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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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196
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3answers
48k views

Surviving under water in air bubble

An incredible news story today is about a man who survived for two days at the bottom of the sea (~30 m deep) in a capsized boat, in an air bubble that formed in a corner of the boat. He was ...
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Why is dry soil hydrophobic? Bad gardener paradox

When I forget to water my plants, and their soil becomes very dry, during the next watering I can see that the soil becomes hydrophobic. I can even see pockets of air between the repelled blob of ...
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7answers
128k views

How can two seas not mix?

How can two seas not mix? I think this is commonly known and the explanation everyone gives is "because they have different densities". What I get is that they eventually will mix, but this process ...
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1answer
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How long would it take for a smelly object to evaporate?

This question is a follow on from this deleted one: https://physics.stackexchange.com/q/177894/26076 as I was writing what I thought to be a valid physics answer to it. Version 1 of this question ...
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2answers
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What does it mean that a substance can be smelled from far away?

I thought about this question in the middle of this video. Ok, Thioacetone takes the price for the World's smelliest chemical, I can accept it (why not?), but what about You can smell one drop of ...
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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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1answer
698 views

Why is Johnson noise a Gaussian process?

Noise processes in engineering and physics are frequently assumed to be Gaussian processes. This allows use of convenient analytical techniques. The question then arises as to why natural processes ...
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2answers
5k views

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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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 ...
11
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5answers
516 views

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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2answers
31k views

Convective and Diffusive terms in Navier Stokes Equations

My question has 2 parts: I just followed the derivation of Navier Stokes (for Control Volume CFD analysis) and was able to understand most parts. However, the book I use (by Versteeg) does not derive ...
10
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1answer
396 views

Diffusion of gases in the atmosphere

Suppose that the atmosphere is composed of 21% $O_2$ and 78% $Kr$ (instead of $N_2$). Since the density of $Kr$ is greater than the density of $O_2$, the lower atmosphere (where we live) should be ...
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6answers
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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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1answer
133 views

Stochastic process generating fractional diffusion

One way to generate Brownian motion is as follows: Define a waiting time probability distribution $\psi(t)$ and step length probability distribution $\lambda(x)$. Require also that $\langle \psi \...
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3answers
1k views

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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Diffusion coefficient for asymmetric (biased) random walk

I want to obtain a Fokker-Planck like equation by taking the continuous limit of a discrete asymmetric random walk. Let the probability of taking a step to the right be $p$, and the probability of ...
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3answers
5k views

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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2answers
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Relation of translational and rotational diffusion of a spherical particle

The mean squared displacement in time $\Delta t$ of a particle undergoing Brownian motion (translational diffusion) in $d$ dimensions is $\langle x^2\rangle = 2 d D \Delta t$, where the diffusion ...
7
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5answers
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No diffusion term in conservation of mass in Navier-Stokes equations?

I have followed derivations of the Navier-Stokes equations and I can see how the various terms arise in the "main equation", the momentum conservation equation. However I don't understand why the ...
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3answers
3k views

Collision time of Brownian particles

Let's assume two spherical particles $p_1$ and $p_2$ of finite radius $r_1$ and $r_2$, which are at locations $(\pm\frac{d}{2},0,0)$ a distance $d$ apart at initial time $t$. These particles diffuse ...
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1answer
801 views

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 ...
7
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2answers
22k views

What is the difference between the words transparent and translucent?

Merriam Webster defines transparent as: Having the property of transmitting light without appreciable scattering so that bodies lying beyond are seen clearly. And translucent as: Transmitting ...
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2answers
3k views

What is the probability density function over time for a 1-D random walk on a line with boundaries?

If a single particle sits on an infinite line and undergoes a 1-D random walk, the probability density of its spatio-temporal evolution is captured by a 1-D gaussian distribution. \begin{align} P(x,t)...
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1answer
193 views

Does QED provide a closed form for Coulomb logarithms?

The classical models for the integrand as well as the cut-offs in computing the Coulomb logarithm are pretty rough. Does quantum electrodynamics have definite expressions for the quantity $\mathrm{...
7
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2answers
346 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf j_{\...
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2answers
428 views

Why is the answer to this diffusion example unintuitive?

Imagine a linear decrease in concentration from left to right. Using Fick's first law, $J = -D \frac{d \psi}{d x}$ for all x, from left to right, we have the same flux amount because the decrease is ...
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2answers
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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 ...
6
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1answer
728 views

What formulas should I use to realistically model the diffusion of a drop of ink in a water?

I am a mathematician and am originally from the math side of stackexchange. I want to model the behaviour of a drop of ink diffusing in water. I dont want to simply use the diffusion equation $u_t(\...
6
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1answer
367 views

Simple question regarding the Green's function for the diffusion equation

The differential operator for diffusion in three dimensions is given by $\partial_t - k \nabla^2$ where $k$ is a constant. The Green's function is (according to Wikipedia) $$\theta(t)\left( \frac{1}{4\...
6
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2answers
207 views

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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2answers
1k views

Time for a particle undergoing brownian motion to reach a point in a volume

I was wondering how one could calculate the average time a particle needs to reach a random point in a small sphere (filled by water) with a radius of maybe $10 \mu m$. I thought of using the Stokes-...
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2answers
208 views

Counting of brownian particles: Point Process

Imagine a point process defined by the passage time of purely brownian particles through a given point (in 1D), line (2D) or plane (3D). I'm interested in the variance of the counts (number of ...
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0answers
332 views

What is the link between path integral source terms and the propagator?

Consider a diffusion process defined by $$\frac{\partial \phi}{\partial t} = D \frac{\partial ^2 \phi}{\partial x^2}$$ where $\phi$ is the probability density of a particle's position and $D$ is the ...
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2answers
615 views

What is the proper way to model diffusion in inhomogeneous media (Fokker-Planck or Fick's law) and why?

I'm quite confused with the following problem. Normally a one-dimensional Fokker-Planck equation is written in the following form: $$\frac{\partial \psi}{\partial t}=-\frac{\partial}{\partial x}(F\...
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2answers
5k views

Units of the Stokes-Einstein rotational diffusion coefficient

The Stokes-Einstein rotational diffusion relation tells us that we can write down a rotational diffusion coefficient for a sphere as: $$D_r \approx \frac{k_B T}{\zeta_f} \approx \frac{k_B T}{(8 \pi \...
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1answer
2k views

Diffusion of gas in a liquid with changing pressure and solubility (chemical potential)

Modelling the diffusion of a gas dissolved in water in a vertical column of water, several meters deep. Also assuming the water is completely still, so only diffusion plays a role. (Actually a model ...
5
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1answer
20k views

What is the difference between dispersion and diffusion?

What is the difference between dispersion and diffusion? Currently I believe, that diffusion is the mixture of molecules due to Brownian motion. So I read everywhere, that it happens with magnitude of ...
5
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1answer
167 views

Everyday example of diffusion unobscured by advection, wetting etc

Diffusion is an important concept in elementary science education, especially because it supports (or seems to support) the notion of matter consisting of very small everyday particles (as opposed to ...
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0answers
108 views

Green's function for moving solidification front

Consider a liquid solid interface $z =\zeta(x,t)$ moving at constant speed $v$, for a two dimensional problem. Due to solidification interface is changing it position. For simplicity heat ...
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3answers
352 views

Guessing what a simple partial differential equation is describing physically

Is there an easy way to look at a partial different equation and get a sense of what kind of phenomena it is physically describing? I have an equation that looks like this: $\partial_tA=C_3\partial^...
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4answers
21k views

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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2answers
432 views

More intuition in understanding diffusion

This is a short conceptual question: (I think I'm confusing some very key concepts, here's an attempt to try and resolve it) Systems whose dynamics are governed by diffusion, for example a particle ...
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1answer
3k views

Why viscosity is diffusive?

I'm studying fluid mechanics in more depth during my Ph. D. and there is something related with the diffusive term that has been bothering me for a long time. Looking at the convection diffusion ...
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3answers
2k views

Physical interpretation of the change of diffusion term in navier stokes equations

In the Navier-Stokes Equations, there is one term accounting for convective flow and one term for diffusive flow. At high flow rates, the diffusive term becomes much smaller compared to convective ...
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2answers
3k views

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?
4
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1answer
18k views

How does smoke move in the air and how can I direct it so it will go to a place I want it to go?

Let us assume there is a closed room with 2 people, only one of them is smoking cigarette. What equation would describe the smoke from the cigarette spreading? Is it “diffusion”? If so, what are the ...
4
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1answer
633 views

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?
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1answer
201 views

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 ...
4
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1answer
91 views

Why do individual clouds not diffuse into a single less dense cloud?

On a partly cloudy day, many individual clouds can be observed in the sky. I would expect that the moisture in the clouds would want to diffuse out into the other less dense non-clouded areas. ...
4
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1answer
98 views

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 ...