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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
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0answers
21 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?
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0answers
26 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
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1answer
27 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
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0answers
14 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
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0answers
8 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
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1answer
39 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
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0answers
22 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
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2answers
63 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
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0answers
27 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
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4answers
104 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
30 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
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2answers
45 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
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3answers
135 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
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2answers
327 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
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3answers
64 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
686 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
51 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
35 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
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0answers
26 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
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0answers
81 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
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1answer
37 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
14 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
63 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
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0answers
32 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
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1answer
19 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
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2answers
43 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
111 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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1answer
200 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
59 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 ...
1
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3answers
363 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 ...
1
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0answers
39 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 ...
1
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0answers
42 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 ...
1
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0answers
14 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 ...
1
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1answer
30 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
49 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 ...
0
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0answers
94 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
votes
1answer
21 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
votes
1answer
89 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 ...
1
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2answers
196 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
59 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, ...
1
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1answer
92 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 ...
0
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1answer
81 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 ...
1
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2answers
141 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
70 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
881 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
110 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 ...
1
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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 ...