Questions tagged [diffusion]

Diffusion is the net movement (spreading out) of molecules or atoms down a concentration gradient: from a region of high concentration to a region of low concentration.

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Why is dry soil hydrophobic? Bad gardener paradox

When I forget to water my plants, and their soil becomes very dry, during the next watering I can see that the soil becomes hydrophobic. I can even see pockets of air between the repelled blob of ...
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1answer
22 views

Influence of air pressure on degassing of sparkling water

We all experience that sparkling water in a closed bottle will degas for a certain time and as the amount of degassed CO2 increases, this process slows down. My question is: can I slow down the ...
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How are drawing common tangents to get diffusion different for concave and convex phase fields?

Whenever there is a concept of diffusion involved and we need to decipher what is going to happen we tend to draw common tangent s in the phase field diagrams and decide which direction the diffusion ...
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44 views

Where does differntial equation of covariance matrix come from?

Does anyone know where the differential equation of covariance matrix comes from? $$\frac{dC(t)}{dt}=AC(t)+C(t)A^T+D$$ where $C$ is the covariance matrix, $A$ is the drift matrix, and $D$ is the ...
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Is $A\cos(kx-wt)$ a valid solution to the diffusion equation? [closed]

I know that for the wave equation $$\frac{\partial^2\psi}{\partial t^2}=c^2\frac{\partial^2\psi}{\partial x^2} \;, $$ we could always plug in the ansatz $A\cos(kx-\omega t)$, since equations of this ...
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1answer
81 views

How much air could an activated charcoal bag or baking soda box actually purify / deodorize?

Someone I know recently bought a set of small stylish and expensive cloth bags (roughly paperback book sized) filled with activated bamboo charcoal, that you place in a room and it purportedly ...
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1answer
43 views

Why does the Einstein relation hold in the derivation of the Goldman equation?

The Einstein relation $D = \mu k_B T$ is derived by assuming an equilibrium between the drift current and the diffusion current. Knowing this I would assume, that the relation is only valid under this ...
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1answer
21 views

Why does wavelength coherence affect diffusion?

Not to be confused with the relationship between wavelength and photon localization. But, laser light is is able to stay concentrated over a vast distance, much more so than every-day lamp light. ...
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72 views

Why do we interpret the first term of the Fokker-Planck equation as drift?

With the derivation of the Fokker-Planck equation we get: $$\frac{\partial}{\partial t}P(x,t)=-\frac{\partial}{\partial x}(A(x,t)P(x,t))+\frac{1}{2}\frac{\partial^2}{\partial x^2}(B(x,t)P(x,t))$$ We ...
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1answer
57 views

Where does the Master equation for the derivation of the Fokker-Planck equation come from?

I'm participating in an introductory course for biophysics. We briefly discussed the derivation of the Fokker-Planck equation and used the so-called Master equation as a starting point. $$ \frac{\...
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1answer
21 views

How to model mass diffusion with half life

I am in the process of writing a model for the diffusion of a chemical in an aqueous medium. Typically, to do this, one would use the diffusion equation $$\frac{\partial}{\partial t}U=\gamma \nabla ^...
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1answer
33 views

Does diffusion MRI measure diffusion or osmosis?

I am trying to understand the physical property which is measured in diffusion weighted imaging (DWI) and diffusion tensor imaging (DTI). I read that these methods estimate the apparent diffusion ...
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1answer
32 views

diffusion of magnetic field and Joule heating effects

Since the magnetic induction equation is $${\frac {\partial {\boldsymbol {B}}}{\partial t}}=\nabla \times ({\boldsymbol {v}}\times {\boldsymbol {B}})+\eta \nabla ^{2}{\boldsymbol {B}}$$ I want to ...
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8 views

Calculating the reflection and solute permeability for a diffusion cell

Here is the question, at which I have some problem. 'The three characteristic parameters $\sigma$, $L_p$ and $\omega$ can be determined from two experiments; in the first experiment 4.6 ml of water ...
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1answer
64 views

Solution to diffusion equation of a random walk

In my class of statistical physics, we studied the classic problem of random walk for the discrete case. In the end, we made the changes necessary for the master equation to be in the continuous ...
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1answer
22 views

Does a mixture of two different gases increase in entropy in a thermally isolated system?

I know gas will increase in entropy as it goes toward equilibrium, but what if there are multiple gases of different densities?
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1answer
26 views

Intrpretting questions on Fickian diffusion

I am considering the Zimm model for polymer dynamics, and have come across a question Find an expression for the time it takes for the polymer to diffuse a distance equal to its contour length $L=...
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23 views

Emptying tank through diffusion

Water ($40 ^{\circ}$, $1.0\, {\rm atm}$) slowly and steadily evaporates into nitrogen at the same temperature and pressure. from the bottom of a cylindrical tank as shown in the figure below. A stream ...
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Diffusion in a Semi-Infinite Medium: Breakaup of a Duhamel Convolution Integral

For a diffusion problem in a semi-infinite domain with a transient boundary condition, the temperature profile can be obtained from Duhamel's Principle as $$ \theta(r,t)= \int_0^t \frac{\partial \phi}...
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1answer
30 views

Water equilibrium while dying of thirst in a confined space

I'm trying to understand what happens with the water while a person is dying from thirst in a deep, narrow mine shaft. Assuming he has dry food for a long time, and some liters of water. Dry air is ...
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1answer
48 views

Diffusion equation with external forces

I am given the diffusion equation including the external forces as follows: $$\frac{\partial c}{\partial t} = D\frac{\partial^2 c}{\partial x^2} - \frac{F}{\gamma} \frac{\partial c}{\partial x}$$ ...
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1answer
86 views

Expression for “rotational diffusivity”; orientation random-walk of thin rod-like particles?

From this answer and from the Stokes-Einstein equation the diffusivity of a particle of radius $R$ in a fluid of viscosity $\eta$ is $$D=\frac{k_B T}{6 \pi \eta R}$$ where $\xi=6 \pi \eta R$ is a ...
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Difference between diffusion and interface mobility?

I have had this question when reading about the growth of ferrite (in steel) that is controlled by carbon diffusion and by interface mobility of Carbon. I would like to know the difference between ...
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Pouring Soda At A Constant Angle And Minimizing Filltime While Accounting For $\mathrm{CO}_2$

I was pouring soda, when the act made me think of a question. If you have an unopended $2L$ bottle of soda, and you wish to fill up a generic cylindrical glass cup - if you hold the $2L$ bottle at a ...
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2answers
61 views

Why doesn't the diffusivity of a particle in a fluid depend on the particle's density?

From this answer and from the Stokes-Einstein equation the diffusivity of a particle of radius $R$ in a fluid of viscosity $\eta$ is $$D=\frac{k_B T}{6 \pi \eta R}$$ where $\xi=6 \pi \eta R$ is a ...
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25 views

what's the difference between viscous flow and diffusion

For a one-componet gas flow in a channel. There are a pressure i.e density difference between two ends of the channel. There will be a mass flux. My question is how to describe this flux? it's a ...
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26 views

The influence of a temperature gradient on the growth of dendrites in a solid liquid interface

Not sure if this is the correct place to ask... My book states that, for a Solid Liquid interface in which the liquid has an increasing positive temperature gradient (increasing temperatures in ...
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38 views

Why and how do holes in the valence band of the p-type material of a p-n junction diffuse through to the valence band of the n-type material

tl;dr -- See the question title I quote from this Wikipedia article on the depletion region: By definition, the N-type semiconductor has an excess of free electrons (in the conduction band) ...
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Why don't we use Leibniz integral rule when solving Diffusion equation using the Fourier transform?

My question concerns the solution to the diffusion equation: $$\frac{\partial{p(x,t)}}{\partial{t}}=D\frac{\partial^2{p(x,t)}}{\partial{x}^2}~.\tag{1}\label{1}$$ I have a question about the solution ...
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1answer
65 views

What formula can serve as an approximate estimate of the time taken for the smell of a perfume to reach somebody?

I am in an attempt to calculate the time required for the smell of a bottle of perfume to reach a person's nose $10$m away. Real life experience tells me that it takes several seconds. I tried to work ...
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1answer
52 views

Classification of 2D time dependent diffusion equation

I was trying to classify the following PDE: $$\frac{\partial{u}}{\partial{t}}=\frac{\partial^2{u}}{\partial{x^2}}+\frac{\partial^2{u}}{\partial{y^2}}$$ where $u = u(x,y,t)$. I was originally using ...
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1answer
38 views

Rand-walk/Brownian-motion on 2D lattice [closed]

I started to learn stochastic processes this year. Only had two classes, but I already have some problem. We learned about Einstein's and Langevin's description of Brownian-motion and now I need to ...
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1answer
117 views

Diffusion equation Lagrangian: what is the conjugate field?

Morse and Feshbach state without elaboration that the diffusion equation for temperature or concentration $\psi$ and its "conjugate" $\psi^*$ (quotation marks theirs) has Lagrangian density: $$L=-\...
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37 views

Diffusion stopping current?

In the forward bias when electrons enter the p-type region of the semiconductor, the charge concentration is increased, and since the movement of electrons is faster than the movement of holes, it ...
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17 views

on diffusion process in semiconductor devices

Consider a PN junction. Say that the P and the N sides are just brought into contact and the diffusion process has started. We say that as the diffusion occurs, the charge carriers leave behind ...
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0answers
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How to fit mean squared displacement data from nanoparticle tracking analysis?

I am trying to independently analyze raw nanoparticle tracking analysis (NTA) data, but my diffusion coefficients calculated directly from x and y pixel values only moderately correlate with reported ...
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Commutation of differential operators with boundary conditions

First post ever. Let's see how this goes... My question concerns the commutation of differential operators in the presence of boundary conditions. If it is of any help, this is relevant to me in the ...
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1answer
23 views

“Regularization” of the stationnary solution for diffusion in spherical coordinates

In spherical coordinates $(r,\theta,\phi)$, the stationnary diffusion equation is a Laplace equation $\Delta f =0$. The solution in a radial symmetry : $f=f_{\infty}-r_0/r$ where $f_{\infty}$ and $r_0$...
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1answer
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How long for released dye to uniformly saturate the oceans?

Suppose a supertanker filled with purple dye breaks open at a particular point in the middle of the Pacific Ocean and spills an enormous volume of purple dye into the ocean all at once. Imagine that ...
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1answer
48 views

Diffusion 2D on a surface : diffusion coefficient and surface friction

We have a particle that is diffusing actively (meaning that the source of energy is a motor; the diffusion is like a Brownian motion, the only difference is that the diffusion coefficient is much ...
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20 views

Aggregation phenomena : How to get from a discrete to a continuous point of view

I'm studying a diffusion limited aggregation phenomenon. The $N$ particles diffuse in a box and when there is a contact they stick with a probability $p$, and let's say to simplify $p=1$. Meaning that ...
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75 views

Alternative to Fick's law of diffusion?

Let's model a concentrate $C$ with a flux vector $\overrightarrow{J}$. From first principle we can obtain the conservation law $\frac{\partial C}{\partial t} + div \overrightarrow{J}$. An adequate ...
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1answer
98 views

How can the analytical solution of the diffusion equation be used for a series of $N$ positions?

Given the exact solution to the diffusion equation: $$C(x,t) = \frac{1}{\sqrt{4 \pi D t}} \exp\left[-\frac{x^2}{4 D t}\right]$$ I am unsure as how it can be applied to a 1D series, as this equation ...
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5answers
457 views

Physical meaning of potential in heat equation

I'm working on the mathematical theory of parabolic equations. The prototype of such equations is heat equation given as follows : Let $\Omega$ be a bounded region of the space and $T>0$ a fixed ...
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1answer
65 views

Dimensional analysis on diffusion equation

I was studying the equation of motion for the probability density function of the position coordinates of the Brownian particles, also known as the Smoluchowski Equation (SE). Particularly, I came ...
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30 views

Mass transfer due to bulk and convection

What is the difference between mass transfer due to bulk flow in diffusion which is (Na+Nb)(mole fraction) and the convective mass transfer which is found by kc(concentration difference)?
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1answer
61 views

Inverse of a matrix in a Path Integral

Good morning! I can't make sense of an inverse of a matrix appearing in a calculation for a Wiener Path Integral. In discretized form: $$\int \prod_{i=1}^N \frac{dx_i}{\sqrt{\pi \epsilon}} e^{-\frac{1}...
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1answer
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The derivation of the advection-diffusion equation uses $\nabla\cdot(c\vec{v})=(\vec{v}\cdot\nabla)c$. Why doesn't the order of the derivative matter?

In a derivation of the advection-diffusion equation, it is exploited that $\vec{\nabla} \cdot (c \vec{v}) = ( \vec{v}\cdot \vec{\nabla})c$, where $\vec{v}$ and c respectively are the velocity and ...
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1answer
31 views

How does flatulence travel through the room when opening a window? [duplicate]

When the smell in my room seems to be full of flatulence(it wasn't me), what happens with the gases when I open a window? Detail: It is winter and the air outside is cold whereas the air in the room ...
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0answers
50 views

Solution of the diffusion equation in a plasma

considering the diffusion equation taking into account diffusion and mobility of charged particules in a plasma of density $n(z)$ and potential $\phi(z)$, we have : $$ \frac{n(z)}{\tau}=\frac{\...