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139 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 ...
38k 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 ...
1k 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 ...
324 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: ...
126 views

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 ...
44k 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 ...
2k 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 ...
721 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 ...
785 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 ...
1k views

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 ...
341 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 ...
79 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 ...
81 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 ...
124 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 ...
6k 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 ...
2k views

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 ...
215 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?
61 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 ...
618 views

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, ...
590 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?
17 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 ...