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121
votes
3answers
38k 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 ...
36
votes
7answers
11k 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 ...
7
votes
1answer
150 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 ...
6
votes
2answers
346 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 ...
6
votes
3answers
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 ...
6
votes
4answers
176 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 ...
6
votes
0answers
135 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 ...
5
votes
1answer
229 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 ...
5
votes
2answers
7k 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 ...
5
votes
2answers
448 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} ...
5
votes
2answers
114 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 ...
5
votes
1answer
95 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 ...
4
votes
3answers
306 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: ...
4
votes
1answer
475 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: ...
4
votes
3answers
6k 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 ...
4
votes
3answers
163 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 ...
4
votes
1answer
79 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( ...
3
votes
2answers
361 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 ...
3
votes
1answer
285 views

What is the return probability for Brownian motion in three dimensions?

I would like to know the probability of return to the initial point in three dimensional Brownian motion. Does someone know an expression for the diffusion constant? (Suggestions of books on this ...
3
votes
1answer
410 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?
3
votes
1answer
111 views

How big an egg can be? [closed]

Please hold on to flag as off-topic. Few days ago I received a question - how big an egg can possibly big? Can it be as big as 1 meter, as a human? (Imagining that there could be really huge animals ...
3
votes
1answer
530 views

Can we explain physical similarities between Black Scholes PDE and the Mass Balance PDE (e.g. Advection-Diffusion equation)?

Both the Black-Scholes PDE{*} and the Mass/Material Balance PDE have a similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive ...
3
votes
1answer
613 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 ...
3
votes
1answer
117 views

Equidistant coffee rings in a mug: pinning boundaries coupled with migration of solute or just sip volume?

I understand that you get coffee rings on a table as a result of solute migration (solutocapillarity) towards the pinning of the circumference of the coffee ring [Deegan et al.]. Below is an ...
3
votes
1answer
59 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 ...
2
votes
1answer
97 views

Integral related to particle diffusion

In the context of particle diffusion, I am trying to understand the equations that describe Brownian motion as a macroscopic process. Assume $N(x,t)$ is a number concentration and $D$ is a diffusion ...
2
votes
1answer
74 views

What interpretive difference is there between defining a function with or without a differential as a postfactor?

I have thought about this and looked for answers for a long time now, but I do not have any name or label for this problem, which is the reason for the long title of this question. I have come across ...
2
votes
2answers
450 views

Diffusion across an interface and conservation of mass

I am reading a physiology book chapter (Mathematical Physiology, by Keener --Respiration chapter) about the gas exchange between capillaries and alveoli. It seems that this gas exchange can be modeled ...
2
votes
1answer
2k 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's assume a close room with 1-2 people who only one of them smoking cigarette. What is the equation describe the smoking spreading? is it diffusion? what are the parameters is so? Is there a ...
2
votes
2answers
133 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 ...
2
votes
1answer
46 views

Must neutron speed and diffusion speed be comparable for neutron scattering experiments to be probe atomic diffusion?

Neutron scattering experiments are sometimes used to study atomic diffusion in solid materials. My intuition is that the typical speeds of the atoms diffusing in the material--say, the diffusion ...
2
votes
1answer
33 views

Diffusion in the standard map

Consider the standard map (also known as Chirikov map): $$ p_{n+1} = p_n + K \sin(\theta_n) \\ \theta_{n+1} = \theta_n + p_{n+1} $$ I know that the diffusion coefficient according to the ...
2
votes
1answer
46 views

Rate of probability loss from absorbing boundary

The following is the solution to the 1D diffusion equation with diffusion coefficient D, initial particle position $x_0$, and a perfectly absorbing boundary at $x=0$ (s.t. $P(x=0)=0$). $$ ...
2
votes
1answer
395 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 ...
2
votes
1answer
199 views

What is the physical basis behind thermal diffusion in a Clusius-Dickel column?

A Clusius-Dickel column allows separation of two species by the application of a thermal gradient. In its simplest form, two bulbs are maintained at two different temperatures $T_1$ and $T_2$ and ...
2
votes
1answer
52 views

Is the diffusion coefficient for a macromolecule sensitive to mass?

Suppose I have two neutrally-buoyant macromolecules diffusing in water. They have the same radius of gyration (i.e. same root-mean-square distance from their center of mass), but one of them is ...
2
votes
1answer
415 views

Rough diffusion rate of sugar water through a larger volume of water

I hope this a question that can be answered and isn't too vague. I'm also only after a very rough answer. I'm adding a small amount (~500mL) of sugar solution into a carboy with a much larger volume ...
2
votes
1answer
48 views

Heat diffusion: evanescent waves?

It has been recently pointed out to me that the solution of the heat equation in a semi-infinite material with an oscillating boundary condition at the surface is not an evanescent wave. The argument ...
2
votes
0answers
58 views

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 ...
2
votes
0answers
79 views

Why does the water diffuse at right angles in my coffee? [closed]

I purchase an espresso shot each morning at my local coffee shop, and I usually water it down slightly to take the edge off as well as to cool it. Recently, I have noticed that when I pour the cold ...
2
votes
3answers
473 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, ...
1
vote
3answers
1k views

Can smoke stay still in the air?

Can a small amount of smoke be dense enough to stay in the air keeping its shape for a minute or so? Or does it always dissipate quickly? If not smoke, can anything else stay in the air for a minute ...
1
vote
1answer
109 views

What are the patterns appear after kernel averaging?

Having a 2D map filled uniformly by random values (Figure:top-left) to demonstrate a disordered phenomena, the next maps are ...
1
vote
1answer
136 views

Temperature rate of change inside a cylinder

I was wondering about this today, mainly for baking a cylindrical cake. Say you have a solid cylinder which is at temperature T0 inside. Say you then move the ...
1
vote
1answer
124 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?
1
vote
1answer
340 views

Example of diffusion process without a gradient

A book I was reading stated that diffusion can exist without a gradient of a physical quantity. Heat is an example of diffusion because of temperature gradient and similar is the case of mass flow in ...
1
vote
2answers
73 views

Where I can find information about how helium gas diffuses through different polymer materials

I need more experimental information about helium gas diffusion in solid materials such as different plastics, metals, ceramics etc. For example I am scientifically curious about what is the polymer ...
1
vote
1answer
56 views

A simple osmosis problem

The following is adapted from a problematic question* asked on the Bio site. I would like to ask it free of those distractions here. If there is anything unduly artificial about the problem please ...
1
vote
1answer
73 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 ...
1
vote
1answer
81 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 ...