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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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1answer
409 views

Diffusion vs Advection

As defined in Wikipedia; diffusion is the net movement of molecules or atoms from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical ...
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42 views

How to proceed with dimensionless recasting of telegrapher's equation?

I am referring to this paper, on page 3 it is given that: The telegrapher's equation is given as $$\partial_t P_+=D\partial_x^2P_+-v\partial_xP_+-\gamma P_++\gamma P_-,$$ $$\partial_t P_-=D\...
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19 views

Rotational diffusion - why isn't $\hat n(t)=\hat n(0) \; \forall t$?

Consider the rotational Langevin equation in the absence of an external force: $$\frac{d \hat n(t)}{dt} =\vec{\xi}(t) \times \hat n(t)$$ where $\vec \xi(t)$ is a Gaussian white noise and $\hat n(t) \...
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Self-consistently solve coupled Poisson-Drift Diffusion eqns. for semiconductor device analysis

I have a system of coupled non-linear ODEs. $$J = \mu e \left( n(x) E(x) + \frac{K T}{e} \frac{dn(x)}{dx}\right)$$ $$\frac{dE(x)}{dx} = \frac{4 \pi e}{\epsilon}[N_D(x) -n(x)]$$ The first ...
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Numerical integration of the heat equation with variable thermal diffusivity using spectral discretization

I want to integrate this equation in time: $$\frac{\partial u(x,t)}{\partial t} = \frac{\partial}{\partial x} \kappa(x) \frac{\partial u(x,t)}{\partial x}$$ with initial condition $$u(x,0) = \frac{...
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301 views

Maxwell's equations and nonlinear media

Are there analytical methods to analyze electromagnetic fields or magnetic diffusion in materials which are not linear using (or starting from) Maxwell’s equations? Nonlinear material could be ...
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48 views

Will a Brownian Particle hit an infinite wall in 3-D geometry with probability 1?

I know that in 3-D the probability of recurring a given point is zero for a Brownian particle. Given an infinite absorbing wall/plane the probability of ultimately getting absorbed, for a Brownian ...
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1answer
50 views

Uniqueness of the square-root of the diffusion matrix?

In the Langevin equation with hydrodynamic interactions the stochastic force on particle $a$ is: $$ \sqrt{2k_BT} A^{ab}_{ij} \xi^{b}_j(t)$$ where $\xi$ is a unit white noise. Here $ A^{ab}_{ij} $ is ...
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125 views

Is drag coefficient in fluid dynamics a constant in every direction?

I am referring the book 'Stochastic Processes in Cell Biology'. In this book the author says that Fokker Plank equation in isotropic diffusion: $$\frac{\partial p(x,t)}{\partial t}=-\frac{F}{\gamma}\...
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44 views

Diffusion equation in energy and magnetic surface coordinates

The isotropic diffusion equation in Cartesian coordinates is $$\frac{\partial f(\mathbf{x},t)}{\partial t}=\nabla[D(f,\mathbf{x})\nabla f(\mathbf{x},t)]$$ Boozer and Kuo‐Petravic (1981) claim that ...
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81 views

Starting and stopping a numerical diffusion equation [closed]

I am asked to solve the following problem numerically with Python with one of Euler methods: Calculate the diffusion of particles with a diffusion constant $D=0.025$ on a surface ($24\times24$ ...
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1answer
302 views

On the derivation of diffusion coefficient in thermodynamic terms

I'm trying to express the diffusion coefficient $D$, regarding particles suspended in a liquid, in terms of thermodynamic parameters. In this, some evident problems were encountered when trying to ...
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118 views

Movement of a random walk in the limit (a particle in diffusion)

I asked this question in Math Exchange and MathOverflow and obtained no answer. This question may lack of mathematical rigorous, but I would like to understand why this type of reasoning is sometimes ...
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1answer
77 views

Diffusion and Effusion confusion!

In both the cases, the molecules of gases move across the hole. Then what is the difference between them. Also, will effusion occur if pressure on both sides of the hole is equal.
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92 views

Modification of Einstein's field theory with cosmological scalar field

I learn about a new model to describe the dynamics of particles undergoing diffusion in general relativity. The evolution of the particle system is described by Vlasov equation without friction. The ...
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1answer
177 views

Free energy in Allen-Cahn PDE

I am a mathematician and I am taking a mathematical physics course. In the part of reaction-diffusion equations, there is something that I do not understand. I have been defined the Allen-Cahn ...
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22 views

Understanding air permeation of a material

I am trying to research on acceptable materials to hold an atmosphere inside of a vacuum. Understanding that air will escape at different rates through all materials, I don't know what the property is ...
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1answer
85 views

Is second principle of thermodynamics translatable as a probability diffusion equation?

The general diffusion equation examples thereof are heat equation and Fick law says the flow of a given extensive quantity like thermal energy or mass is proportionnal to the gradient of a related ...
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71 views

Relation of the Heat kernel and the solution of the discrete diffusion equation

As is well known, the solution to the continuous 1D diffusion equation $\partial_t f=D\,\partial_x^2 f$ is given by the Heat kernel $$f(x,t)=\frac{\mathrm{e}^{-x^2/4Dt}}{\sqrt{4\pi Dt}} \ .$$ On the ...
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344 views

Physical Interpretation of the Diffusion Constant $k$

I have read technical explanations of the interpretation: ''Diffusion coefficient is the proportionality factor D in Fick's law (see Diffusion) by which the mass of a substance dM diffusing in ...
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3k views

Characteristic time for heat diffusion

I often see that one can write the characteristic time (or time scale) of a diffusive process as: $\tau = \frac{L^2}{d}$ where $L$ is the characteristic length and $d$ is the diffusion coefficient. ...
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232 views

Confusion about Fick's first law

Consider a binary system of mass transport (A, B). Some of mass transfer books (Skelland and Welty) say that the relation $$J_A= -C D_{AB} \frac{dx_A}{dz} \tag{I}$$ is more general than $$J_A= -D_{AB} ...
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225 views

Deriving Flux by Fick's Law with weighted Random Walk

Fick's first law of diffusion, $J=-D\nabla \phi$, is nicely derived from a random walk on wikipedia's page. https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion The physical argument is that if ...
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1D diffusion: two opposing currents with 'flux continuity' and 'no flux' at edges

Consider two currents with diffusion coefficient $D$, and drift velocities $v$ and $u$ in opposite directions: At steady state: $\frac{d^2 c_v(x)}{dx^2}=\frac{v}{D}\frac{dc_v(x)}{dx}\rightarrow c_v(...
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69 views

Why is flux at an interface purely diffusion?

In many textbooks, the flux at the point of interface of two phases/regions is given through Fick's first law, with purely diffusive flux, even when there can be bulk convection in both phases/regions....
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592 views

Meaning of minus sign in the first Fick's law

What is the meaning of minus sign in the first Fick's law, $$ J=-D\nabla\varphi, $$ where $J$ is the diffusion flux, $D$ the diffusivity and $\varphi$ the concentration? I read that the flux goes ...
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483 views

Difference between and diffusion and heat equations?

I read everywhere that diffusion and heat equations are similar. The same differential equations can be solved for both. Consider a finite one-dimensional diffusion or heat transfer where one end is ...
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2answers
135 views

Another way to find the energy diffusion time in the Sun?

I was surprised when I first heard that the energy produced at the Sun's core takes a long time to escape the Sun. The process is often explained as a photon traveling a "drunkard's walk" based on ...
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38 views

Trouble in understanding the formula for drift current in Stokes-Einstein relation

In the derivation Stokes-Einstein relation, which relates diffusion and damping, we basically use the fact that diffusion current and drift current must balance each other at equilibrium. But I have ...
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1answer
118 views

How do I quantify diffusive flux with two interacting gases crossing a distance of tissue?

Full disclosure (if you won't be able to tell by the end of my question): I'm a biologist, not a physicist but I'm finding myself with a rather physics-intensive question that I imagine the bright ...
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3answers
710 views

Heat equation: Heat Kernel as $t\to0$

Consider heat flow on an infinite, 1D wire. The temperature T(x,t) obeys the diffusion equation, $$ \frac{∂T}{∂t} = D \frac{∂^2T}{∂x^2} $$ with initial condition $T(x,0) = δ(x)$. The heat kernel is ...
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615 views

What is the proper way to model diffusion in inhomogeneous media (Fokker-Planck or Fick's law) and why?

I'm quite confused with the following problem. Normally a one-dimensional Fokker-Planck equation is written in the following form: $$\frac{\partial \psi}{\partial t}=-\frac{\partial}{\partial x}(F\...
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1answer
128 views

Explain Egawa Electric field with reference to PIN diode?

By Egawa electric field I meant the flattening of electric field in the intrinsic field. And after that, when avalanche multiplication occurs, the dipping of electric field in the intrinsic region and ...
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1answer
108 views

Mixing in connected gases [closed]

(This question is about the making of a box to enclose a 3D printer and its filament. 3D printer filaments are sensitive to ambient moisture. The model described below is only a simplification of the ...
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69 views

Interference in electron conductance through e.g. single molecule or semiconductor?

Imagine attaching electrodes to a complex sample, e.g. a semi-conductor or a single chemical molecule, leading to some electric current. Can we decompose this electron flow into local flows? - like ...
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1answer
27 views

Rayleigh scattering and dimension of oscillator compared to wavelenght

Why is Rayleigh scattering suitable only for cases where the oscillator dimensions are much smaller than incindent wavelenght?
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1answer
57 views

Why do living tissues need to be moist for oxygen to diffuse across them?

If an earthworm's skin dries out, oxygen can't diffuse across its skin any more and the worm suffocates and dies. Why does the skin have to be moist to allow oxygen to diffuse across? If there is ...
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1answer
307 views

How to solve the Fick's partial differential equation? [closed]

Consider a finite diffusion in which the concentration profiles at different times are like How to solve the differential equation as opposed to the common solution for semi-infinite/infinite ...
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1answer
240 views

What is the maximum flux in Fick's diffusion?

Solving the Fick's second law with common boundary conditions and applying to the first law will result in a common expression of one-dimensional diffusion as $$J_{(x=0)} = D\frac{\partial c(x,t)}{\...
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2answers
112 views

Easy question on math of diffusion equation

I have the following well-known diffusion equation: $$\frac{\partial{\sigma}}{\partial t}=D\nabla^2\sigma$$ where $\sigma$ is the hydrostatic stress. I also know the relationship between stress and ...
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1answer
124 views

Is there a relation between fluctuations, temperature and time dilation?

I saw these 2 threads: Does Heat Cause Time Dilation? Does temperature affect time like gravity and velocity do? However, I don't find the answers addressing my question. Einstein relation connects ...
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1answer
526 views

Does the diffusion coefficient depend on units of concentration?

I'm sure this is an elementary question, but I was struggling to explain the following concept to a (math) student recently and it exposed my own deficiencies in discussing units. In Fick's law(s), ...
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2answers
206 views

Why do lighter atoms and molecules diffuse upwards?

If a relatively light atom such as helium is released in the middle of a room, it will tend to diffuse or random-walk upwards. If a relatively heavy atom such as argon is released in the middle of a ...
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1answer
160 views

What is the difference between intradiffusion and interdiffusion?

How one can differentiate between the intradiffusion and interdiffusion? What is the criteria which separates them? As both suggest the molecular motion under the concentration gradient.
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Biophysics: kinetics of diffusion and dissociation

I have a spherical mass of cells say $150\mu m$ in diameter.The ball of cells are surrounded by a "bag" $100nm$ thick. These cells constantly express a receptor called avidin.The concentration of ...
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73 views

How to validate a code written for solution of 1D heat conduction problem in a line.

Consider the following conceptual model of heat conduction in a bar. There is a heat source at left side and heat is observed at point Ho after a distance L from the source. If we consider only heat ...
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2answers
307 views

Do electrons 'diffuse' through materials

Consider a material $A$ having $5N_A$ electrons per $m^3$ and another material $B$ with $10N_A$ electrons per $m^3$. Now a meter cube of material B has a rather larger concentration of electrons when ...
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What does it mean that a substance can be smelled from far away?

I thought about this question in the middle of this video. Ok, Thioacetone takes the price for the World's smelliest chemical, I can accept it (why not?), but what about You can smell one drop of ...
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0answers
77 views

Gaussian random walk of drifting electrons in $\Delta t \rightarrow 0$ limit

Consider the movement of electrons due to diffusion in a liquid as described by the solution of the diffusion equation $$\phi(\vec x, t) = \frac{1}{\sqrt{(4\pi t)^3 D_xD_yDz}}\exp\left(-\frac{x^2}{4 ...
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1answer
36 views

Pouring bottled-water into a glass of syrup

Everytime I am pouring bottled-water into a glass of syrup, I am thinking: Water molecules are travelling in all directions in the water-body. While pouring bottled-water into a cup of syrup, the ...