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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.

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.

564 questions
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Expression for "rotational diffusivity"; orientation random-walk of thin rod-like particles?

From this answer and from the Stokes-Einstein equation the diffusivity of a particle of radius $R$ in a fluid of viscosity $\eta$ is $$D=\frac{k_B T}{6 \pi \eta R}$$ where $\xi=6 \pi \eta R$ is a coefficient of friction Stokes' law such that for…
uhoh
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Einstein's relation and osmotic pressure

How can I derive the Einstein's relation $D=k_{b}TB$, where $D$ is the diffusion coefficient and B is the mobility coefficient, from the concept of osmotic pressure?
Andy Bale
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Why is the mean free path divided by $\sqrt{2}$?

In the equation in the picture, the mean free path $\lambda$ is described as the volume occupied by a molecule, divided by the volume of the molecule times root two. I do not exactly grasp the purpose of dividing by $\sqrt{2}$, could someone…
Vera Marya
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Interpreting an anomalous subdiffusion exponent

I'm studying a process that involves diffusion through a porous film; as such, subdiffusion is expected for this system. My experimental data is consistent with subdiffusion, with an exponent of $\sim 0.2$ (in the Wikipedia notation, $\alpha=0.4$).…
Pete
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Rigorous derivation of Fick's first law

I am looking for a rigorous derivation of Fick's law, i.e. that the current density $\mathbf{j}$ satisifies $\mathbf{j} = - D \nabla u$ where $u$ is e.g. some concentration and $D$ the diffusion constant. I know how it could be done in one…
Étienne Bézout
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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 lower density regions?
Aria
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Fick's first law inhomogeneous proof

I have seen Fick's first law of diffusion derived for a homogeneous material many times, however I am struggling to find a satisfactory proof for inhomogeneous, particularly for particle diffusion. Why does it take the form: $$D {\partial \phi \over…
user2350366
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Diffussivity of gases, molecular weight and Lewis number

I am trying to understand the following figure of laminar premixed flames: The Lewis number is defined as $Le = \frac{\alpha_{mix}}{D_{fuel}}$ where $\alpha_{mix}$ is the thermal diffusivity of the mixture and $D_{fuel}$ is the mass diffusivity of…
l3win
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How to model tea diffusion/osmosis?

How should I model the tea concentration as a function of time after a tea bag has been submerged? Is there a simple way of measuring the tea concentration?
user1778
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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 here). Let $j(x+dx/2,y)$ be the flux across the…
Our
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Factor of 1/3 in diffusion constant

In Feynman's Lectures on Physics, it says that the diffusion constant for a diffusive gas may be written as $$D=\frac{1}{3}lv$$ where $D$ is the diffusion constant, $l$ is the mean free path between collisions, and $v$ is the average velocity.…
Ian
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Why doesn't the diffusivity of a particle in a fluid depend on the particle's density?

From this answer and from the Stokes-Einstein equation the diffusivity of a particle of radius $R$ in a fluid of viscosity $\eta$ is $$D=\frac{k_B T}{6 \pi \eta R}$$ where $\xi=6 \pi \eta R$ is a coefficient of friction Stokes' law such that for…
uhoh
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vote
1 answer

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 the definition of $B^2-4AC$ and found this equation…
Shaun
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Diffusion vs Advection

As defined in Wikipedia; diffusion is the net movement of molecules or atoms from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical potential) as a result of random motion of the molecules…
user65035
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2 answers

Proving diffusion spreads perpendicular to level curves

So this has been bothering me for a little while. When you consider scalar diffusion like $\frac{dc}{dt} = D\nabla^2 c$, where $c=c(x,y)$, most people would say that the scalar will move downhill. Now it is certainly true that the scalar is going to…
tnevins
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