# Tagged Questions

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### Chemical Potential of Interacting Particles

I'm interested in studying the diffusion of (classical) particles that have some interaction with each other. More specifically, let the potential energy of any two of particles separated by a ...
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### How does a minority carrier diffuse?

I have gone through a lot of questions but none of them ask how do the minority carriers approach the depletion layer in the first place. When a p-n junction is formed, negative space charge ...
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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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### 1-D Fick's first law - partial derivative?

I've recently been reviewing some concepts, including diffusion. Fick's 1st law: $$J = -D\frac{\partial C(x,t)}{\partial x}$$ as I understand it, applies to the steady state. For 1-D diffusion and ...
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### Diffusion Equation for Particle Hopping with drift

First of all, I haven't studied partial differential equations yet, hence this question might sound silly. I am doing a simulation for particle hopping on a lattice with python. I was said that in ...
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### The gas in a can of coke can escape?

If I have a can of coke that's 5 years old for example, how will the gas (CO$_2$) exit the can? Will the CO$_2$ pass through the metal of the can (100 microns thick) or justwhere it's precut (to ...
46k 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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### Diffusion of carbon monoxide in air

I have been reading about carbon monoxide online. It is lighter than air; Yet, in the case of fire, most online sources claim it spreads evenly throughout a room. Why is this the case? How is it ...
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### Random walk of a polymer in an annular space - filling in some steps

In Muthukumar, M., 2003. Polymer escape through a nanopore, J. Chem. Phys., 118, 5174–5184, the author solves the diffusion equation for the probability $P(\vec{r},\vec{r_0},N)$ that the ends of a ...
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### 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 way/...
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### Diffusion barriers on surface?

Can the barrier to diffuse on the surface, be it amorphous or a crystalline be greater than the binding energy between the adatom and the surface ?
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### Fick's first law inhomogeneous proof

I have seen Fick's first law of diffusion derived for a homogeneous material many times, however I am struggling to find a satisfactory proof for inhomogeneous, particularly for particle diffusion. ...
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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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### 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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### Diffuse laser light in a surface

Im building a laser target. It consists of a box, with a black plexiglass circle in the center of one of its sides, and a larger white circle around it. The black for the inside shots, and the white ...
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### Room with open door and heater : use inside boundary conditions or heat source for PDE?

I want to model the stationary temperature in a room (=square) that has one open door (=side) is otherwise perfectly insulated is heated through a (circular) heater that is placed somewhere in the ...
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### Stokes-Einstein Relationship to find time taken to diffuse $x$ distance? [closed]

A molecule has a diffusion coefficient of 0.5 × 10-9 m2s-1. Calculate how long it would take on average for the molecule to diffuse 10 µm. So I have the above ...
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### Spread of gases in a room

I have had some thermodynamics and statistical mechanics, but I don't know much fluid mechanics. I am not sure how to model the spread of gases in a room in the case of a fire or some leaking vent. ...
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### Calculation of charged sphere distribution near a wall in Cartesian coordinates

I am following a similar derivation as found in the beginning of this paper "Quantitative aspects of the growth of (charged) silica spheres" by A.P. Philipse. This paper calculates the growth of a ...
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### Understanding various types of motion

In classical statistical mechanics, given a system of particles, one often goes about classifying various dynamics (or types of motion) the system may exhibit on different time scales, but studying ...
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### 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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### can 3D diffusion be interpreted as superposition of 1D diffusion

Is diffusion of a substance in water independent in the X, Y and Z directions? In other words, if I want to solve how a substance diffuses through a volume, can I separately solve equations for its ...
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### Extension of the advection diffusion equation with diffusion perpendicular to the flow

Assume you model particle flow in fluid in a cylinder by an advection-diffusion equation, thus taking into account both diffusion and bulk flow. What would happen to the model if you would, at some ...
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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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### Thermal diffusion equation with heat per unit length?

Let us say we have a metal rod. Along that rod there is a rate of heat generation of H per unit length. If we assume we are in the steady state then I would expect us (from the thermal diffusion ...
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### Time for a particle undergoing brownian motion to reach a point in a volume

I was wondering how one could calculate the average time a particle needs to reach a random point in a small sphere (filled by water) with a radius of maybe $10 \mu m$. I thought of using the Stokes-...