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-4
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0answers
18 views

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

I was wondering if someone could help me with this problem. I think it's quite simple, but I'm not sure how to do it! An infinite horizontal plate moves with speed $U$ in its on plane relative to ...
2
votes
1answer
62 views

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

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 ...
2
votes
0answers
34 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 $\lambda(t)$. Require also that $\langle \psi ...
1
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0answers
26 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 ...
0
votes
3answers
64 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
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0answers
36 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 ...
1
vote
0answers
32 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 ...
4
votes
5answers
110 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 ...
0
votes
1answer
22 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
18 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
vote
3answers
38 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
19 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 ...
0
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0answers
12 views

How to calculate diffusion lenghth in a constant source and sink model?

Here is the context: in 1D, a pathogen cell sits in a homogenous bath of antibiotic. It can express a protein that destroy the antibiotic molecule to protect itself. Given the concentration of ...
6
votes
1answer
140 views

Why is Johnson noise a Gaussian process?

Noise processes in engineering and physics are frequently assumed to be Gaussian processes. This allows use of convenient analytical techniques. The question then arises as to why natural processes ...
5
votes
1answer
142 views

Why is it difficult to mix helium and nitrogen gases?

I recently learned an interesting fact: That it's difficult to mix helium and nitrogen gases in a compressed gas cylinder. Gas suppliers that need to mix the two gases have to rotate the cylinders for ...
0
votes
0answers
36 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 ...
1
vote
1answer
25 views

Soliton solution for a diffusive system [closed]

With a simple model for bacterial diffusion, I get this partial derivative equation : $$\frac{\partial n}{\partial t} = D\frac{\partial^2 n}{\partial x^2} + d_1 n -d_2 n^2$$ where $n(x,t)$ is the ...
1
vote
0answers
34 views

Contradiction (?): DNA ion mobility vs diffusion constant

There is a certain confusion about DNA ion mobility and diffusion constant in the literature. Consider double-stranded DNA ions in pure water. DNA ions are negatively charged due to phosphoric acid ...
0
votes
2answers
75 views

Modeling $k$-logistic diffusion process

I'm trying to model a diffusion process characterized by subsequent logistic diffusion processes. To give a better idea of what I'm trying to model, you can take a look at the attached figure. In such ...
1
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0answers
33 views

What is a diffusionless fluid?

I'm taking a course in astrophysical fluid dynamics and have come across a problem involving "small diffusionless disturbances" of a fluid. Based on the nature of the course I expect the examiner to ...
18
votes
1answer
1k views

How long would it take for a smelly object to evaporate?

This question is a follow on from this deleted one: http://physics.stackexchange.com/q/177894/26076 as I was writing what I thought to be a valid physics answer to it. Version 1 of this question ...
1
vote
0answers
25 views

In the process of Diffusion Limited Aggregation (DLA), why do the particles prefer to form something which has the shape of a tree?

In the process of Diffusion Limited Aggregation (DLA), why do the particles prefer to form something which has the shape of a tree instead of just a front line?
1
vote
0answers
54 views

Diffusion of a chemical proof (fick's law general) [closed]

I want to prove that: $$C(x,t)= \frac{C_0}{\sqrt{4\pi Dt}} \exp\left[{\frac{-x^{2}}{4Dt}}\right]$$ I've proven so far that Fick's law coupled with the conservation of mass (assuming no influx or ...
1
vote
1answer
39 views

How do i mathematically represent reflection in a (diffusion) Problem?

I am trying to formulate boundary conditions and it occurred to me that I never had to implement a reflective boundary before. The example is a one dimensional diffusion, where at $x=0$ the ...
2
votes
0answers
17 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 ...
0
votes
0answers
28 views

Ratio between thermal conductivity heat transfer coefficient

Consider the Robin boundary condition for the diffusion/heat equation $u_t=a(t)u_{xx}+f(x,t)$: $$\mathrm{-k(t)u_x(0,t)=h(t)u(0,t)}$$ or $$\mathrm{u_x(0,t)+\frac{h(t)}{k(t)}u(0,t)=0}$$ where ...
3
votes
1answer
87 views

Diffusion vs Gravity in water: does a dissolved ion tend to “sink”?

Im a french student in geochemistry. My question might be silly, but I became really too confused to answer it myself. Does gravity affect the diffusion of ions in water ? Lets imagine a vertical ...
0
votes
0answers
49 views

Modelling the diffusion of gas in a container with non uniform temperature

I want to model diffusion of a gas (e.g. water vapor diffusion in air) in a container with a temperature gradient. One side of the container has a hole, but for simplicity of boundary conditions I can ...
2
votes
2answers
103 views

What is the correct form of heat diffusion equation taking into account temperature dependence of specific heat

What is the correct form of the heat diffusion equation in 1D if we take into account the temperature dependency of specific heat capacity? $$ \rho\frac{d(cT)}{dt} = ...
1
vote
0answers
37 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 ...
0
votes
4answers
194 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 ...
1
vote
1answer
53 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 ...
0
votes
2answers
74 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 ...
4
votes
3answers
2k 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?
2
votes
2answers
329 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 ...
0
votes
3answers
79 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 ...
7
votes
1answer
704 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
votes
1answer
89 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?
0
votes
0answers
43 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 ...
0
votes
0answers
42 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 ...
1
vote
0answers
144 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 ...
1
vote
1answer
49 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 ...
1
vote
0answers
75 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 ...
1
vote
0answers
215 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 ...
0
votes
0answers
42 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 ...
1
vote
1answer
26 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 ...
2
votes
2answers
55 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 ...
0
votes
1answer
154 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
1answer
256 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
vote
1answer
95 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 ...