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1
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0answers
38 views

Is Gas flow rate or Volumertric flow rate right one to use for thick wall?

I will make container from steel or aluminium ( 0.5 mm thickness ) and fill it with air (2 bar) and I want to know how much pressure would the container loose overtime (20 years) ? I have asked this ...
4
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1answer
28 views

Why do individual clouds not diffuse into a single less dense cloud?

On a partly cloudy day, many individual clouds can be observed in the sky. I would expect that the moisture in the clouds would want to diffuse out into the other less dense non-clouded areas. ...
2
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0answers
21 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}{\...
0
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0answers
23 views

Diffusion Equation for Particle Hopping with drift

First of all, I haven't studied partial differential equations yet, hence this question might sound silly. I am doing a simulation for particle hopping on a lattice with python. I was said that in ...
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0answers
64 views

The gas in a can of coke can escape?

If I have a can of coke that's 5 years old for example, how will the gas (CO$_2$) exit the can? Will the CO$_2$ pass through the metal of the can (100 microns thick) or justwhere it's precut (to ...
2
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0answers
40 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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0answers
23 views

Random walk of a polymer in an annular space - filling in some steps

In Muthukumar, M., 2003. Polymer escape through a nanopore, J. Chem. Phys., 118, 5174–5184, the author solves the diffusion equation for the probability $P(\vec{r},\vec{r_0},N)$ that the ends of a ...
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0answers
17 views

Diffusion barriers on surface?

Can the barrier to diffuse on the surface, be it amorphous or a crystalline be greater than the binding energy between the adatom and the surface ?
3
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0answers
38 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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1answer
24 views

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

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
26 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. ...
1
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1answer
43 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 ...
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0answers
43 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
107 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 ...
1
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0answers
96 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 R^...
1
vote
1answer
37 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 ...
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0answers
23 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 ...
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 ...
5
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1answer
110 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 ...
0
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0answers
24 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 ...
4
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0answers
35 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
34 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
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1answer
46 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
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0answers
20 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
37 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
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2answers
85 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 ...
0
votes
1answer
52 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
1answer
107 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
60 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 n}...
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0answers
50 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
33 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
35 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
210 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
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1answer
22 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 ...
1
vote
2answers
164 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
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0answers
25 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
29 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 ...
0
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0answers
37 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 ...
0
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0answers
19 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. ...
2
votes
1answer
32 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 \...
3
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2answers
117 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 ...
0
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2answers
58 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 ...
0
votes
1answer
67 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 $...
3
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1answer
75 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 see,...
0
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0answers
33 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
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1answer
91 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
23 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 ...
3
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2answers
135 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
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2answers
139 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
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1answer
78 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 ...