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1answer
53 views

1-D Fick's first law - partial derivative?

I've recently been reviewing some concepts, including diffusion. Fick's 1st law: $$J = -D\frac{\partial C(x,t)}{\partial x}$$ as I understand it, applies to the steady state. For 1-D diffusion and ...
1
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1answer
164 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 ...
0
votes
1answer
139 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 ...
3
votes
1answer
37 views

Derivation of the diffusion coefficient?

The diffusion coefficient relates the particle flux $J$ to the gradient in the number density (of the 'labelled' particles) $\frac{\partial \bar n}{\partial z}$ such that; $$J=-D \frac{\partial \bar ...
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0answers
44 views

Does nature really follow the heat equation?

I think the heat equation says that the first derivative of temperature with respect to time in a stationary solid varies as the negative of the second derivative of temperature with respect to ...
1
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0answers
14 views

can 3D diffusion be interpreted as superposition of 1D diffusion

Is diffusion of a substance in water independent in the X, Y and Z directions? In other words, if I want to solve how a substance diffuses through a volume, can I separately solve equations for its ...
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0answers
13 views

Extension of the advection diffusion equation with diffusion perpendicular to the flow

Assume you model particle flow in fluid in a cylinder by an advection-diffusion equation, thus taking into account both diffusion and bulk flow. What would happen to the model if you would, at some ...
1
vote
1answer
66 views

Rigorous derivation of Fick's first law

I am looking for a rigorous derivation of Fick's law, i.e. that the current density $\mathbf{j}$ satisifies $\mathbf{j} = - D \nabla u$ where $u$ is e.g. some concentration and $D$ the diffusion ...
0
votes
3answers
417 views

How does the dissolution of salt affect the solution density?

Suppose you have a container of water as a solvent and you a certain amount of salt as a solute sitting at the bottom of the container that has yet to start dissolving. Supposing temperature and ...
3
votes
2answers
168 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
votes
1answer
12 views

Thermal diffusion equation with heat per unit length?

Let us say we have a metal rod. Along that rod there is a rate of heat generation of H per unit length. If we assume we are in the steady state then I would expect us (from the thermal diffusion ...
5
votes
2answers
249 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 ...
1
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2answers
48 views

Heat Losses from water pan due to vaporisation before boiling

I'm studying heat transfer from an electric heater to a cooking pan (Stainless steel) filled with water; specifically, my problem is related to water vaporisation, as I've already found good models to ...
1
vote
0answers
22 views

Waterproof Case Time Limits [closed]

A lot of cellphone cases are rated safe for one hour at two meter depth. I assume this is due to water molecule diffusion along case seams (like the zipped zipper in a ziplock bag), right? Is ...
0
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0answers
25 views

trying to figure out an expansion in Brownian motion derivation

In the derivation for the diffusion equation on the wikipedia article for Brownian motion, they have these equations: I can't figure out how $\rho(x+\Delta,t)$ gets expanded, though. For a Taylor ...
6
votes
4answers
6k 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?
0
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0answers
31 views

The change in time of a concentration in a fluid can be described by Reynolds' theorem. Is that the whole story?

Let $d\in\left\{2,3\right\}$ and $\Omega_t\subseteq\mathbb R^d$ be the bounded set occupied by a fluid at time $t\ge 0$. Moreover, let $\eta_t:\Omega_t\to[0,\infty)$ be the concentration of imaginary ...
2
votes
1answer
29 views

The validity of constitutive diffusive fluxes

In transport phenomena the diffusive fluxes for mass, energy and momentum are the constitutive laws: $$\boldsymbol{j}_c=-D\boldsymbol{\nabla}c \quad \boldsymbol{j}_T=-k\boldsymbol{\nabla}T \quad ...
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0answers
15 views

Fluid flow in porous medium with moving boundary

Everyone, I would like to numerically model axisymmetric fluid flow in a porous medium with a moving boundary, where the fluid pressure is specified on the boundary, whose radius increases with time. ...
3
votes
2answers
78 views

More intuition in understanding diffusion

This is a short conceptual question: (I think I'm confusing some very key concepts, here's an attempt to try and resolve it) Systems whose dynamics are governed by diffusion, for example a particle ...
3
votes
2answers
1k views

Units of the Stokes-Einstein rotational diffusion coefficient

The Stokes-Einstein rotational diffusion relation tells us that we can write down a rotational diffusion coefficient for a sphere as: $$D_r \approx \frac{k_B T}{\zeta_f} \approx \frac{k_B T}{(8 \pi ...
4
votes
3answers
13k views

What is the physical meaning of diffusion coefficient?

In Fick's first law, the diffusion coefficient is velocity, but I do not understand the two-dimensional concept of this velocity. Imagine that solutes are diffusing from one side of a tube to another ...
0
votes
0answers
97 views

Derivation of diffusion coefficient

For diffusion transport considering the "random walk" of electrons, I have the following derivation that leads to the diffusion coefficient $D$: $$d_1=d_2=\dots=d_n=\tau v \implies\\ \sum_n ...
0
votes
2answers
41 views

Why do we need Diffusion currents to explain semiconductor current flow?

Why do we need the idea of carrier concentrations to explain current flow? Can we simply not associate the disparity in carrier concentrations between two samples to a disparity in relative charge ...
3
votes
1answer
62 views

Heuristics behind Dirac delta function in Master equation for probability?

I'm reading this paper [Phys. Rev. Lett. 106, 160601 (2011)] and it studies simple diffusion where a particle stochastically resets to its initial position $x_0$ at a constant rate $r$. As you can ...
0
votes
1answer
62 views

Speed of spontaneous mixing of different gases

Suppose we have a rectangular box divided into two equal cubic parts by a vertical impenetrable wall. Part 1 of the box contains a standard state mixture of $(1-x)$ mole of gas $A$ (e.g. Oxygen) and ...
0
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0answers
31 views

Is it possible that my 750ml water bottle contains spent fuel from a space shuttle launch

Firstly I live in New Zealand which is very distant from USA which is where the space shuttle was originally launched from. So what is the possibility of molecules from the rocket engines spent ...
2
votes
1answer
38 views

alternative derivation of Einstein relation

Is there a derivation of the Einstein–Smoluchowski relation without the assumption of the Boltzmann distribution? Every time I see a derivation, it always assumes the Boltzmann distribution, such as ...
1
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0answers
12 views

Diffusion of magnetization (NMR)

In the context of MRI I'm trying to understand the mechanisms of magnetization diffusion. Consider a sample that is magnetized by an external magnetic field. We have displacement of magnetic moment ...
1
vote
3answers
951 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 ...
3
votes
1answer
89 views

Fick's first law inhomogeneous proof

I have seen Fick's first law of diffusion derived for a homogeneous material many times, however I am struggling to find a satisfactory proof for inhomogeneous, particularly for particle diffusion. ...
0
votes
1answer
56 views

Brownian motion, net displacement, and diffusion - conceptual

I'm having trouble reconciling some conceptual issues of brownian motion. Let's say we have a box with two compartments separated by a membrane. Solute is at a high concentration on one side, and at ...
1
vote
2answers
51 views

diffusion velocity

i understand that diffusion is the movement of particles from high concentration areas to low concentration, but what is the cause of that movement atomically. And especially in the case of charge ...
0
votes
1answer
91 views

Does diffusion current in semiconductor always exist?

According to what I understand, diffusion current is caused by the change in concentration of charge carriers in semiconductor (free electrons and holes) from higher concentration region to lower ...
2
votes
2answers
118 views

Show that the boundary layers diffuse out from the plate with speed $\sqrt{\frac{\nu}{t}}$ [closed]

I was wondering if somebody would be able to help me with this problem. I know how to solve it using dimension arguments but I'm unsure what is meant by transformation techniques. Any help would be ...
0
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0answers
41 views

How long does it take for an Oxygen to diffuse around Earth?

We drill into the ground and find a huge pocket of oxygen. How long does it take for that oxygen to diffuse around Earth? I'd like to know for the first oxygen molecule how long it takes to effect the ...
0
votes
2answers
110 views

Diffusion of gas into vaccum

I'm interested in solving the diffusion equation for gas in vacuum. I have a general question and a more specific questions. What I know: The Diffusion Equation: For density function ...
0
votes
0answers
36 views

How can I get the boundary and initial conditions of the convection–diffusion equation consistant?

I want to solve the 1D convection–diffusion equation. The boundary conditions are a flux in from the bottom and a flux out on the top. Furthermore I want no concentration inside at the beginning. I ...
1
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0answers
63 views

Riemannian generalization/adaption of the Hubbard–Stratonovich transformation

I'd like to write the Hubbard–Stratonovich (HS) transformation of a scalar function on a Riemannian manifold. This transformation is quite simple in Euclidean space. One can consider it as a Fourier ...
0
votes
0answers
53 views

Confusion regarding interpretation of a diffusion related PDE?

So I was reading Keller & Segel paper related to mathematical model of cellular aggregation in slime molds. In the model (considering 2D assumption) we have an equation like below: ...
4
votes
0answers
58 views

Stochastic process generating fractional diffusion

One way to generate Brownian motion is as follows: Define a waiting time probability distribution $\psi(t)$ and step length probability distribution $\lambda(x)$. Require also that $\langle \psi ...
1
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0answers
65 views

How do I apply a renormalization technique to estimate the fractal dimension of a diffusion limited aggregate?

Diffusion Limited Aggregation (DLA) is an interesting phenomena observed in nature and discussed here. From a theoretical view point, it'd be nice to know about the fractal dimension of a DLA formed ...
1
vote
0answers
83 views

Analytic solution to diffusion in composite medium for long times

I am trying to find an analytical solution to the transient 1D diffusion equation in a composite medium (e.g. binary liquid): $$\partial_t c_i = D\partial_x^2 c_i$$ where the domain for species $i$ is ...
0
votes
0answers
110 views

1D drift-diffusion equation with single absorbing boundary

If we have just the simple diffusion equation (in 1D): $$ \frac{\partial P(x,t)}{\partial t} = D \frac{\partial^2 P(x,t)}{\partial x^2} $$ with an absorbing boundary at x=0 and initial condition ...
4
votes
5answers
193 views

No diffusion term in conservation of mass in Navier-Stokes equations?

I have followed derivations of the Navier-Stokes equations and I can see how the various terms arise in the "main equation", the momentum conservation equation. However I don't understand why the ...
1
vote
0answers
82 views

How does fluid velocity affect the dissolution of some solute in the fluid?

Suppose we have a perfect sphere of some solute such as sugar and we place it in a fluid such as water, at a certain temperature, that is not moving. It will dissolve and diffuse into the water due to ...
0
votes
1answer
30 views

Can the energy/power required to mix two fluids together be calculated?

Given two fluids; say for example oxygen and nitrogen gases. By simply introducing, again for example 1 liter of each gas into a closed container, the process of diffusion alone will eventually cause ...
2
votes
0answers
32 views

What physical processes govern the formation and shape of clouds?

There are many kinds of cloud shapes that appear in the sky. In fact, it's not unusual to see several different kinds of clouds in the same sky. What kind of physics equations and processes govern ...
1
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3answers
89 views

Diffuse laser light in a surface

Im building a laser target. It consists of a box, with a black plexiglass circle in the center of one of its sides, and a larger white circle around it. The black for the inside shots, and the white ...
0
votes
0answers
51 views

Anomalous diffusion dynamic exponent calculation

I'm trying to calculate this $\alpha$ (dynamic exponent, I think) from an equation from this wikipedia article. The equation (anomalous diffusion power law): $r^2 \propto t^\alpha$ The problem is ...