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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What is the link between path integral source terms and the propagator?

Consider a diffusion process defined by $$\frac{\partial \phi}{\partial t} = D \frac{\partial ^2 \phi}{\partial x^2}$$ where $\phi$ is the probability density of a particle's position and $D$ is the ...
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Green's function for moving solidification front

Consider a liquid solid interface $z =\zeta(x,t)$ moving at constant speed $v$, for a two dimensional problem. Due to solidification interface is changing it position. For simplicity heat ...
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Interpreting an anomalous subdiffusion exponent

I'm studying a process that involves diffusion through a porous film; as such, subdiffusion is expected for this system. My experimental data is consistent with subdiffusion, with an exponent of $\sim ...
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Fokker-Planck equation for 2D SDE

Consider the following two-dimensional SDE \begin{align*} \mathrm{d}\mathbf{X}(t) &= {\mathbf{f}(\mathbf{X}(t))}\mathrm{d}t+\mathrm{d}\mathbf{W}(t)\\ \end{align*} where $\mathbf{X}(t)=\begin{...
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I can't find the Einstein relation for spin diffusivity

I'm studying the article "Thermodynamic analysis of interfacial transport and of the thermomagnetoelectric system" (PhysRevB.35.4959, Mark Johnson and R. H. Silsbee); they use this relation $$ D=\frac{...
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1answer
57 views

Why do living tissues need to be moist for oxygen to diffuse across them?

If an earthworm's skin dries out, oxygen can't diffuse across its skin any more and the worm suffocates and dies. Why does the skin have to be moist to allow oxygen to diffuse across? If there is ...
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53 views

Diffusion of Hydrogen through Molybdenum alloy

I have been performing experiments to study the diffusion of Hydrogen through Molybdenum. According to Sievert's law diatomic molecules would diffuse as atoms. But according to my experiments I notice ...
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78 views

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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142 views

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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128 views

How does air going through silica gel change its humidity

Assume that the properties(temperature,humidity,velocity and so on) of the incoming air flow stay constant. The air flow goes through a silica gel plate. Humidity of the air will decrease, but how to ...
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1answer
125 views

How much air could an activated charcoal bag or baking soda box actually purify / deodorize?

Someone I know recently bought a set of small stylish and expensive cloth bags (roughly paperback book sized) filled with activated bamboo charcoal, that you place in a room and it purportedly ...
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1answer
33 views

Does a mixture of two different gases increase in entropy in a thermally isolated system?

I know gas will increase in entropy as it goes toward equilibrium, but what if there are multiple gases of different densities?
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38 views

Diffusion law for continuous domains

I'm an engineer, so don't expect too much :) I'm modelling with FEM the convection-diffusion-reaction equation which is derived by the continuity equation. $\frac{\partial c}{\partial t} +\nabla \...
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1answer
133 views

Do electrons really diffuse when a temperature gradient is applied?

In many websites and books, it is generally said that the charge carriers, be it electrons or holes, diffuse through the considered material when a temperature gradient is applied. However I have ...
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About thermal diffusion in air and water

I have a fairly simple question: Why does heat spread faster in air than in water? For me it is counterintuitive compared to the higher thermal conductivity of water. The only "empirical" answer I ...
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48 views

Will a Brownian Particle hit an infinite wall in 3-D geometry with probability 1?

I know that in 3-D the probability of recurring a given point is zero for a Brownian particle. Given an infinite absorbing wall/plane the probability of ultimately getting absorbed, for a Brownian ...
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74 views

Relation of the Heat kernel and the solution of the discrete diffusion equation

As is well known, the solution to the continuous 1D diffusion equation $\partial_t f=D\,\partial_x^2 f$ is given by the Heat kernel $$f(x,t)=\frac{\mathrm{e}^{-x^2/4Dt}}{\sqrt{4\pi Dt}} \ .$$ On the ...
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159 views

Neumann boundary condition for Laplace's equation in 2D axisymmetric coordinates?

I have the Laplace's equation, say, describing the density $\rho(r,z)$ distribution in a 2D axisymmetric coordinate: $$\nabla^2 \rho=\frac{1}{r}\frac{\partial}{\partial r}\left(r\frac{\partial \rho}{\...
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52 views

How to estimate loss of water from skin?

The question came to while hiking. We are often told that we must drink at least 8 glasses of water regularly to compensate water loss by evaporation from the skin. So how does one compute the rate ...
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1answer
135 views

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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59 views

Viscous accretion disk, green formula

I have this problem. I am studying a the viscous accretion disk problem and in the assumption of constant viscosity the equation of diffusion of the superficial density becomes: $$ \frac{\partial}{\...
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110 views

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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48 views

Random walk with self-transitions taking continuum limit

does anyone have any suggestions regarding how to correctly treat the continuum limit of a random walk that has non-zero self-transition probabilities? To put this concretely, let's say that the ...
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334 views

Is the diffusion coefficient time-dependent?

It is known that in the partial differential equation: $$u_t=au_{xx} $$ within the limits $0<x<1$ and $a>0$, the diffusion coefficient, arises in the mathematical modelling of a process of ...
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1k views

Diffusion in a chemical potential gradient

I am having troubles to understand to connection between equilibrium and non equilibrium thermodynamics. I am studying a mixture of molecules $A,B,C$ and solvent $S$. The free energy $F$ is given by ...
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1answer
71 views

Thermal healing of defects in crystals

Thermal treatment can heal point defects due to the diffusion of atoms towards empty points. In a solid crystal structure, atoms do not diffuse at room temperature (correct?) Energy of thermal ...
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606 views

Diffussivity of gases, molecular weight and Lewis number

I am trying to understand the following figure of laminar premixed flames: The Lewis number is defined as $Le = \frac{\alpha_{mix}}{D_{fuel}}$ where $\alpha_{mix}$ is the thermal diffusivity of the ...
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1answer
52 views

Diffusion equations and classical mechanics

In Wikipedia it is stated that the diffusion equation can be derived from the continuity equation. It is not clear to me how the classical mechanics affect the diffusion equation. For example, if the ...
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49 views

Factor of 1/3 in diffusion constant

In Feynman's Lectures on Physics, it says that the diffusion constant for a diffusive gas may be written as $$D=\frac{1}{3}lv$$ where $D$ is the diffusion constant, $l$ is the mean free path between ...
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47 views

Where does differntial equation of covariance matrix come from?

Does anyone know where the differential equation of covariance matrix comes from? $$\frac{dC(t)}{dt}=AC(t)+C(t)A^T+D$$ where $C$ is the covariance matrix, $A$ is the drift matrix, and $D$ is the ...
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24 views

Why does wavelength coherence affect diffusion?

Not to be confused with the relationship between wavelength and photon localization. But, laser light is is able to stay concentrated over a vast distance, much more so than every-day lamp light. ...
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1answer
31 views

Intrpretting questions on Fickian diffusion

I am considering the Zimm model for polymer dynamics, and have come across a question Find an expression for the time it takes for the polymer to diffuse a distance equal to its contour length $L=...
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63 views

Pouring Soda At A Constant Angle And Minimizing Filltime While Accounting For $\mathrm{CO}_2$

I was pouring soda, when the act made me think of a question. If you have an unopended $2L$ bottle of soda, and you wish to fill up a generic cylindrical glass cup - if you hold the $2L$ bottle at a ...
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The influence of a temperature gradient on the growth of dendrites in a solid liquid interface

Not sure if this is the correct place to ask... My book states that, for a Solid Liquid interface in which the liquid has an increasing positive temperature gradient (increasing temperatures in ...
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94 views

Alternative to Fick's law of diffusion?

Let's model a concentrate $C$ with a flux vector $\overrightarrow{J}$. From first principle we can obtain the conservation law $\frac{\partial C}{\partial t} + div \overrightarrow{J}$. An adequate ...
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77 views

How long does it take for oil to coalesce in water?

I was studying the process of coalescence in emulsions. We considered $N$ bubbles of liquid 1 floating in liquid 2. The result we derived, is that if there are some dissipative forces (diffusion) the ...
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30 views

Diffusion through wire cloth using Darcy's law

I am currently working on a heat pipe project and I am stuck at this point where I need to calculate if methanol can diffuse through 15 complete turns of a stainless steel wire mesh( seen in pic). I ...
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36 views

What is the decoherence rate and the thermal de Broglie wavelength in quantum Brownian motion?

I know that when the thermal de Broglie wavelength is on the order of the interparticle distance, the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. I ...
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57 views

Diffusing in narrow chanels, markers and distribution of particles

I noticed 'Mixing of diffusing particles' research by E. Ben-Naim taking into account Mahonian distribution which tends to normal distribution for very large number of particles (infinite number). ...
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40 views

Impurity diffusion from solid to air

I have to put up a simple 1D model to simulate the diffusion of impurities in a bulk material, to a top thin layer made of another material, and compare it to experimental data. I first did it with ...
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146 views

Density Fluctuation in N-Particle Brownian Motions

I am studying spatial population movement and would like to model the density fluctuation by assuming a Brownian movement for each individual. Because the total number of individual ($N$) is large but ...
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2answers
100 views

Numerical scheme Fokker-Planck Diffusion

assuming the diffusive motion of a substance $u(x,t)$ depends on a variable $b(u(x,t))$. Fickian Diffusion then reads $$ \frac{\partial u}{\partial t}=\frac{\partial}{\partial x}\left(D(b(u(x,t)))\...
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143 views

Critical mass (radius) of U235

I am calculating the critical mass (radius) of $U^{235}$ sphere. I want to calculate the mass for three different cases: 1. air/vacuum surrounds the sphere (diffusion coefficient is infinite) 2. ideal ...
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36 views

diffusion of gases in both directions

I am a technical specialist that works on analytical equipment. Gas chromatographs use carrier gases like helium and hydrogen that flow through long, thin glass tubes coated on the inner surface with ...
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19 views

Can a mechanical forced oscillation of a gas column significantly affect diffusion rates through the column?

High Frequency Ventilation (HFV) is a special type of mechanical ventilation used in critical intensive care units. Rather than moving gas volumes in bulk at conventional breath rates, HFV operates at ...
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1answer
967 views

Diffusion and Drift currents in forward bias

Why do the current in diode in forward bias configuration called "Diffusion current" even if this current is a resultant of external voltage supply which create electric field in diode ,hence should ...
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56 views

Numerical integration of the heat equation with variable thermal diffusivity using spectral discretization

I want to integrate this equation in time: $$\frac{\partial u(x,t)}{\partial t} = \frac{\partial}{\partial x} \kappa(x) \frac{\partial u(x,t)}{\partial x}$$ with initial condition $$u(x,0) = \frac{...
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1answer
315 views

On the derivation of diffusion coefficient in thermodynamic terms

I'm trying to express the diffusion coefficient $D$, regarding particles suspended in a liquid, in terms of thermodynamic parameters. In this, some evident problems were encountered when trying to ...
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1answer
95 views

Modification of Einstein's field theory with cosmological scalar field

I learn about a new model to describe the dynamics of particles undergoing diffusion in general relativity. The evolution of the particle system is described by Vlasov equation without friction. The ...
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Trouble in understanding the formula for drift current in Stokes-Einstein relation

In the derivation Stokes-Einstein relation, which relates diffusion and damping, we basically use the fact that diffusion current and drift current must balance each other at equilibrium. But I have ...