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9
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252 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 ...
5
votes
0answers
84 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 ...
4
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0answers
37 views

How does air going through silica gel change its humidity

Assume that the properties(temperature,humidity,velocity and so on) of the incoming air flow stay constant. The air flow goes through a silica gel plate. Humidity of the air will decrease, but how to ...
4
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0answers
66 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 $\lambda(x)$. Require also that $\langle \psi \...
3
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0answers
38 views

Why would oscillation of a gas column inhibit rather than promote mixing?

Many years ago I helped to support an experiment conducted in Japan which investigated the effects of high frequency oscillation ventilation (HFOV) on the mixing and distribution of gas into the lungs....
3
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0answers
107 views

Understanding various types of motion

In classical statistical mechanics, given a system of particles, one often goes about classifying various dynamics (or types of motion) the system may exhibit on different time scales, but studying ...
2
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0answers
21 views

Viscous accretion disk, green formula

I have this problem. I am studying a the viscous accretion disk problem and in the assumption of constant viscosity the equation of diffusion of the superficial density becomes: $$ \frac{\partial}{\...
2
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0answers
40 views

Diffusion of carbon monoxide in air

I have been reading about carbon monoxide online. It is lighter than air; Yet, in the case of fire, most online sources claim it spreads evenly throughout a room. Why is this the case? How is it ...
2
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0answers
27 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 ...
2
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0answers
83 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 ...
2
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0answers
351 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 ...
2
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0answers
250 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 ...
1
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0answers
40 views

Is Gas flow rate or Volumertric flow rate right one to use for thick wall?

I will make container from steel or aluminium ( 0.5 mm thickness ) and fill it with air (2 bar) and I want to know how much pressure would the container loose overtime (20 years) ? I have asked this ...
1
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0answers
96 views

How to derive equation for time it takes photons to diffuse through the Sun

I am wanting to use the Rosseland radiative heat flux equation to find the time it takes for photons to diffuse through the sun. The answer I am wanting to derive is: $$\tau_D~\frac{\rho \bar C_p R^...
1
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0answers
16 views

Overdamped Fokker-Planck equation with general force field (gradient + ratation)

I am looking for general formulation of the overdamped Fokker-Planck equation (='Smoluchowski eq.') for a diffusing particle in general force field $F = -\nabla U + \nabla\times A$ . So far I have ...
1
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0answers
34 views

can 3D diffusion be interpreted as superposition of 1D diffusion

Is diffusion of a substance in water independent in the X, Y and Z directions? In other words, if I want to solve how a substance diffuses through a volume, can I separately solve equations for its ...
1
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0answers
23 views

Diffusion of magnetization (NMR)

In the context of MRI I'm trying to understand the mechanisms of magnetization diffusion. Consider a sample that is magnetized by an external magnetic field. We have displacement of magnetic moment ...
1
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0answers
80 views

Riemannian generalization/adaption of the Hubbard–Stratonovich transformation

I'd like to write the Hubbard–Stratonovich (HS) transformation of a scalar function on a Riemannian manifold. This transformation is quite simple in Euclidean space. One can consider it as a Fourier ...
1
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0answers
72 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 ...
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0answers
120 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 ...
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0answers
74 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 ...
1
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0answers
37 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 ...
1
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0answers
69 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
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0answers
89 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
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0answers
687 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 ...
1
vote
0answers
84 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
119 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
36 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: $$\mu_i=\mu_i^...
1
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0answers
67 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 ...
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0answers
73 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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0answers
42 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 ...
1
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0answers
177 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 ?
1
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0answers
92 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 the ...
1
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0answers
249 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 equation....
0
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0answers
23 views

Diffusion Equation for Particle Hopping with drift

First of all, I haven't studied partial differential equations yet, hence this question might sound silly. I am doing a simulation for particle hopping on a lattice with python. I was said that in ...
0
votes
0answers
64 views

The gas in a can of coke can escape?

If I have a can of coke that's 5 years old for example, how will the gas (CO$_2$) exit the can? Will the CO$_2$ pass through the metal of the can (100 microns thick) or justwhere it's precut (to ...
0
votes
0answers
23 views

Random walk of a polymer in an annular space - filling in some steps

In Muthukumar, M., 2003. Polymer escape through a nanopore, J. Chem. Phys., 118, 5174–5184, the author solves the diffusion equation for the probability $P(\vec{r},\vec{r_0},N)$ that the ends of a ...
0
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0answers
17 views

Diffusion barriers on surface?

Can the barrier to diffuse on the surface, be it amorphous or a crystalline be greater than the binding energy between the adatom and the surface ?
0
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0answers
26 views

Spread of gases in a room

I have had some thermodynamics and statistical mechanics, but I don't know much fluid mechanics. I am not sure how to model the spread of gases in a room in the case of a fire or some leaking vent. ...
0
votes
0answers
43 views

Calculation of charged sphere distribution near a wall in Cartesian coordinates

I am following a similar derivation as found in the beginning of this paper "Quantitative aspects of the growth of (charged) silica spheres" by A.P. Philipse. This paper calculates the growth of a ...
0
votes
0answers
24 views

Copper vs Tungsten (Diffusion)

I've been studying on how to compare the activation energy for (void-) diffusivity of Copper versus Tungsten. I ended up finding $E_a[cu] = 1.1[eV]$ and $E_a[W] = 5.2[eV]$ in literature where the ...
0
votes
0answers
24 views

Fick's Law for material extraction in a spherical material

I'm looking for a text which talks about how to extract a material from some object (spherical to be easier), (for example, water from the food) and learn about these formulation using the Fick's Law ...
0
votes
0answers
34 views

What happens when a semipermeable membrane allows only one solute to pass through?

I'm essentially a medical student where we deal a lot with osmosis. But when we are taught, it is done generally with only a single solute in consideration. What if two different solutes are used on ...
0
votes
0answers
21 views

Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?

Say the diffusion coefficient of the concentration of a particle in a fluid in 3-dimensions is $D_{3\textrm{d}}$. Can we estimate the diffusion coefficient of the same particle in the same fluid, in a ...
0
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0answers
50 views

Does nature really follow the heat equation?

I think the heat equation says that the first derivative of temperature with respect to time in a stationary solid varies as the negative of the second derivative of temperature with respect to ...
0
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0answers
35 views

Extension of the advection diffusion equation with diffusion perpendicular to the flow

Assume you model particle flow in fluid in a cylinder by an advection-diffusion equation, thus taking into account both diffusion and bulk flow. What would happen to the model if you would, at some ...
0
votes
0answers
29 views

trying to figure out an expansion in Brownian motion derivation

In the derivation for the diffusion equation on the wikipedia article for Brownian motion, they have these equations: I can't figure out how $\rho(x+\Delta,t)$ gets expanded, though. For a Taylor ...
0
votes
0answers
37 views

The change in time of a concentration in a fluid can be described by Reynolds' theorem. Is that the whole story?

Let $d\in\left\{2,3\right\}$ and $\Omega_t\subseteq\mathbb R^d$ be the bounded set occupied by a fluid at time $t\ge 0$. Moreover, let $\eta_t:\Omega_t\to[0,\infty)$ be the concentration of imaginary ...
0
votes
0answers
19 views

Fluid flow in porous medium with moving boundary

Everyone, I would like to numerically model axisymmetric fluid flow in a porous medium with a moving boundary, where the fluid pressure is specified on the boundary, whose radius increases with time. ...
0
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0answers
33 views

Is it possible that my 750ml water bottle contains spent fuel from a space shuttle launch

Firstly I live in New Zealand which is very distant from USA which is where the space shuttle was originally launched from. So what is the possibility of molecules from the rocket engines spent ...