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1answer
33 views

Room with open door and heater : use inside boundary conditions or heat source for PDE?

I want to model the stationary temperature in a room (=square) that has one open door (=side) is otherwise perfectly insulated is heated through a (circular) heater that is placed somewhere in the ...
-1
votes
1answer
17 views

Stokes-Einstein Relationship to find time taken to diffuse $x$ distance? [on hold]

A molecule has a diffusion coefficient of 0.5 × 10-9 m2s-1. Calculate how long it would take on average for the molecule to diffuse 10 µm. So I have the above ...
0
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0answers
21 views

Spread of gases in a room

I have had some thermodynamics and statistical mechanics, but I don't know much fluid mechanics. I am not sure how to model the spread of gases in a room in the case of a fire or some leaking vent. ...
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0answers
33 views

Calculation of charged sphere distribution near a wall in Cartesian coordinates

I am following a similar derivation as found in the beginning of this paper "Quantitative aspects of the growth of (charged) silica spheres" by A.P. Philipse. This paper calculates the growth of a ...
3
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0answers
69 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 ...
0
votes
1answer
33 views

Concentration of pollutant in the pool [on hold]

I'm a beginner in the Mathematical Modeling. I'm trying to solve one problem from our book, where the point is to compute the concentration of pollutant in the pool. I tried to solve it by Fourier ...
1
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0answers
90 views

How to derive equation for time it takes photons to diffuse through the Sun

I am wanting to use the Rosseland radiative heat flux equation to find the time it takes for photons to diffuse through the sun. The answer I am wanting to derive is: $$\tau_D~\frac{\rho \bar C_p ...
0
votes
3answers
507 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 ...
0
votes
1answer
124 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 ...
3
votes
2answers
176 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 ...
3
votes
1answer
119 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. ...
1
vote
1answer
33 views

Physical reason why Prandtl number is order unity for gases?

Is there a physical reason behind the fact that for gases the thermal diffusivity is on the same order of magnitude as kinematic viscosity (and as such a Prandtl number of order unity) and if so what ...
0
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0answers
16 views

Copper vs Tungsten (Diffusion)

I've been studying on how to compare the activation energy for (void-) diffusivity of Copper versus Tungsten. I ended up finding $E_a[cu] = 1.1[eV]$ and $E_a[W] = 5.2[eV]$ in literature where the ...
0
votes
1answer
161 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 ...
5
votes
1answer
71 views

Diffusion coefficient for asymmetric (biased) random walk

I want to obtain a Fokker-Planck like equation by taking the continuous limit of a discrete asymmetric random walk. Let the probability of taking a step to the right be $p$, and the probability of ...
1
vote
3answers
125 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
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2answers
58 views

When I open a window to air out the room, how does the smell disperse?

Let's say I'm in a room with some kind of noxious stink, possibly of flatulent nature. The quickest way to right the world that comes to mind is to open a window. When I open a window, how do the ...
1
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0answers
16 views

Overdamped Fokker-Planck equation with general force field (gradient + ratation)

I am looking for general formulation of the overdamped Fokker-Planck equation (='Smoluchowski eq.') for a diffusing particle in general force field $F = -\nabla U + \nabla\times A$ . So far I have ...
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0answers
19 views

Fick's Law for material extraction in a spherical material

I'm looking for a text which talks about how to extract a material from some object (spherical to be easier), (for example, water from the food) and learn about these formulation using the Fick's Law ...
2
votes
2answers
238 views

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

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 ...
3
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0answers
26 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 ...
0
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0answers
29 views

What happens when a semipermeable membrane allows only one solute to pass through?

I'm essentially a medical student where we deal a lot with osmosis. But when we are taught, it is done generally with only a single solute in consideration. What if two different solutes are used on ...
2
votes
1answer
42 views

Deriving a diffusion equation from a given mass flux density [closed]

I am given that the mass flux density $q$ of a substance in a medium obeys the following physical law. $$q=-D\frac{n^3}{n-n_0}\frac{\partial n}{\partial x}+nv,$$ where $n(x,t)$ is the ...
0
votes
1answer
46 views

Dependance of diffusion coefficient on size?

What's the dependance of the diffusion coefficient on size? More explicitly, suppose I have a particles of characteristic length $l$, dissolved in a liquid. How does $D$, the diffusion coefficient of ...
0
votes
0answers
17 views

Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?

Say the diffusion coefficient of the concentration of a particle in a fluid in 3-dimensions is $D_{3\textrm{d}}$. Can we estimate the diffusion coefficient of the same particle in the same fluid, in a ...
0
votes
1answer
29 views

Diffusion (2 species) versus advection (1 species)

Why do we see diffusion with 2 species but advection with a single species if both cases involve molecules spreading to increase entropy? To take a physical example: Let's say I have a box with two ...
0
votes
1answer
87 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 ...
4
votes
1answer
48 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 ...
0
votes
0answers
49 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
26 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 ...
0
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0answers
23 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
124 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
1answer
19 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
271 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
vote
2answers
110 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
24 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
votes
0answers
26 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
9k 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
votes
0answers
33 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
31 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 ...
0
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0answers
18 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
105 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
2k 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
14k 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
128 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
52 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
70 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
63 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
32 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
62 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 ...