a surface : diffusion coefficient and surface friction

We have a particle that is diffusing actively (meaning that the source of energy is a motor; the diffusion is like a Brownian motion, the only difference is that the diffusion coefficient is much ...
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Aggregation phenomena : How to get from a discrete to a continuous point of view

I'm studying a diffusion limited aggregation phenomenon. The $N$ particles diffuse in a box and when there is a contact they stick with a probability $p$, and let's say to simplify $p=1$. Meaning that ...
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Alternative to Fick's law of diffusion?

Let's model a concentrate $C$ with a flux vector $\overrightarrow{J}$. From first principle we can obtain the conservation law $\frac{\partial C}{\partial t} + div \overrightarrow{J}$. An adequate ...
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How can the analytical solution of the diffusion equation be used for a series of $N$ positions?

Given the exact solution to the diffusion equation: $$C(x,t) = \frac{1}{\sqrt{4 \pi D t}} \exp\left[-\frac{x^2}{4 D t}\right]$$ I am unsure as how it can be applied to a 1D series, as this equation ...
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Physical meaning of potential in heat equation

I'm working on the mathematical theory of parabolic equations. The prototype of such equations is heat equation given as follows : Let $\Omega$ be a bounded region of the space and $T>0$ a fixed ...
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55 views

Dimensional analysis on diffusion equation

I was studying the equation of motion for the probability density function of the position coordinates of the Brownian particles, also known as the Smoluchowski Equation (SE). Particularly, I came ...
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Mass transfer due to bulk and convection

What is the difference between mass transfer due to bulk flow in diffusion which is (Na+Nb)(mole fraction) and the convective mass transfer which is found by kc(concentration difference)?
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Inverse of a matrix in a Path Integral

Good morning! I can't make sense of an inverse of a matrix appearing in a calculation for a Wiener Path Integral. In discretized form: $$\int \prod_{i=1}^N \frac{dx_i}{\sqrt{\pi \epsilon}} e^{-\frac{1}...
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The derivation of the advection-diffusion equation uses $\nabla\cdot(c\vec{v})=(\vec{v}\cdot\nabla)c$. Why doesn't the order of the derivative matter?

In a derivation of the advection-diffusion equation, it is exploited that $\vec{\nabla} \cdot (c \vec{v}) = ( \vec{v}\cdot \vec{\nabla})c$, where $\vec{v}$ and c respectively are the velocity and ...
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How does flatulence travel through the room when opening a window? [duplicate]

When the smell in my room seems to be full of flatulence(it wasn't me), what happens with the gases when I open a window? Detail: It is winter and the air outside is cold whereas the air in the room ...
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Solution of the diffusion equation in a plasma

considering the diffusion equation taking into account diffusion and mobility of charged particules in a plasma of density $n(z)$ and potential $\phi(z)$, we have : $$ \frac{n(z)}{\tau}=\frac{\...
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How long does it take for oil to coalesce in water?

I was studying the process of coalescence in emulsions. We considered $N$ bubbles of liquid 1 floating in liquid 2. The result we derived, is that if there are some dissipative forces (diffusion) the ...
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Diffusion through wire cloth using Darcy's law

I am currently working on a heat pipe project and I am stuck at this point where I need to calculate if methanol can diffuse through 15 complete turns of a stainless steel wire mesh( seen in pic). I ...
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What is the decoherence rate and the thermal de Broglie wavelength in quantum Brownian motion?

I know that when the thermal de Broglie wavelength is on the order of the interparticle distance, the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. I ...
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45 views

Diffusion flux Einstein relation

I want to derive the diffusion flux $J_D$ of charged particles with charge $e$ moving in the z direction where we apply an electric field $\vec{E}=E\hat{z}$ in order to proof the Einstein relation ...
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38 views

Modelling Oxygen Diffusion [closed]

I am creating a system of differential equations to model oxygen diffusion in tissue. I have: $\frac{dP}{dt}=D_o\nabla^2P-qn$ where $q$ represents the sink rate at positions occupied by cells, $n$ ...
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Growth of bubbles in supersaturated liquid

I have read the following section which I don't fully understand (I have no technical background). It's from this article which is about the formation of bubbles of CO2 in soda drinks. When a ...
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Diffusion law for continuous domains

I'm an engineer, so don't expect too much :) I'm modelling with FEM the convection-diffusion-reaction equation which is derived by the continuity equation. $\frac{\partial c}{\partial t} +\nabla \...
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84 views

Stressing Over Stress Tensor Symmetry in the Navier-Stokes Equations

How do we know that the stress tensor must be symmetric in the Navier-Stokes equation? Here are some papers that discuss this issue beyond the usual derivations: Behavior of a Vorticity Influenced ...
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Diffusing in narrow chanels, markers and distribution of particles

I noticed 'Mixing of diffusing particles' research by E. Ben-Naim taking into account Mahonian distribution which tends to normal distribution for very large number of particles (infinite number). ...
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Derivation of diffusion equation from Fokker-Planck equation

I need your help, could you please explain me the sentence "The diffusion equation is the Fokker-Planck equation for the Brownian motion". I have tried to use some assumption and transform a ...
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Solution of diffusion equation with spherical sink

I hope this question is not too basic, but I have no experience with partial differential equations and would like to ask for some hints on how to solve the following problems: The visual idea is to ...
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Impurity diffusion from solid to air

I have to put up a simple 1D model to simulate the diffusion of impurities in a bulk material, to a top thin layer made of another material, and compare it to experimental data. I first did it with ...
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A question on $\pi=iCRT$

I was given this pretty basic question about the osmotic pressure: 1) At 25$^{\circ}$C what osmotic pressure would develop across a membrane permeable to water but not starch if there was 300 mM ...
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Random walk with Ammonia molecule [closed]

This question is from Keith Stowe's Introduction to Thermodynamics book under Random walk. The question is something like this: I am aware that I am not supposed to post homework questions like this ...
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113 views

Density Fluctuation in N-Particle Brownian Motions

I am studying spatial population movement and would like to model the density fluctuation by assuming a Brownian movement for each individual. Because the total number of individual ($N$) is large but ...
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87 views

Do electrons really diffuse when a temperature gradient is applied?

In many websites and books, it is generally said that the charge carriers, be it electrons or holes, diffuse through the considered material when a temperature gradient is applied. However I have ...
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Numerical scheme Fokker-Planck Diffusion

assuming the diffusive motion of a substance $u(x,t)$ depends on a variable $b(u(x,t))$. Fickian Diffusion then reads $$ \frac{\partial u}{\partial t}=\frac{\partial}{\partial x}\left(D(b(u(x,t)))\...
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probability density distribution: From free diffusion to presence of a barrier

I am a biologist and I am not very comfortable with statistical mechanics. However, I want to learn and I am trying to understand. I just need some clues from people that handle these topics easily. ...
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Does Fick's law of diffusion applies between mediums of different pressures with no membrane?

Imagine a stainless steal container with an unsealed lid that contains normal air, inside a room containing normal air. Now, pump a steady flow of CO2 in that container, bringing it to positive ...
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Critical mass (radius) of U235

I am calculating the critical mass (radius) of $U^{235}$ sphere. I want to calculate the mass for three different cases: 1. air/vacuum surrounds the sphere (diffusion coefficient is infinite) 2. ideal ...
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Boundary Conditions - Stratified Storage Tank Model (1D)

My task is about determining the temperature distribution through the tank height with time. So I try to solve the one-dimensional convection-diffusion-reaction equation, details in the below picture: ...
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Dimensionless numbers and fluxes

What is the meaning of dimensionless fluxes? Which are Nusselt number in case of heat transfer and Sherwood number in case of mass transfer. What is the use of these numbers? What is the difference ...
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Transport phenomenon

What is the difference between heat transfer coefficient and the thermal diffusion coefficient? What is the practical thinking of this? How would we define it practically? Like Imagining the both , I ...
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diffusion of gases in both directions

I am a technical specialist that works on analytical equipment. Gas chromatographs use carrier gases like helium and hydrogen that flow through long, thin glass tubes coated on the inner surface with ...