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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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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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47 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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Advection diffusion equation in the limit of fast exchange

Consider the following advection diffusion equation for some material with concentration $c(x,t)$ $$\frac{\partial c(x,t)}{\partial t}=v \frac{\partial c(x,t)}{\partial x}+D \frac{\partial^2 c(x,t)}{\...
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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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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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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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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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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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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 ...
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About thermal diffusion in air and water

I have a fairly simple question: Why does heat spread faster in air than in water? For me it is counterintuitive compared to the higher thermal conductivity of water. The only "empirical" answer I ...
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Diffusion: equilibrium concentration at some distance from source

Say I have a point source producing molecules X at a rate of R moles/s. X diffuses away from the point source in 3D. The diffusion coefficient of X is D m2/s. By common sense, I expect the ...
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When Pin diode is no longer junction?

For p-i-n junction with intrinsic region d, I need to answer what happened when d is very large. So from simple logic, I believe that at some point there will be no diffusion of charge carriers from p-...
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Scaling of diffusion coefficients in solids with atomic/molecular weight

I have a molecule with the atomic weight of 74 Da (KCl). It is diffusing through a solid material. I have measured the diffusion coefficient D for KCl through the solid. Can I now derive what D would ...
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Can a mechanical forced oscillation of a gas column significantly affect diffusion rates through the column?

High Frequency Ventilation (HFV) is a special type of mechanical ventilation used in critical intensive care units. Rather than moving gas volumes in bulk at conventional breath rates, HFV operates at ...
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Diffusion of electromagnetic fields

In magnetotelluric method, inside earth EM field has diffusion equation as opposed to wave equation in air. Physically diffusion of atoms is intuitive. But what does diffusion of EM field mean ...
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How exactly does diffusion of two polished metals in solid state work?

I've just learned that if you keep two polished metals pressed hard to each other surface to surface for a prolonged period of time substantial diffusion will occur. I understand how diffusion works ...
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Is there some literature where diffusing molecules have to encounter a reflecting boundary which is absorbing at some places?

I am familiar with the concept of diffusion with reflecting and absorbing boundary in 1D. My question is, is there a way by which we can write Green's equation for a boundary, in 2D, that is primarily ...
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When modeling diffusion through a tube, what surface area is used for Permeability?

Permeability is usually measured on flat specimen and it generally has these units: [amount of stuff]-[distance through which it diffused]/[surface area diffused through]-[time to diffuse]-[driving ...
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What's the difference between Brownian motion and diffusion?

I find it hard to see the differences between Brownian motion and diffusion. As I understand, both are represented by the diffusion equation – am I right? And if I'm not, how is Brownian ...
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I can't find the Einstein relation for spin diffusivity

I'm studying the article "Thermodynamic analysis of interfacial transport and of the thermomagnetoelectric system" (PhysRevB.35.4959, Mark Johnson and R. H. Silsbee); they use this relation $$ D=\frac{...
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Diffusion Coefficient from Gibbs Free Energy

I am working on a problem in diffusion and I would like to get some professional feedback. The problem is as follows: I have two substances that I want to model as ideal, non-interacting gases. Let's ...
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130 views

3D rotational diffusion coefficient and angular mean-squared displacement

I would like to calculate the rotational diffusion coefficient of a sphere to verify that my simulation algorithm is working correctly. I know that for 2D rotation (e.g. about a single axis), the ...