Diffusion Definition and 476 Threads

I thought I would do a little physics for fun, since it has been over 20 years since I last did any. I picked up Sethna's Stat Mech book. He gives a derivation of the diffusion equation that goes as follows: A particle makes random steps, ie x(t+Δt)=x(t) + l(t). The steps l(t) are given...

Homework Statement Solve for the flux distribution using the 1D neutron diffusion equation in a finite sphere for a uniformly distributed source emitting S0 neutrons/cc-sec. My problem right now is that I can't figure out the boundary conditions for this problem. We usually work with...

Homework Statement Find the diameter of one atom of argon given that Dp = 2 where D is diffusion and p is pressure. The Attempt at a Solution molar mass of argon is 40g/mol using that for one atom can find mass in kgs. but that's its! im not given V, T or p. can put V in terms...

Hi guys, I have a question regarding ways to investigate diffusion. Here's the case, I have a fruit which is used for solvent (eg methanol) extraction to extract active compounds from the fruit. Now I have to do a sub-study to study the diffusion of these active compounds from the fruit to...

Ok so I wish to try solve a problem at work I will try explain as best I can . Problem Definition; Filling of a bundle of cylinders 17 x 50litre ( 850 000 k/m^3). 30 % Co2 in the cyindrical vessal followed by input of Nitrogen 70% to a final pressure of 200 bar Due to production...

You can put a diffuser in front of a visual light source (i.e. lightbulb) that will scatter light in all directions. In effect, the diffuser acts as an analog lightsource by making light go in all directions (some of the enegry will be absorbed). LCD screens use diffusers to spread out their...

Hello everyone, I have a question that is bothering me a bit. I would be happy if you could give an idea or tell me a specific point to look at. Lets say that we have an arbitrary function that obeys diffusion equation: f = f(η), here η is the scaling parameter for pde which equals to...

Hi everybody! Currently I'm working on 3-dimensional diffusion models using finite element method (FEM). I am familiar with the basic diffusion theory; i mean constant diffusion coefficients, diffusion-reaction problems, numerical methods (from Crank-Nicolson to FEM), isotropic materials...

Homework Statement 1. Estimate the concentration of oxygen in the Earth's atmosphere (in molecules / m^3), at room temperature and at sea-level, assuming the fact that oxygen comprises 21 percent of the Earth's atmosphere by volume. 2. If you were to place a perfect oxygen sensor of...

Hi, I have read a lot about Diffusion Equation and solving neutron flux problems in different mediums, planes and groups, but I can't grasp this topic. In other words, I don't know why they mention: 1. Infinite/finite medium 2. Homogeneous/non-Homogenous medium 3. One/two or multi-group...

Homework Statement I'm having some difficulty deriving the equation for a concentration of CO2 as a function of length and time. Ultimately I end up with an equation that includes the summation of two error function terms that appear to have incorrect signs. Given: A cylinder of...

I am a graduate student in physics. Can someone recommend a book that explores transport phenomena or diffusion from a physical sciences (instead of engineering) point of view? I would like that because I'm not dealing with industrial equipment and don't want to spend chapters wading through...

diffusion coefficient meaning is the coefficient of particles diffuse when different in concentration. How about diffusion coefficient of a particle? the trajectory where a particle diffuse?

Hi there, This could be absolute nonsense but I just got thinking about this. Say you had a certain metal into which a quantity of hydrogen had diffused, and then you placed it in communication with another hydrogen-free metal (say, titanium), would it be possible that the hydrogen would move...

On an undergrad engineering level of talk, is there any difference between conduction and diffusion ways of heat transfer? Conduction occurs because of the vibrational freedom of atoms. And diffusion is, I think, because of diffusing of atoms?

does anyone know how dirac diffusion looks like, i.e. The solution of dirac equation with no potential and initial condition for 1 spinor component psi(x,t0) being delta(x-x0) ? Are the solution gaussian like the schroedinger case ? Thanks.

Homework Statement Calculate the time needed for a perfectly spherical balloon with rahis R to reduce its volume to R/2 due to diffusion by applying Fick's law of diffusion. Assuming the young modulus of balloon is E and the gas filled is nitrogen. diffusion constant of nitrogen is D. Please...

How to calculate the time needed for a perfectly spherical balloon with radius R to become R/2 due to diffusion of the gas inside, which is assumed to be nitrogen, by using Fick's Law of diffusion. Let the Young's Modulus be E. Fick's First law: J=-D∂C/∂x the change in pressure...

Homework Statement Find the mean speed of the molecules escaping through a hole of area \sigma. The vessel has volume V and the molecules mass m.Homework Equations dN_w^e = \frac {dA}{4V} w \frac{dN_w}{dw} dw w is the speed. dN_w = \frac {4N}{\sqrt \pi c^3} w^2 \exp {\frac {-w^2}{c^2} }dw...

Homework Statement I had a homework problem that asked "Which compound in each pair will diffuse with a higher rate through lipid bilayer? a) Asp or Glu; b) Thymidine or TMP; c) glucose or glucosamine" And i figured the compound that is most nonpolar will go through fastest. So I said...

I was working on my cloud chamber today, and I ran into two problems: A) It's not working :) To be more specific, I used compressed air to get the bottom extremely cold. The structure itself is a small plastic throw away cup, with a sponge with 91% alcohol stuck to the top. The bottom (the open...

Hi all, I'm working on a heat transfer problem with a gas stream in a tiny tube. At my dimensions and flow rates, the flow still has a parabolic velocity profile. The mean radial velocity of the gas is zero, and I've treated the radial aspect of the heat transfer as strictly diffusion...

I'm looking for the analytical solution for the 1D convection diffusion equation with a constant heat flux. Boundary conditions: The domain I'm looking at is x from 0 meters to 1 meter. The temperature at x=0 is T=0 degrees Celsius. At x=1, T=100 C. I'm given the equation...

Please I need help to understand how diffusion current can occur in a circuit that contains an N-type or P-type semiconductor without being connected to an electric souce such as a battery.And how can both drift and diffusion current occur when the circuit is connected to a battery?

The concept of diffusion is confusing me, as it seems to contradict gravity. x = particles of matter with a mass of 1 | = a barrier particle x can permeate Situation A: xxxxx|x (1) Result of Situation A (tested approximately) xxx|xxx The explanation of this is that the...

BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is channel's length...

Homework Statement BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is...

Recently there was a discussion concerning whether an electron in the conduction band was localized or delocalized. The back and forth arguments seemed inconclusive, difficult to follow (too brief too couched in jargon/unrealistic models) and ended in something close to insults back and forth...

Hi In this online lecture (click "View Presentation"), Prof. Allam discusses the solution of a diffusion-capture problem. On slide 8, he formulates two equations I = C_0 (\rho_0 - \rho_S)\\ I = A \frac{dN}{dt} = A k_F N_0 \rho_S from which he arrives at an expression for N(t), namely...

Homework Statement Solve ut=kuxx u(x,0)=0 (ψ(x)) u(0,t)=1 on the half line 0<x<infinity (exercise 2, 3.1, Strauss) Homework Equations The Attempt at a Solution There are two bits I don't get: First, I know I have to make an odd or even extension to the whole line. But for...

One can show that mass diffusion without chemical reactions obeys the same basic equation as heat conduction. The one dimensional equation in dimensionless variables is given by $$ D_{AB}\frac{\partial^2 C_A}{\partial x^2} = \frac{\partial C_A}{\partial t} $$ where C_A is the concentration...

Show the diffusion equation is invariant to a linear transformation in the temperature field $$ \overline{T} = \alpha T + \beta $$ Since $\overline{T} = \alpha T + \beta$, the partial derivatives are \begin{alignat*}{3} \overline{T}_t & = & \alpha T_t\\ \overline{T}_{xx} & = & \alpha T_{xx}...

This one comes from Duderstadt and Hamilton, Problem 7-3. In multi-group diffusion theory What percentage of neutrons slowing down in hydrogen will tend to skip energy groups if the group structure is chosen such that \frac{E_{g-1}}{E_{g}}=100= 1/\alpha_{approx}. I know that the...

Hi, This isn't a homework problem - this is to help with the design of an experiment. I know the questions below are probably fairly simple physics questions, but I've got lost in laws and units! Please help me out. The experiment A cylinder 20cm long and 2cm wide is filled with 6cm of...

For part of my coursework I am asked to look at gas application in polymer manufacture and while looking through sources I found articles on the use of pentane in polystyrene resin. I was wondering at what rate the pentane diffuses out of the polystyrene? Any equations would help tremendously as...

I'm curious how to solve Fick's second law of diffusion \frac{∂c}{∂t}=D \frac{∂^2c}{∂x^2}For conditions:c(x,0)=0c(0,t)=Ac(\infty,t)=0Physically this means: -c(x,t) is the concentration at point x at time t. -Initially there is no concentration of diffusing species. -At x=0 for all t the is a...

Homework Statement The edges of a thin plate are held at the temperature described below. Determine the steady-state temperature distribution in the plate. Assume the large flat surfaces to be insulated. If the plate is lying along the x-y plane, then one corner would be at the origin...

I have been wondering if there is an explanation to why diffusion always goes down the concentration gradient? If it is a random molecular movement than why do we always end up with a uniform distribution of molecules?

i need a help in solving ,using 1 group approxmation , estimate the critical size of cube consisting of 75% zirconium-91 and 25% plutonium--239 by volume , when the cube is surrounded by a vacumm. zr-91 microscopic cross section (capture)=0.00335 microscopic cross section (scattering )=5.89...

I'm reading about osmosis, and the textbook I'm reading states "osmosis of water is not diffusion of water: osmosis occurs because of a pressure difference" and then goes on to state that osmotic pressure is the driving force of osmosis. I had previously just understood osmosis to be the...

Hello everyone! I hope you may be able to shed light on a recent problem that i have to deal with. I keep working on a numerical solution on a heat diffusion problem. It is a numerical solution for the PDE θT/θt=a*(θ^2T/θx^2 + θ^2Τ/θy^2), that describes the heat diffusion on a two...

I have a sphere of radius 4.8mm surrounded by a membrane .2 mm that has a drug in the inner sphere and is diffusing out through the membrane. I know the saturation concentration, the partition coefficient and diffusivity of the drug. I also know that the concentration outside of the membrane is...

Hello all, I built an expansion cloud chamber and noted that an electrostatic field was needed to see the ionizing radiation. I know this is needed to prevent recombination of the ions and their free electrons. However, I built a diffusion cloud chamber a while ago that called for no electric...

Homework Statement The equation for the probability distribution of the price of a call option is \frac{\partial P}{\partial t} = \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 P}{\partial S^2} + rS\frac{\partial P}{\partial S} - rP with the conditions P(0,t) = 0, P(S,0) = \max(S-K,0), and...

_{}Dear Fellows, I am just using a Green Naghdi heat transport equation which is represented as, ρ\timesC\timesT''+aT_0\timesU'_i,i=K\timesT'_i,i+K*\timesT_i,i where (')=derivative with respect to time (,i)= derivative with respect to space. I am being informed that U_i,i= is a...

I am working through a paper in which the chemical diffusion coefficient is related to the self-diffusion (or tracer) through the following derivation, on which I am a little hung up. AB2 metal. Overall diffusion D= XADB+XBDA meaning the chemical diffusion of B is...

Homework Statement Solve the diffusion equation with the boundary conditions v(0,t)=0 for t > 0 and v(x,0) = c for t=0. The method should be separation of variables. Homework Equations The separation of variables method. The Attempt at a Solution Attempting a solution of the form...

Imagine a wall (membrane). Concentration of a specimen A on one side of the wall is cA and it has the temperature TA. The concentration of a specimen B on another side of the wall is cB and it has the temperature TB. Specimen A nad B diffuse against each other (assume steady state). Can somebody...

Homework Statement I'm working with a 0ne-dimensional random walk and looking at Fick's second law, below. All I've read seems to take D = 1/2 as a given for ordinary diffusion, but where does this come from? Is there a way to derive it? Homework Equations \frac{\partial } {{\partial...

Hi all, I was wondering if anyone knows of any literature that explains why larger grains "absorb" smaller grains during cross-boundary diffusion in solid state diffusion. I read a book that explains it analogously in terms of pressure differences and boundary tension but I'm not quite happy...