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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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5k views

### Schrödinger equation derivation and Diffusion equation

I am aware of the debate on whether Schrödinger equation was derived or motivated. However, I have not seen this one that I describe below. Wonder if it could be relevant. If not historically but for ...
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### What is the exact difference between diffusion, convection and advection?

I have tried to explore the information but still not very clear on the exact difference between diffusion, convection and advection. Can anyone help me out to clear my concept?
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### How do I set up the tridiagonal matrix for a heat diffusion with layers of different thermal diffusivity?

I have Scala code that recreates the Crank-Nicolson solutions for the diffusion equations, and matches 'Excel for Scientists and Engineers' (Joe Billo, Wiley). However, I would like to be able to ...
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### What is the difference between the diffusion equation and the heat equation?

I know that the diffusion equation is a more general version of the heat equation. But what is the exact difference informally?
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### Show that the boundary layers diffuse out from the plate with speed $\sqrt{\frac{\nu}{t}}$ [closed]

I was wondering if somebody would be able to help me with this problem. I know how to solve it using dimension arguments but I'm unsure what is meant by transformation techniques. Any help would be ...
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### Characteristic length for the diffusion equation (temperature)

The background: I'm doing some simulation work involving the diffusion equation in 1D. Specifically I have some temperature profile, constant thermal conductivity and fixed temperature at each end of ...
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### How quickly do farts spread?

Basically I started thinking this question in regard to farts. I thought to myself, say Alice and Bob are in a room. If Alice farts, how long would it take for Bob to pick up on the smell? After a bit ...
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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 ...
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### What is the difference between solutions of the diffusion equation with an imaginary diffusion coefficent and the wave equation's?

The diffusion equation of the form: $$\frac{\partial u(x,t)}{\partial t} = D\frac{\partial ^2u(x,t)}{\partial x^2}$$ If one chooses a real value for $D$, the solutions are usually decaying with ...
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### What is the physical meaning of diffusion coefficient?

In Fick's first law, the diffusion coefficient is velocity, but I do not understand the two-dimensional concept of this velocity. Imagine that solutes are diffusing from one side of a tube to another (...
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### Do particle velocities in liquid follow the Maxwell-Boltzmann velocity distribution?

The Maxwell-Boltzmann velocity distribution arises from non-reactive elastic collisions of particles and is usually discussed in the context of the kinetic theory (for gases). There are various ...
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### Why is it difficult to mix helium and nitrogen gases?

I recently learned an interesting fact: That it's difficult to mix helium and nitrogen gases in a compressed gas cylinder. Gas suppliers that need to mix the two gases have to rotate the cylinders for ...
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### Characteristic time for heat diffusion

I often see that one can write the characteristic time (or time scale) of a diffusive process as: $\tau = \frac{L^2}{d}$ where $L$ is the characteristic length and $d$ is the diffusion coefficient. ...
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### Dependance of diffusion coefficient on size?

What's the dependance of the diffusion coefficient on size? More explicitly, suppose I have a particles of characteristic length $l$, dissolved in a liquid. How does $D$, the diffusion coefficient of ...
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### How fast will sublimed dry ice mix with air?

I saw this photo and wondered: Will the CO2 stay mostly in a layer on the floor with the rest of the atmosphere resting on top, or will it quickly diffuse throughout the room? This lab is probably ...
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### Why do lighter atoms and molecules diffuse upwards?

If a relatively light atom such as helium is released in the middle of a room, it will tend to diffuse or random-walk upwards. If a relatively heavy atom such as argon is released in the middle of a ...
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### How fart is transported through air?

As we know diffussivity of gas is really slow (e.g. $\require{mhchem}\ce{O2}$ and $\ce{H2O}$ in the air are respectively $0.176$ and $0.282 ~\text{cm}^2/\text{s}$). here is a example to specify how ...
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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 ...
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### Does nature really follow the heat equation?

I think the heat equation says that the first derivative of temperature with respect to time in a stationary solid varies as the negative of the second derivative of temperature with respect to ...
Say the diffusion coefficient of the concentration of a particle in a fluid in 3-dimensions is $D_{3\textrm{d}}$. Can we estimate the diffusion coefficient of the same particle in the same fluid, in a ...