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22 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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4answers
94 views

Why doesn't fire flow back INTO the cylinder?

Let us take into a consideration a (pressurized) kerosene stove. The pressure drives fuel out of the nozzle, like or in a much simpler arrangement as in Question- Why doesn't fire flow back ...
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1answer
21 views

Getting the velocity of self-diffusion from the einstein relation

I have been reading about self-diffusion of a particle here: http://www-hsc.usc.edu/~rfarley/Diffusion-SI-2003.pdf and on page 9 it gives Einstein's relation as $(\Delta x)^2 = 2 D t$ and I can ...
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2answers
37 views

Why do the free electrons in N-type want to diffuse?

I'm trying to understand how a diode works and for this I've used(among other resources) the book written by Albert Malvino, Electronic Principles. Everywhere I read about this topic, it says that ...
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3answers
58 views

What is the exact difference between diffusion, convection and advection?

I have tried to explore the information but still not very clear on the exact difference between diffusion, convection and advection. Can anyone help me out to clear my concept?
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2answers
324 views

Existence of gusts of wind, an anomaly?

Enthusiast + Student, not a pro, so pardon my ignorance. How can wind possibly flow in gusts? The way I understand it, a gust is a pocket of air which hits you at slightly higher speed. But how ...
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0answers
59 views

Standard partial differential equation? [migrated]

Is there any standard equation which looks like this one, $$ u_{t}(x,t) = \alpha \, u_{xx}(x,t) - \beta(t) \, u(x,t) + S(x,t), $$ where $\beta(t)$ is nonlinear in time, and $\alpha$ is a constant? ...
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3answers
55 views

Force causing diffusion

I was curious if there was an equation describing the force acting on a particle (say, sitting in a fluid) that causes it to diffuse. If so, does it include the diffusion coefficient D? Based on ...
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1answer
627 views

How fast will sublimed dry ice mix with air?

I saw this photo and wondered: Will the CO2 stay mostly in a layer on the floor with the rest of the atmosphere resting on top, or will it quickly diffuse throughout the room? This lab is probably ...
2
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1answer
39 views

What is the difference between the diffusion equation and the heat equation?

I know that the diffusion equation is a more general version of the heat equation. But what is the exact difference informally?
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0answers
32 views

Mathematical Model For Osmosis

We already know that physical phenomena like diffusion could be modelled using PDEs. For example, denoting the concentration by $u$, the diffusion process reads: $$ \partial_t{u} = \Delta{u} $$ Now my ...
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0answers
25 views

Heat sink simulation with a fan

I am trying to solve this problem using advection-diffusion model and finite element method for solving it due to the complex geometry. Basically the problem i'm trying to solve using OpenFOAM is see ...
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0answers
60 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
34 views

Reaction-diffusion. From kinetic parameters in 3D, can we infer their equivalent in 1D?

I am studying a reaction-diffusion system : $A+B ⇌_{k_{-}}^{k_{+}} C$. From experimental data I have all the kinetic parameters : diffusion coefficients $d$ and reaction rates $k_+$, $k_-$. Beside I ...
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0answers
11 views

Analytic solution to diffusion in composite medium for long times

I am trying to solve the transient 1D diffusion equation in a composite medium where the interfacial concentration is described by a Henry condition. I have found an adequate solution for short times ...
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0answers
41 views

How can one calculate diffusion velocity given the diffusion coefficient?

I am creating a basic simulation of 2-D diffusion and was wondering how diffusion velocity of a particle can be calculated if the diffusion coefficient is known (using no other information). Is this ...
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0answers
21 views

Diffusion modeled by Levy process and Wiener process

I'm reading about diffusion and see that both Levy process and Wiener process can be used to model the diffusion of a particle. Why Levy process is more general than Wiener process, especially in term ...
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0answers
30 views

Martensitic transformation in ceramics

What is the specification of Martensite (displacive) transformation in ceramics comparing to yhe one in metals? I just know about Martensite transformation in metals. For example, these ...
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1answer
18 views

Dynamic equations for propagation of light through dust

For smoothly inhomogeneous media light propagation can be modeled by Maxwell's equations with non-constant $\varepsilon$ and $\mu$. This allows to relatively easily model propagation in the medium ...
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2answers
40 views

Energy Flux due to Diffusion

Per the Fundamental Thermodynamic Relation, I know that the chemical potential of $i$ represents the energy which would added to a system if a particle of $i$ were added with all other system ...
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1answer
91 views

Time for a particle undergoing brownian motion to reach a point in a volume

I was wondering how one could calculate the average time a particle needs to reach a random point in a small sphere (filled by water) with a radius of maybe $10 \mu m$. I thought of using the ...
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1answer
144 views

Rate of Temperature Change due to Heat addition

I might be wrong but I will give a little background leading to my question. I am trying to calculate the heat generation in the advection-diffusion equation for heat generation due to friction by ...
1
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1answer
54 views

Does water diffuse trough rubber of car tire of when liquid or only as gas

Does Water difuse trough rubber of car tire when its liquid or only when its a gas. Can also be that is diffuses but slower when liqiud. I want to know this for my argumentation that filling car tire ...
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3answers
298 views

Schrödinger equation derivation and Diffusion equation

I am aware of the debate on whether Schrödinger equation was derived or motivated. However, I have not seen this one that I describe below. Wonder if it could be relevant. If not historically but for ...
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0answers
35 views

Why is it valid to assume that the liquid-vapour interface is always saturated during evaporation?

For steady state evaporation, I read from two textbooks which simply states that the partial pressure of vapour of interest (say water) at the liquid-vapour interface is equal to the saturation ...
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0answers
39 views

Is phase defined for species undergoing diffusion?

If we have a gas diffusing through say a solid metal, or gas diffusing into a liquid, what phase is the diffusing molecules considered to be in (or is it even possible to define this)? Is it possible ...
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0answers
12 views

Conventional flux in centrifuge?

The molecules sediment in centrifuge, which is rotating with angular velocity $\omega$. The chemical potential of molecule (considering potential associated with centrifuge force) is: ...
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0answers
54 views

Diffusion of particles

If $n(\vec{r},t)$ is the number of particles per unit volume and $V$ the volume, then $N = nV $is the number of particles in volume $V$ For a small volume, it should be $dN = d(nV) = Vdn + ndV$ But ...
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1answer
29 views

How big are soluted salts in drinking water?

I have just seen the TED talk Michael Pritchard: How to make filthy water drinkable where a device called LifeSaver bottle that filters particles that are bigger than 15nm out of water. I have heard ...
1
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1answer
40 views

How do I set up the tridiagonal matrix for a heat diffusion with layers of different thermal diffusivity?

I have Scala code that recreates the Crank-Nicolson solutions for the diffusion equations, and matches 'Excel for Scientists and Engineers' (Joe Billo, Wiley). However, I would like to be able to ...
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0answers
86 views

Temperature dependence for specific thermal diffusivity in the diffusion formula

I recently found this answer about the diffusion equation (nice one actually), but have one doubt about the temperature dependence of this formula. If the "packet" of energy (terminology suggested ...
2
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1answer
19 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 ...
5
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0answers
67 views

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 ...
2
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1answer
84 views

Diffusion in the standard map

Consider the standard map (also known as Chirikov map): $$ p_{n+1} = p_n + K \sin(\theta_n) \\ \theta_{n+1} = \theta_n + p_{n+1} $$ I know that the diffusion coefficient according to the ...
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2answers
165 views

Where I can find information about how helium gas diffuses through different polymer materials

I need more experimental information about helium gas diffusion in solid materials such as different plastics, metals, ceramics etc. For example I am scientifically curious about what is the polymer ...
1
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0answers
55 views

Validity of a steady state solution of reaction-diffusion equation

I am performing a simulation involving growth of bacteria. This is an agent-based simulation where the solutes (glucose, oxygen etc.) are represented as a concentration field discretised over space, ...
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1answer
83 views

1D Smoluchowski diffusion equation in a linear potential

I am interested in solving a 1D Smoluchowski diffusion equation in a linear potential $U(x) = cx$ for a constant force $c$. This problem follows chapter 4 of the theoretical biophysics script by ...
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1answer
70 views

How does a minority carrier diffuse?

I have gone through a lot of questions but none of them ask how do the minority carriers approach the depletion layer in the first place. When a p-n junction is formed, negative space charge ...
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2answers
137 views

Can diffusion produce energy?

A friend and I recently got into a silly argument where I stated pure diffusion can't produce energy since diffusion are a part of passive transport. He stated if we If we have tinny ...
2
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2answers
68 views

optical diffusion (scattering) versus refraction

When an electromagnetic wave meets an interface a part of it is reflected and part of it is refracted (and from the refractive index I can calculate the angles of propagation and the intensities using ...
1
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1answer
740 views

Understanding the mean square displacement in molecular dynamics

In a Molecular Dynamics (MD) simulation, the mean square displacement $\text{MSD}$ is given by $$\text{MSD}(\delta t) = \left\langle\left|\vec{r}(\delta t)-\vec{r}(0)\right|^2\right\rangle,$$ where ...
3
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1answer
108 views

Heat diffusion: evanescent waves?

It has been recently pointed out to me that the solution of the heat equation in a semi-infinite material with an oscillating boundary condition at the surface is not an evanescent wave. The argument ...
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1answer
87 views

A simple osmosis problem

The following is adapted from a problematic question* asked on the Bio site. I would like to ask it free of those distractions here. If there is anything unduly artificial about the problem please ...
1
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1answer
101 views

Gillespie's stochastic framework valid for particles in aqueous solution?

Gillespie proposed a stochastic framework for simulating chemical reactions which is predicated on non-reactive elastic collisions serving to 'uniformize' particle position so that the assumption of ...
5
votes
1answer
166 views

Simple question regarding the Green's function for the diffusion equation

The differential operator for diffusion in three dimensions is given by $\partial_t - k \nabla^2$ where $k$ is a constant. The Green's function is (according to Wikipedia) $$\theta(t)\left( ...
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4answers
724 views

Do particle velocities in liquid follow the Maxwell-Boltzmann velocity distribution?

The Maxwell-Boltzmann velocity distribution arises from non-reactive elastic collisions of particles and is usually discussed in the context of the kinetic theory (for gases). There are various ...
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1answer
174 views

Boundary conditions for the heat equation when solving a mass density gradient

I'm working with a mass density gradient with length $L$ and I'm trying to solve the heat equation in 1-D (mass diffusion equation, $\partial_t\rho(t,x)=D\Delta\rho(t,x)$), but I'm not sure which ...
1
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1answer
2k views

Characteristic length for the diffusion equation (temperature)

The background: I'm doing some simulation work involving the diffusion equation in 1D. Specifically I have some temperature profile, constant thermal conductivity and fixed temperature at each end of ...
3
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1answer
99 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
0
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0answers
108 views

First passage time of diffusing particle with partially absorbing boundary

Given the solution to the spatiotemporal evolution of a single particle on a 1-D surface $P(x,t)$ a nice result (that I gleaned elsewhere on physics.SE) is that for a boundary at $x=0$ where ...