The diffusion tag has no wiki summary.
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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 ...
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2answers
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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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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 ...
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1answer
23 views
heat spread from hot coil: diffusion, radiation?
When modeling the heat spread from a hot object through a vacuum (or a gas), what is the dominant physical process for heat energy transportation? Thermal diffusion, thermal radiation, a mix of the ...
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2answers
151 views
Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation
Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
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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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Concentration of Proteins
You release a billion protein molecules at position $x = 0$ in the middle of a narrow capillary test
tube. The molecules’ diffusion constant is $10^{−6} \ cm^2 s^{−1}$. An electric field pulls ...
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1answer
70 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 ...
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1answer
24 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
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1answer
25 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 ...
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46 views
Ask for help: the Reaction-Diffusion related problem
In container there are two kinds of molecules A and B which are distributed uniformly. Initially the quantities of A and B are $N_A$ and $N_B$ respectively A and B are distributed uniform, i.e., in ...
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3answers
228 views
Solving the diffusion equation
I am trying to clarify the relation between random walk and diffusion, and the source book proposes the following which I can't get. Starting from the diffusion equation
$$ \frac{\partial C}{\partial ...
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1answer
92 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 ...
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3answers
1k 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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4answers
174 views
Is infrared light diffused on walls?
Lamps that produce visible light can light up a whole room because the ceiling and the walls diffuse light. This way, when there is a single lamp in a room, something that is in the shadows is not ...
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1answer
54 views
Mass diffusion: is $D_{AB} \neq D_{BA}$ at high pressures? If so, why?
From [Takahashi][2], I validated some models I have for estimating diffusion coefficients (methods of Fuller modified by Riazi for high-pressures, all pulled from [Poling][3]). Here is the figure ...
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0answers
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Mechanical effects of convective flow in steady-state stagnant film diffusion
When analysing diffusion problems in the context of the simplified film model, two limiting cases are ussually introduced during the solution of the differential chemical species mass balance ...
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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 ...
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1answer
236 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 ...
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1answer
150 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 ...
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1answer
361 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 ...
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1answer
532 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 ...
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1answer
544 views
What's the temperature distribution of a plane wall insulated on one side with no internal heat gen.?
Let's say we have a plane wall that is insulated on one side, exposed to a fluid on the other side, and has no internal heat generation. Would the shape of the temperature distribution be a constant? ...
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1answer
214 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 ...
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3answers
285 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:
...
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1answer
100 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 ...
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3answers
1k 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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3answers
369 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, ...
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3answers
494 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 ...
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1answer
61 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 ...
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2answers
323 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 ...
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2answers
430 views
How to model tea diffusion/osmosis?
How should I model the tea concentration as a function of time after a tea bag has been submerged? Is there a simple way of measuring the tea concentration?
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1answer
331 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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2answers
280 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 ...
