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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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Neutron diffusion equation cylinder question

Hi there I was wondering if anyone could help me with how to approach this problem that I have. I'm looking to find the neutron flux outside of a cylindrical container which is made of steel, however ...
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The roles of convection and advection in the absolute flux for species $i$ in mass transfer

I am confused as I have been reading on mass transport on multiple sources and they seem to use "advection" and "convection" interchangeably in the equation for the absolute flux ...
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Does diffusion current "consume" thermal energy?

My (possibly erroneous) understanding of solid state physic has led me to the belief that diffusion current may "consume" thermal energy. Here is my (possibly erroneous) understanding. When ...
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Diffusion from a rod with constant concentration

Suppose I have an infinite rod that is suddenly brought into a medium where some substance starts to diffuse radially outwards from the rod. During this, the concentration in the rod is kept constant....
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Need help identifying missing boundary condition in charge transport problem

The system I am considering consists of a conducting liquid sandwiched between two electrodes. The electrodes supply a constant flux of electrons $J_{ext}$. In the liquid there are also uncharged ...
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Surfactant diffusion with Fick's 2nd law

Normally, the dynamic surface excess from fresh surface in aqueous surfactant solution is given by Ward-Tordai equation $$ \begin{align*} \Gamma(t) &= \sqrt{\frac{D}{\pi}} (2c_b \sqrt{t}-\int_0^t \...
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Diffusion of van der waals gas

the problem is diffusion of non-ideal gas i think, in this situationm the change of internal energy, work, and heat during process is zero because this process is free expansion(diffusion) but, how ...
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Mean squared displacement of a free Brownian particle moving in harmonic potential

For a free Brownian particle moving under harmonic potential ($\frac{1}{2}m\omega^2x^2$), the equation of motion can be written as, $$m\ddot{x}=-m\omega^2 x-m\gamma\dot{x}+R(t)\;,$$ where, $\gamma$ is ...
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Interpretation of Diffusion Coefficient in Photon Diffusion Equation

The diffusion coefficient in photon diffusion, as explained/defined here: Factor of 3 in Photon Diffusion coefficient seems counterintuitive because diffusion is inversely proportional to the ...
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How to calculate the diffusion length in modulation doping?

I have read a paper(dx.doi.org/10.1021/nl201206d) about an application of modulation doping in bulk thermoelectric materials, in this paper, the nanoparticles diffuse carriers to the host materials, ...
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Is the drift current of minority carriers negligible in the continuity equation?

When deriving the ambipolar transport equations for an extrinsic semiconductor under low injection, I have found certain discrepances between different references. For instance, in Neamen's ...
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Will self-diffusion take place in a hydrostatic equilibrium?

To be specific,I've been considering a simple case where a fluid is under uniform gravity. For hydrostatic equilibrium,$\nabla P=-\rho g$and the distribution will be like $\rho(z)=\rho_0 exp[-mgz/kT]$....
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Isotopic exchange and SIMS diffusion profile measurement

Suppose there is a cylindrical (pellet) sample in the oxygen atmosphere as shown on the photo attached. Oxygen diffuses from the outside to the sample interior everywhere on the outer surface of the ...
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The nature of Entropy in the Gibbs free energy in thermodynamics

I struggle with understandinng the Gibbs free energy $G$ for a very long time now. I still managed to pass the thermodynamic courses, but this lack of understanding haunts me till today. So finally I ...
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Self-diffusion and Fick's 2nd law

If I have a solid sample material inside the atmosphere of oxygen-16, after some time diffusion will make the concentration of oxygen-16 uniform inside the sample. If then oxygen-18 (the tracer) is ...
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How to modify heat conduction equation when air is not at rest?

The heat conduction equation is usually written as $$\frac{\partial T}{\partial t} = \alpha \vec \nabla^2 T$$ But what if a moving air parcel is considered? The standard derivation of the equation ...
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In Langevin equation of stochastic oscillator, can the system has only fluctuation force with no fraction?

I am new to fluctuation statistical mechanics, In all examples that I encountered, the Langevin equation always has the fluctuation force accompanied by a friction force. $$\frac{d^2x}{dt^2}+\gamma \...
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Time constant for diffusive process with radiation and convection

I'm studying the thermal comportement of a "mass stove". I would like to do a materials selection. My first constraint is to have a temeperature of my "mass" between a lower and an ...
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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 ...
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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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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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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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