# 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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### Question about diffusion current in semiconductor?

I'm reading semiconductor physics by Neamen and when the disscusion about the diffusion current density he wrote this (I'll cite the image from the book because it has an important graph that will ...
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### Fluid viscosity, mass diffusion and Navier-Stokes equation

With the increase of fluid viscosity, mass diffusion of a fluid decreases. Then how the diffusion term in Navier-Stokes equation has a dominant effect at high viscosity? Also how the mass convection ...
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### Can oxygen 'leach' along a wire? [closed]

[If this is not the right SE for this question, apologies.] Automobile gasoline engine controls use oxygen sensors in the exhaust stream. The Wikipedia article on Oxygen Sensors notes that (some) ...
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### Solving the generalized Smoluchwski equation

The generalization of the Smoluchowski equation for $N$ interacting particles reads $$\frac{\partial w}{\partial t} = \sum_{i, j=1}^N \nabla_i \cdot D_{ij} (\nabla_j - \bar{F}_j/kT) w,$$ where $D_{ij}$...
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Considering the following current in flat Minkowski space $$J^\mu=nu^\mu -\sigma \Delta^{\mu\nu}\partial_\nu \mu,$$ where $n$ and $\sigma$ depend on chemical potential $\mu$: $$\mu=\mu_0+\varepsilon \... 0 votes 0 answers 15 views ### How does a diffusive wave behave differently than a traditional wave at an interface? Traditional wave phenomena (I.E. Electromagnetic, Acoustic etc.) can be described by the Hyperbolic wave equation \bigtriangledown^2\psi(r,t) + \frac{d^2\psi(r,t)}{dt^2} = q(r,t)*e^{i\omega t}. ... • 101 0 votes 0 answers 6 views ### Carbon dioxide Diffusion in solids vs Liquid, such as water or solid-state plasticized polymer Carbon dioxide say when released from a gas pump into water contained into an uncovered beaker will diffuse and also solublize in water and form carbonic acid. But what about the dehydration of ... 2 votes 0 answers 39 views ### Connection between diffusion and non-integrable 1D spin chains My question concerns non-integrable (à la Bethe) 1D spin chains. Consider, for example, the 1D non-integrable Ising model \begin{equation} H = \sum_{i \in \mathbb{Z}}\sigma_{i}^{z} \sigma_{i+1}^{z} + ... 4 votes 2 answers 185 views ### Chapman–Enskog theory and a Noether's invariant of energy? So in this answer: Folks figured out thermodynamics before statistical mechanics. In particular, we had thermometers. People measured the "hotness" of stuff by looking at the height of a ... • 1,021 0 votes 0 answers 44 views ### What's the difference between the mass equilibrium equation and the diffusion equation? Was wondering whether the mass equilibrium ODE and the diffusion equation PDE stem from the same physical concepts (at least when the mass represents Chemical Pollution): In my own words, the "... 1 vote 0 answers 51 views ### Diffusion from an instantaneous spherical source with a continuous spherical sink I assume this is a solved problem, but I cannot find the solution in some common sources, so I am asking here. Suppose you have diffusion of a molecule (diffusion coefficient D) from an ... • 11 3 votes 1 answer 81 views ### Under what conditions is mean square displacement \text{MSD}(t)=4Dt+v^2t^2 a valid asymmetric random walk model? I am reading the paper Actin dynamics drive microvillar motility and clustering during brush border assembly by Meenderink et al. (2019). In this paper, the authors fit the mean square displacement (... • 54.7k 0 votes 1 answer 41 views ### Survival function of particles with different starting points I am studying diffusion equations to model the diffusion of fluorescence particles into a cell monolayer. The easiest way is to model them starting from a point source (x = 0 at t = 0 -> x_\mathrm{... 0 votes 0 answers 35 views ### On the derivation of Fick's first law from first principles I risk repeating a question that has been asked too many times, but ... is there a rigorous (but not too complicated) way to derive Fick's first law? In this post the answer starts from what is ... • 1,386 0 votes 0 answers 18 views ### Does diffusion of a spring depend on the spring’s equilibrium length? Say we perform a random walk on \mathbb{Z} with two equal particles that are connected by a spring with spring constant K and equilibrium length a, where at each time step each particle has ... 1 vote 0 answers 116 views ### Partition function for a 1 dimensional polymer A one-dimensional polymer (a chain), made of (N + 1) monomers, is diffusing on top of a one-dimensional lattice having a lattice constant a = 1. The i-th monomer (i = 0, 1, 2,..., N) is located at a ... • 129 1 vote 0 answers 34 views ### Kirkendall effect: equilibrium vacancy concentration and pair interaction energy I am reading the following article on Kirkendall effect leading to the Formation of a Hollow Binary Alloy Nanosphere: A Kinetic Monte Carlo Study. I am unable to understand or find in references the ... 0 votes 0 answers 15 views ### Diffusion problem: number of droplets in the air I'm having a big brain block here and want to check if my reasoning is correct. I'm considering a room of volume V, with p persons, during the time dt. We want to know the number of droplets ... 0 votes 0 answers 34 views ### What real life applications does diffusion limited aggregation have? While studying DLA - diffusion limited aggregation - in the field of fluid dynamics I started wondering what real life application does this phenomena have? We observe fractals in experiments such as ... 1 vote 0 answers 50 views ### Sense for a viscoelastic term of Maxwell type I go reference the book of Jan Prüss (Evolutionary Integral Equations and Applications, 2012) as needed. In this book (pg. 128) it is explored some concepts of stress and strain considering the ... 1 vote 1 answer 38 views ### 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 ... • 13 0 votes 0 answers 17 views ### 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 ... • 2,195 2 votes 1 answer 24 views ### Relation between the diffusion coefficients My course is giving me a strange relation I have difficulties to understand. In the context of thermodynamics and evolution, we define: The mass diffusion flux: (Newton's law)$$J_{M_d} = -D\frac{dc}{... 1 vote
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### Simulating diffusion for particles undergoing Brownian motion

I am trying to do a computer simulation as part of a research project of the diffusion of a few particles undergoing brownian motion along a two-dimensional canvas. I am having some holes in my ...
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### Do pressure gradients affect diffusion speed for gases dissolved in liquids (scuba offgassing question)

This question comes from a scuba forum where we are discussing the technical scuba technique of breathing 100% O2 during stops at shallow depths to speed up the offgassing of nitrogen (N2) from body ...
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### Where can I find/derive these equations?

I am currently investigating the behavior of the smoke and I will need to account for the velocity of the smoke as soon as the flame is smothered. There is also the behavior where the smoke expands in ...
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### Generalized random walk process: Fokker-Planck equation

The diffusion equation $$\frac{\partial p(x,t)}{\partial t} = D \frac{\partial^2 p(x,t)}{\partial x^2}$$ can be derived from a simple random walk on a line. For example, if the probability of ...
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### Understanding the Markovian and Gaussian approximations in Brownian motion

I am trying to understand in the original derivation of Brownain diffusion, where does the assumption of Markovian and Gaussian nature factor in. In Albert Einstein's original work on Brownian motion ...
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### Diffusion of gas mixtures through a membrane

Suppose we have a mixture of gases $k = 1,2 \ldots$ in a large volume with constant pressure and temperature (via external pressure and temperature control). We immerse a small volume separated via a ...
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### Where does the negative sign in the Cahn-Hillard model of diffusion come from?

In the Cahn-Hillard model of diffusion, motion of a particle field phi is defined by the diffusion of a potential mu For electrodynamics, phi can be thought of as charge, M as the conductivity of the ...
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### Diffusion Equation vs. Gradient Flow

I am trying to understand the connection between the 'common' diffusion equation and the evolution equation of the concentration as a gradient flow of the free energy. So let's simply assume an ideal ...
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### What is the entropy associated with a diffusion process?

Is it possible to calculate entropy from the solution of a diffusion equation(with natural boundary conditions) by using the formula of Shanon entropy? Could anyone help me to understand the entropic ...
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### Is diffusion a nonequlibrium process?

We know that the diffusion equation can be viewed as the continuum limit of a discreet unbiased random walk. My question is the following: Is diffusion (or an unbiased random walk) a non-equilibrium ...
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### Is it possible to define concepts like free energy in the diffusion process?

How does the idea of free energy (which we derive from the canonical partition function) fit in the domain of non-equilibrium processes like diffusion?
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### Henry's Law - When scuba diving, why is breathing pure $\rm O_2$ not the same as going to outer space?

In Short I had a discussion with my dive instructor the other day. He said that for "decompression dives" you can cut down decompression time to 1/3 if you switch to pure $\rm O_2$ at 6m. ...
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### Doubts about how to apply Fick's law to gas

According to Fick's law the flux of gas through a membrane depends on the concentration gradient and then on the pressure gradient: $$\Delta P = P_a - P_b$$ where $P_a$ is the pressure of container $A$...
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### Can mass transfer occur without a concentration difference? (analogous to the question, can energy transfer occur without a temperature difference?)

The driving force for diffusion of mass is a concentration gradient. However, mass can be transported both in a diffusive and a convective (due to the flow of a fluid) way. By definition, the combined ...
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### Random walk in finite VERSUS infinite space: Probability density functions and their interpretation

I am studying the probability density function of a random walk in a confined geometry (2D-BOX). I am also comparing this probability density function to its equivalent in infinite two-dimensional ...
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### Properties of random-walk in infinite and finite two-dimensional space: probability of two particles being in the same location at time t

I have been told that one of the property of the continuous-time random walk in two dimensions is that: $$\int_{Z} \, G(z, t | p_1) \, G(z, t | p_2) \,dz = \,G(p_1,p_2,2t)$$ where ...
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### How can NO charge carriers exist in the depletion region?

I learned that no charge carriers exist in the depletion region of a PN junction due to the balance between the diffusion current and the drift current due to the electric field created by charged ...
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### Singularities/infinities of continuity equation in polar coordinate

I encountered a bit of a difficulty in solving the continuity equation for polar coordinates. For a "fluid" or density of particles moving radially outwards with constant velocity, its flux ...
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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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