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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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2answers
236 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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3answers
453 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
226 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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7answers
10k 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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4answers
465 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
90 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
162 views

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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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 ...
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1answer
338 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
281 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
524 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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2answers
6k 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 ...
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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 ...
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1answer
1k 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
408 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
305 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
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 ...
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3answers
983 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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3answers
470 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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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 ...
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2answers
446 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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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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2answers
569 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
405 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
343 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 ...