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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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6answers
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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535 views

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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2answers
528 views

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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1answer
18k views

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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1answer
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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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Finite difference formulation of the heat equation with thermal conductivity in 1D

This may seem trivial, but I'm having some trouble deriving the finite difference form of the heat equation with a thermal conductivity function $a(x)$ depending on $x$: $$\frac{\partial u(x, t)}{\...
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2answers
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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 ...
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4answers
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How does the dissolution of salt affect the solution density?

Suppose you have a container of water as a solvent and you a certain amount of salt as a solute sitting at the bottom of the container that has yet to start dissolving. Supposing temperature and ...
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3answers
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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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7answers
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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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2answers
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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 ...
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3answers
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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
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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
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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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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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3answers
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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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4answers
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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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4answers
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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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3answers
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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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2answers
4k views

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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1answer
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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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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 ...
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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
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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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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 ...
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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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2answers
364 views

Existence of gusts of wind, an anomaly?

Enthusiast + Student, not a pro, so pardon my ignorance. How can wind possibly flow in gusts? The way I understand it, a gust is a pocket of air which hits you at slightly higher speed. But how ...
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1answer
1k views

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 ...
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Why would oscillation of a gas column inhibit rather than promote mixing?

Many years ago I helped to support an experiment conducted in Japan which investigated the effects of high frequency oscillation ventilation (HFOV) on the mixing and distribution of gas into the lungs....
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1answer
2k views

Diffusion vs Gravity in water: does a dissolved ion tend to “sink”?

Im a french student in geochemistry. My question might be silly, but I became really too confused to answer it myself. Does gravity affect the diffusion of ions in water ? Lets imagine a vertical ...
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0answers
270 views

Why is it valid to assume that the liquid-vapour interface is always saturated during evaporation?

For steady state evaporation, I read from two textbooks which simply states that the partial pressure of vapour of interest (say water) at the liquid-vapour interface is equal to the saturation ...
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1answer
177 views

Gillespie's stochastic framework valid for particles in aqueous solution?

Gillespie proposed a stochastic framework for simulating chemical reactions which is predicated on non-reactive elastic collisions serving to 'uniformize' particle position so that the assumption of ...
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0answers
732 views

Temperature dependence for specific thermal diffusivity in the diffusion formula

I recently found this answer about the diffusion equation (nice one actually), but have one doubt about the temperature dependence of this formula. If the "packet" of energy (terminology suggested ...
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1answer
223 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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2answers
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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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0answers
112 views

What physical processes govern the formation and shape of clouds? [closed]

There are many kinds of cloud shapes that appear in the sky. In fact, it's not unusual to see several different kinds of clouds in the same sky. What kind of physics equations and processes govern ...
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1answer
99 views

Reaction-diffusion. From kinetic parameters in 3D, can we infer their equivalent in 1D?

I am studying a reaction-diffusion system : $A+B ⇌_{k_{-}}^{k_{+}} C$. From experimental data I have all the kinetic parameters : diffusion coefficients $d$ and reaction rates $k_+$, $k_-$. Beside I ...
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3answers
345 views

Physical Interpretation of the Diffusion Constant $k$

I have read technical explanations of the interpretation: ''Diffusion coefficient is the proportionality factor D in Fick's law (see Diffusion) by which the mass of a substance dM diffusing in ...
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3answers
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When I open a window to air out the room, how does the smell disperse?

Let's say I'm in a room with some kind of noxious stink, possibly of flatulent nature. The quickest way to right the world that comes to mind is to open a window. When I open a window, how do the ...
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2answers
813 views

Why do the free electrons in N-type want to diffuse?

I'm trying to understand how a diode works and for this I've used(among other resources) the book written by Albert Malvino, Electronic Principles. Everywhere I read about this topic, it says that ...
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1answer
257 views

How to measure percentage of nitrogen present in Nitro Coffee

Starbucks had launched nitro coffee. Unlike carbonated, this coffee contains nitrogen gas which makes that peculiar down draft waviness in the drink. In carbonated beverages, the gas effervescence and ...
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1answer
233 views

Confusion about Fick's first law

Consider a binary system of mass transport (A, B). Some of mass transfer books (Skelland and Welty) say that the relation $$J_A= -C D_{AB} \frac{dx_A}{dz} \tag{I}$$ is more general than $$J_A= -D_{AB} ...
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1answer
225 views

Speed of spontaneous mixing of different gases

Suppose we have a rectangular box divided into two equal cubic parts by a vertical impenetrable wall. Part 1 of the box contains a standard state mixture of $(1-x)$ mole of gas $A$ (e.g. Oxygen) and $...
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0answers
73 views

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 ...
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0answers
779 views

Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?

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 ...
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1answer
2k views

How does air escape from a pneumatic tire?

Obviously, it is caused by the difference in pressure between the inside of the tire and its surrounding environment; but how specifically is the air escaping?