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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Electromagnetic Diffusion Equation

I am looking at a derivation for the electromagtic diffusion equation. It starts with Maxwells equations for the magneto-quasi-static case ($\frac{\partial \vec{D}}{\partial t} = 0$). $$ \begin{align} ...
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How can concentration gradient field come into existence immediately at all points in non-stationary diffusion?

Suppose there is a non-stationary diffusion process in 2D rectangular plane. Component diffuses from the outside through all four faces of the plane. When I think about the simulations of the non-...
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Diffusion to growing adsorbing sphere

I'm working on a model where particles with concentration $\phi$ diffuse to an adsorbing sphere. For the non-growing case, I assume a steady-state solution and Fick's second law $\frac{\partial\phi}{\...
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What is $\lambda$ in Maxwell's EM diffusion equation?

I am reading an old paper from the 1970s regarding a line current EM induction. In the paper they say that (under certain assumptions), Maxwell's equations can be simplified to a diffusion equation of ...
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How to calculate mean squared displacement (MSD) value as function of Tau (lag-time)

I'm doing a research on Brownian motion (in 2D) and I want to calculate the MSD values in order to find the diffusion coefficient $D$. However, online I find different approaches on how to calculate ...
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What are the benefits/weaknesses of different diffusion models in radiation transport?

Can anyone summarize or point me toward references for why someone would choose one diffusion model over another, particularly in relation to radiation transport during a nuclear blast? The diffusion ...
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Can you have two different Bohm velocities within a multispecies plasma?

How would you calculate 2 different bohm velocities in a multi species plasma, say H+ and N gas excited by a microwave reactor.
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2D advection-diffusion in a quasi 1D system

I wish to solve the advection-diffusion equation for the concentration $c(x)$ at steady state inside a 2d circle, where the advection is only in one direction (along the x-axis). The picture here ...
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What is the true motivation behind diffusion of components in solution?

I am very well aware that chemical potential or concentration is typically said to be the reason for molecular diffusion but consider a case, We have a cube filled with gas containing minor amount of ...
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Why do ( within my limited understanding.) Energy and matter act in opposite ways [closed]

I would like to preface this by stating this type of research is my hobby not my profession. If I understand the basic explanation correctly, energy tends to spread out evenly within a closed system ...
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Diffusion in a Sphere - Average concentration considering initial and final concentration

I am looking a diffusion in sphere, but I am afraid that, as a chemist, my limited understanding of mathematics and differential equation is hindering me, but I am hoping that perhaps some of you can ...
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Can a tea light really heat a greenhouse?

It is a common suggestion amongst greenhouse enthusiasts that a long-burning tea light inside an upturned terracotta pot can be enough to keep frost away from plants. Is this possible? Instinctively, ...
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Salt concentration versus depth due to diffusion and gravity

Suppose we have a container of water with dissolved salt in it. Though it begins as a homogeneous mixture, gravity will have a tiny effect on the distribution of the ions. Another user found the ...
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How to use point-kinetics approximation to go from diffusion to point kinetics?

I understand that we get to point kinetics by neglecting spatial dependence in the diffusion equation, but I'm somewhat stuck on the details here. Robert E. Masterson's Introduction to Nuclear Reactor ...
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Diffusion without mass conservation?

I'm looking for the physical description of a certain diffusion process, but I don't know how to precisely express it, making the search fruitless. I'd like to have some help formulating, or rather ...
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Mean squared displacement of a particle on a biased random walk [closed]

Given a particle on a 1-D random walk with some drift velocity $\nu_d = \frac{\Delta x_d}{\Delta t}$, the position in at some time step j is given by $$x_j=x_{j-1}+k_j L + \Delta x_d$$ where $L$ is ...
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Autocorrelation functions - haven ratio

I'm studying Haven coefficients (I created similar question but with MSD). Right now I have question referring to calculating haven ratio using velocity-velocity autocorrelation functions. What I have ...
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Calculating cross terms for Haven coefficient using windowed MSD

My problem is that from this site: MSD Module I'm taking an equation that expresses the windowed mean squared displacement (MSD): $$MSD(m) = \frac{1}{N}\sum_{i=1}^{N}\frac{1}{N-m}\sum_{k=0}^{N-m-1}(\...
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How to calculate windowed mean squared displacement for multiple particles?

I'm new to molecular dynamics and I find this equation pretty confusing: $MSD(\tau)=<r(t+\tau)-r(t)>$ For example take a structure with N mobile ions (e.g. oxygen particles). In different ...
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Modeling contamination diffusion in a draining container

I have a 250-mL bottle filled with pure water and a sampling line at the bottom slowly draining the bottle to analyze, say 2.5 mL/min. The bottle is on the order of 10 cm high. Since the bottle is ...
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What's the quantum operator for the diffusion Green's function?

I am trying to understand the following equation about the diffusion Green's function ("Principles of condensed matter physics" by Paul Chaikin, chapter 7.4 Diffusion) $$n(x,t)=\int G(x-x',t-...
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How does the rate of heat exchange relate to the rate of particle exchange, when opening my office window?

We know that opening the window lets in some fresh air. But in the winter, this fresh air could be uncomfortably cold. To what extent does the room being cold imply that the air is fresh? For ...
Second Wind's user avatar
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Calculating upwards drift velocity of hydrogen in air, where is the error in my calculations?

I have the following problem: I'm charging a lead-acid battery in a container. The charger could fail, producing too many amperes at too many volts. Too many amperes I can easily handle in a fuse, so ...
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Diffusion current because of internal field of semiconductor

Suppose we have an isolated n-type semiconductor having varying concentrations of carriers over x. After some finite time, the concentration becomes uniform for a given constant temperature. We ...
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How fast do $\rm CO_2$ molecules transfer between air and water at equilibrium?

Suppose a bath of water is in equilibrium with the air above it at temperature T and pressure P. The concentration of $\rm CO_2$ in the air is, say, 400ppm, and the concentration of $\rm CO_2$ in the ...
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Expansion and visibility of particles because of diffusion

A cloud forms as a point source containing a fixed quantity of particles and then expands according to the diffusion equation. Let's analyze how the visible size of the cloud changes with time. When ...
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Most general Green-Kubo relation for transport coefficient - $\beta/V$ dependence of diffusion

Hansen & McDonald write that a the most general Green-Kubo formula for some microscopic dynamical variable $A$ can be written as: $K=\frac{\beta}{V} \int_0^\infty \bigg\langle \dot{A}(t) \cdot \...
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How to numerically solve non-linear 1D diffusion equation in time-domain?

The equation to be solved is this: $$\frac{\partial H_y(x,t)}{\partial t}=\left(\frac{1}{\sigma\:\mu(H_y)}\right)\frac{\partial^{2}{H_y(x,t)}}{\partial{x^{2}}}$$ But note that the magnetic ...
Luiz Oliveira's user avatar
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Jet of gas striking a disc, what fraction of the total volume is in contact with the disc [closed]

In a catalysis experiment, I have a jet of gas coming through a nozzle of cross-sectional area A_1 at a volumetric flow rate F. This strikes a circular disc of area A_2 coated with catalyst, at right ...
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How high pressure, high temperature liquid refrigerant exiting a Thermostatic Expansion Valve (TXV) turns into low pressure, low temperature liquid?

In a refrigerator or heat pump, how does high pressure, high temperature liquid refrigerant exiting a Thermostatic Expansion Valve (TXV) turn into low pressure, low temperature liquid? Is this a ...
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What would the measurement device show me if I measured the dye concentration at the pipe location where all of the mass is concentrated at?

I was studying the methods for solving the diffusion equation. Here I found an example problem with the Dirac delta distribution initial condition and zero boundary conditions (example $9.5.1$): $$ {\...
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How does evaopration and diffusion affect concentration of solute at the solvent surface?

Imagine a long, thin tube with one end sealed and the other end open. It is filled with a volatile solvent with a dissolved non-volatile solute. As the solvent evaporates at the liquid surface, the ...
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Solving diffusion equation for a semi infinite tube filled with water with a source of ink pouring ink into the tube [closed]

I am trying to understand diffusion in a semi infinite space.Suppose we have a semi infinite horizontal tube with a valve filled with water just like this: Suppose we start pouring black ink into the ...
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Limitations and application of the Einstein relation

The Einstein relation says that the diffusion coefficient $D$ and it's mobility $\mu$ under a force are related to each other as follows: $$ D = \mu k_B T $$ I don't completely understand the ...
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Diffusion versus dispersion

What is the difference between diffusion and dispersión in porous media? In my model mathematical, Advection-Diffusion-Reaction Equation Or Advection-Dispersion-reaction Equation ? Help please
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How to show that the diffusion of a species is given by $\frac{\dot{m}}{A}=-\rho_i D \ln(C_i)$?

I'm reading a textbook on viscous flow which says that you can go from Fick's Law for the diffusion of a species $$\dot{m_i}/A = -D \nabla \rho_i$$ to an equivalent formulation using the species ...
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Anomalous diffusion in a system of confined interacting particles

I have a system of charged particles confined parabolically. I want to analytically study anomalous diffusion in such a system using Langevin Dynamics. In a system of non-interacting particles there ...
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Why $w = 10/m$ is the single major Fourier component? (Statistical Mechanics: Entropy, Order Parameters and Complexity 2nd Edition)

An initial density profile $\rho(x,t=0)$ is perturbed slightly away from a uniform density $\rho_0$, as shown in follows The density obeys the diffusion equation $\frac{\partial \rho}{\partial t} = D\...
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Using Peltier module for heat diffusion experiement [closed]

I'm trying to use a Peltier module (e.g. TEC1-12703) for heat diffusion physical experiment. An external power source provides around 8V with 1A current, so the generated heat from the surface of the ...
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Why the density will decrease?(Statistical Mechanics Entropy, Order Parameters And Complexity 2nd Edition)

Consider the diffusion equation in an external force $F$ and suppose $\rho$ is the density of a conserved quantity of the system(e.g. particle density), the diffusion equation is $$\frac{\partial \rho}...
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Any restrictions on drift vector in Fokker-Planck equation?

The most general Fokker-Planck equation for a probability density $f$ over phase space is $$\partial_t f = -\partial_i(u^i f) + \frac{1}{2} \partial_i \partial_j (D^{ij} f)$$ where $u^i$ is the drift ...
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Reason for Voltage drop in Depletion Region in a PN Junction [closed]

So I've been reading about the PN Junction and depletion region quite a lot, but I haven't really found a concrete explanation for the existence of a Voltage Drop, or Barrier Potential associated with ...
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Diffusion in a harmonic potential

I am just looking for the correct Ansatz to a one-dimensional diffusion equation with a harmonic potential. Let $n(x,t)$ be the density of particles and $\Phi(x)=\frac{1}{2}\alpha x²$ a potential. ...
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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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Charge diffusion

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 \...
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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} + ...
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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 ...
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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 "...
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