# Questions tagged [diffusion]

Diffusion is the net movement (spreading out) of molecules or atoms down a concentration gradient: from a region of high concentration to a region of low concentration.

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### Relation between time it take to diffuse and temperature

I was reading Reif's Statistical physics. In problem 7 in chapter 2, It says "Consider a thin copper wire stretched out along the $x$-axis. A few of the copper atoms, located near $x=0$, are ...
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### 3D information from shadows

I was holding a 1 inch diameter pipe recently on a sunny morning. I noticed that the turning the pole at various orientations changed the shadow on the ground. The closer portion of the pipe to the ...
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### Estimate diffusion coefficient from 2D projections of 3D trajectories?

Given the projections x(t) y(t) of the trajectories of several particles moving in 3D in a water solution, is there a way to estimate the diffusion coefficient of the 3D diffusion, if we assume it ...
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### If the inclination of a cloud of oxygen in outer space is to diffuse, then how do nebulae form?

If a cruise ship-size object in outer space were surrounded by a spherical cloud of oxygen, and there were no other bodies exerting significant gravitational force in the vicinity, would the cloud of ...
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### What is the mathematical derivation for no diffusion term in the mass continuity equation of the Navier-Stokes/Euler equations?

In this post the fact that the mass continuity equation in a mixture of gases has no diffusion term, i.e., $$\frac{\partial\rho}{\partial t}+\nabla\cdot(\rho\vec{v})=0$$ has been discussed. ...
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### What resources are you aware of and can recommend me to study and model spectral diffusion?

I am looking for textbooks, papers, etc. that cover this topic in some detail and would allow me to develop a simple model to use in my BSc thesis. I'm having a hard time finding the resources I need. ...
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### Brownian motion and multi-scale stochastic processes

The Stokes-Einstein equation for the diffusion coefficient of small colloidal particles in suspension is canonically derived under the assumption that the primary motion of the particle is ...
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### Differences in interactions of light with different mediums

I am trying to figure out this problem, I apologize in advance if the question is silly. If i am correct sunsets are red because red light doesnt get diffounded as much as blue light, which eventually ...
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### How can I model convection in a simple and effective way?

I have a project in which we're trying to model heating of a room. We are modelling the room in 3D. The room has realistic walls, windows and a door, which will loose heat through them. To balance the ...
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### Physical Interpretation of Large-Time Decay Estimates of Solutions to Navier-Stokes

It is well known (see for example Hoff-Zumbrun (1995)) that solutions to the compressible Navier-Stokes equation converge in $L^p$ spaces to the heat kernel. Formally, to keep things simple, we can ...
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### An intuitive reason for the fourth derivative in the beam equation?

The appearance of the second derivative (or Laplacian in higher dimensions) in the diffusion equation ($u_t=u_{xx}$) and the wave equation ($u_{tt}=u_{xx}$) seems intuitive to me. The quantity simply ...
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### What differentiates an alloy from diffusion at an interface?

For the thin film deposition of some metal A onto another metal B, I understand it is possible for a bit of metal a to diffuse into grain boundaries of metal B. How are these diffused atoms of metal A ...
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### In a forward biased P_N junction, "Why does the diffusion current increase while the density difference between the carriers on both sides decreases?"

In forward bias of a P_N junction the density of minority carries increases while the density of majorities doesn't change considerably. So compared with equilibrium the difference of densities ...
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### Poisson-Nearst-Planck equations with normal distribution as initial condition

I am having a hard time trying to think of this model: Imagine you have a normal distribution of +q charges in 2D $$\rho(r,t=0)=\rho_0 e^{-\frac{r^2}{\sigma_0^2}}$$ where $\sigma_0$ is the width of ...
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### How does dye move in water?

My understanding is that dye moves through water primarily through diffusion. The introduction to these lecture notes seems to confirm: If you we put a drop of red dye in water, it will slowly ...
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### Diffusion of a quantity down the gradient of another one?

This might be a stupid question. Let's look at the diffusion equation for, say, the temperature: $$\frac{\partial T}{\partial t}=\nabla\cdot(D\nabla T).$$ It's simple, the temperature diffuses down ...
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### Diffusion rate of two mixed gases

From my previous post Dependancy of molar mass, i came to know that rate of diffusion depends on molar mass of gas only. Here is a particular problem. In a container under standard condition, a fixed ...
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### Heat transfer vs calorimetry equation

I'm trying to understand the difference between the equations $$Q=mc\Delta T$$ and, $$\frac{dQ}{dt}=\frac{-\kappa\alpha\Delta T}{l}$$ Suppose, we have two metal rods at $T_1$ and $T_2$ temperature, ...
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### A question concerning gas diffusion

We are discussing the one dimension diffusion in a tube. To simplify the analysis, we isolate two adjacent thin layers sharing a same surface, in which gas concentration could be assumed as even ...
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### Threaded Ring Polymer - Scaling approach to Diffusion

A monodisperse melt of linear chains is mixed with ring polymers, when a linear chain threads through the opening of a ring, that rings movement becomes confined along the backbone of the chain. (A ...
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### Is my book's method of using Graham's law of effusion correct?

Problem: Let the container which contains NH3 gas be A, and which contains HCl gas is B. If both the stopcocks are opened at the same time, then determine the distance from container A at which white ...
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### Is there a way to calculate the so-called 'diffusion velocity' of neutrons?

I am conducting some deterministic multigroup pulsed-neutron die away simulations where the neutron diffusion equation is being solved via finite difference methods and would like a way of verifying ...
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### Diffusion to capture on the surface of a cylinder wall

Hi all, is it correct to use equation 10.3.4 on the above textbook for the flux of particles onto a surface of the cylinder wall (radius a, length L)? If yes, then the rate of collisions of particles ...
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