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5
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1answer
167 views

Simple question regarding the Green's function for the diffusion equation

The differential operator for diffusion in three dimensions is given by $\partial_t - k \nabla^2$ where $k$ is a constant. The Green's function is (according to Wikipedia) $$\theta(t)\left( ...
6
votes
4answers
755 views

Do particle velocities in liquid follow the Maxwell-Boltzmann velocity distribution?

The Maxwell-Boltzmann velocity distribution arises from non-reactive elastic collisions of particles and is usually discussed in the context of the kinetic theory (for gases). There are various ...
-1
votes
1answer
177 views

Boundary conditions for the heat equation when solving a mass density gradient

I'm working with a mass density gradient with length $L$ and I'm trying to solve the heat equation in 1-D (mass diffusion equation, $\partial_t\rho(t,x)=D\Delta\rho(t,x)$), but I'm not sure which ...
1
vote
1answer
2k views

Characteristic length for the diffusion equation (temperature)

The background: I'm doing some simulation work involving the diffusion equation in 1D. Specifically I have some temperature profile, constant thermal conductivity and fixed temperature at each end of ...
3
votes
1answer
99 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
0
votes
0answers
39 views

Deriving diffusion coefficients from velocity field?

If I know the velocity, $\mathbf{v}(\mathbf{r},t)$, everywhere, is it possible to determine the diffusion coefficient, $D(\mathbf{r},t)$ everywhere as well? Would it be possible from using Fick's ...
2
votes
1answer
67 views

Rate of probability loss from absorbing boundary

The following is the solution to the 1D diffusion equation with diffusion coefficient D, initial particle position $x_0$, and a perfectly absorbing boundary at $x=0$ (s.t. $P(x=0)=0$). $$ ...
2
votes
1answer
3k views

What is the difference between dispersion and diffusion?

What is the difference between dispersion and diffusion? Currently I believe, that diffusion is the mixture of molecules due to Brownian motion. So I read everywhere, that it happens with magnitude of ...
2
votes
0answers
96 views

Diffussivity of gases, molecular weight and Lewis number

I am trying to understand the following figure of laminar premixed flames: The Lewis number is defined as $Le = \frac{\alpha_{mix}}{D_{fuel}}$ where $\alpha_{mix}$ is the thermal diffusivity of ...
3
votes
1answer
233 views

Why viscosity is diffusive?

I'm studying fluid mechanics in more depth during my Ph. D. and there is something related with the diffusive term that has been bothering me for a long time. Looking at the convection diffusion ...
1
vote
1answer
61 views

Can you equate the diffusivity constant in random walks with the one in Brownian motion (Einstein relation)?

In an unbiased random walk in one dimension, the coefficient of diffusion is $D = l^2/2\tau$, where $l$ is the size of the jump and $\tau$ is time taken for that jump. In simple Brownian motion, ...
2
votes
2answers
637 views

Units of the Stokes-Einstein rotational diffusion coefficient

The Stokes-Einstein rotational diffusion relation tells us that we can write down a rotational diffusion coefficient for a sphere as: $$D_r \approx \frac{k_B T}{\zeta_f} \approx \frac{k_B T}{(8 \pi ...
4
votes
3answers
385 views

Physical interpretation of the change of diffusion term in navier stokes equations

In the Navier-Stokes Equations, there is one term accounting for convective flow and one term for diffusive flow. At high flow rates, the diffusive term becomes much smaller compared to convective ...
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0answers
27 views

Solid state diffusion as a function of shear stress

I am hoping to get some clarification on the impact of shear stress or shear strain on atomic diffusion in a metallic solid. More specifically, will the kinetics for the dissolution of secondary phase ...
0
votes
2answers
83 views

Simulating diffusion from bulk to individual particles

I have a 2 compartment simulation. The first compartment simulates reactions using ODEs. The second compartment uses Brownian motion. I want to be able to have molecules from the ODE compartment ...
4
votes
1answer
3k views

What is the difference between the words transparent and translucent?

Merriam Webster defines transparent as: Having the property of transmitting light without appreciable scattering so that bodies lying beyond are seen clearly. And translucent as: ...
1
vote
1answer
325 views

Temperature rate of change inside a cylinder

I was wondering about this today, mainly for baking a cylindrical cake. Say you have a solid cylinder which is at temperature T0 inside. Say you then move the ...
1
vote
1answer
263 views

How does air escape from a pneumatic tire?

Obviously, it is caused by the difference in pressure between the inside of the tire and its surrounding environment; but how specifically is the air escaping?
0
votes
0answers
41 views

Should particles in Smoothed Particle Hydrodynamics (SPH) always move during a simulation?

Or can they just be used as an interpolation points and use some other "transported property" which are just evolved and propagated from boundary conditions like for eg. heat conduction through a ...
5
votes
2answers
138 views

Counting of brownian particles: Point Process

Imagine a point process defined by the passage time of purely brownian particles through a given point (in 1D), line (2D) or plane (3D). I'm interested in the variance of the counts (number of ...
3
votes
1answer
975 views

Diffusion of gas in a liquid with changing pressure and solubility (chemical potential)

Modelling the diffusion of a gas dissolved in water in a vertical column of water, several meters deep. Also assuming the water is completely still, so only diffusion plays a role. (Actually a model ...
3
votes
1answer
136 views

How big an egg can be? [closed]

Please hold on to flag as off-topic. Few days ago I received a question - how big an egg can possibly big? Can it be as big as 1 meter, as a human? (Imagining that there could be really huge animals ...
7
votes
1answer
156 views

Does QED provide a closed form for Coulomb logarithms?

The classical models for the integrand as well as the cut-offs in computing the Coulomb logarithm are pretty rough. Does quantum electrodynamics have definite expressions for the quantity ...
5
votes
1answer
114 views

Everyday example of diffusion unobscured by advection, wetting etc

Diffusion is an important concept in elementary science education, especially because it supports (or seems to support) the notion of matter consisting of very small everyday particles (as opposed to ...
2
votes
1answer
268 views

What is the physical basis behind thermal diffusion in a Clusius-Dickel column?

A Clusius-Dickel column allows separation of two species by the application of a thermal gradient. In its simplest form, two bulbs are maintained at two different temperatures $T_1$ and $T_2$ and ...
1
vote
0answers
138 views

Leakage rate Calculation

I have to calculate leak rate for helium/air from an enclosure which is made of fabric. This is similar to helium balloons. There are small holes in the fabric. How should i proceed ?
5
votes
2answers
745 views

What is the probability density function over time for a 1-D random walk on a line with boundaries?

If a single particle sits on an infinite line and undergoes a 1-D random walk, the probability density of its spatio-temporal evolution is captured by a 1-D gaussian distribution. \begin{align} ...
7
votes
0answers
161 views

Diffusion of gases in the atmosphere

Suppose that the atmosphere is composed of 21% $O_2$ and 78% $Kr$ (instead of $N_2$). Since the density of $Kr$ is greater than the density of $O_2$, the lower atmosphere (where we live) should be ...
3
votes
2answers
614 views

How fart is transported through air?

As we know diffussivity of gas is really slow (e.g. $\require{mhchem}\ce{O2}$ and $\ce{H2O}$ in the air are respectively $0.176$ and $0.282 ~\text{cm}^2/\text{s}$). here is a example to specify how ...
2
votes
1answer
120 views

Integral related to particle diffusion

In the context of particle diffusion, I am trying to understand the equations that describe Brownian motion as a macroscopic process. Assume $N(x,t)$ is a number concentration and $D$ is a diffusion ...
141
votes
3answers
41k views

Surviving under water in air bubble

An incredible news story today is about a man who survived for two days at the bottom of the sea (~30 m deep) in a capsized boat, in an air bubble that formed in a corner of the boat. He was ...
2
votes
0answers
107 views

Why does the water diffuse at right angles in my coffee? [closed]

I purchase an espresso shot each morning at my local coffee shop, and I usually water it down slightly to take the edge off as well as to cool it. Recently, I have noticed that when I pour the cold ...
0
votes
1answer
66 views

heat spread from hot coil: diffusion, radiation?

When modeling the heat spread from a hot object through a vacuum (or a gas), what is the dominant physical process for heat energy transportation? Thermal diffusion, thermal radiation, a mix of the ...
2
votes
1answer
61 views

Must neutron speed and diffusion speed be comparable for neutron scattering experiments to be probe atomic diffusion?

Neutron scattering experiments are sometimes used to study atomic diffusion in solid materials. My intuition is that the typical speeds of the atoms diffusing in the material--say, the diffusion ...
2
votes
1answer
63 views

Is the diffusion coefficient for a macromolecule sensitive to mass?

Suppose I have two neutrally-buoyant macromolecules diffusing in water. They have the same radius of gyration (i.e. same root-mean-square distance from their center of mass), but one of them is ...
3
votes
1answer
132 views

Equidistant coffee rings in a mug: pinning boundaries coupled with migration of solute or just sip volume?

I understand that you get coffee rings on a table as a result of solute migration (solutocapillarity) towards the pinning of the circumference of the coffee ring [Deegan et al.]. Below is an ...
0
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0answers
65 views

Ask for help: the Reaction-Diffusion related problem

In container there are two kinds of molecules A and B which are distributed uniformly. Initially the quantities of A and B are $N_A$ and $N_B$ respectively A and B are distributed uniform, i.e., in ...
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0answers
82 views

Concentration of Proteins

You release a billion protein molecules at position $x = 0$ in the middle of a narrow capillary test tube. The molecules’ diffusion constant is $10^{−6} \ cm^2 s^{−1}$. An electric field pulls ...
1
vote
2answers
258 views

Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation

Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
0
votes
3answers
685 views

Solving the diffusion equation

I am trying to clarify the relation between random walk and diffusion, and the source book proposes the following which I can't get. Starting from the diffusion equation $$ \frac{\partial C}{\partial ...
5
votes
1answer
337 views

What formulas should I use to realistically model the diffusion of a drop of ink in a water?

I am a mathematician and am originally from the math side of stackexchange. I want to model the behaviour of a drop of ink diffusing in water. I dont want to simply use the diffusion equation ...
38
votes
7answers
18k views

How can two seas not mix?

How can two seas not mix? I think this is commonly known and the explanation everyone gives is "because they have different densities". What I get is that they eventually will mix, but this process ...
1
vote
4answers
697 views

Is infrared light diffused on walls?

Lamps that produce visible light can light up a whole room because the ceiling and the walls diffuse light. This way, when there is a single lamp in a room, something that is in the shadows is not ...
1
vote
1answer
101 views

Mass diffusion: is $D_{AB} \neq D_{BA}$ at high pressures? If so, why?

From [Takahashi][2], I validated some models I have for estimating diffusion coefficients (methods of Fuller modified by Riazi for high-pressures, all pulled from [Poling][3]). Here is the figure ...
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0answers
203 views

Mechanical effects of convective flow in steady-state stagnant film diffusion

When analysing diffusion problems in the context of the simplified film model, two limiting cases are ussually introduced during the solution of the differential chemical species mass balance ...
4
votes
3answers
10k views

What is the physical meaning of diffusion coefficient?

In Fick's first law, the diffusion coefficient is velocity, but I do not understand the two-dimensional concept of this velocity. Imagine that solutes are diffusing from one side of a tube to another ...
1
vote
1answer
402 views

Example of diffusion process without a gradient

A book I was reading stated that diffusion can exist without a gradient of a physical quantity. Heat is an example of diffusion because of temperature gradient and similar is the case of mass flow in ...
3
votes
1answer
375 views

What is the return probability for Brownian motion in three dimensions?

I would like to know the probability of return to the initial point in three dimensional Brownian motion. Does someone know an expression for the diffusion constant? (Suggestions of books on this ...
3
votes
1answer
634 views

Can we explain physical similarities between Black Scholes PDE and the Mass Balance PDE (e.g. Advection-Diffusion equation)?

Both the Black-Scholes PDE{*} and the Mass/Material Balance PDE have a similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive ...
5
votes
2answers
9k views

Convective and Diffusive terms in Navier Stokes Equations

My question has 2 parts: I just followed the derivation of Navier Stokes (for Control Volume CFD analysis) and was able to understand most parts. However, the book I use (by Versteeg) does not ...