Diffusion Definition and 399 Threads

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...

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}...

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...

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...

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...

Homework Statement The one-dimensional heat diffusion equation is given by : ∂t(x,t)/∂t = α[∂^2T(x,t) / ∂x^2] where α is positive. Is the following a possible solution? Assume that the constants a and b can take any positive value. T(x,t) = exp(at)cos(bx) Homework Equations...

Hi all I have been working on some unique solutions to advection-diffusion type problems. One inverse Laplace transform that I seem to continue to encounter is the following: Inverse Laplace[F(s)] where F(s)=[(1/(((s-α)^2)+β)*exp(-x*sqrt(s/D))] In their classic 1959 text, Carslaw...

Homework Statement Mathews and Walker problem 8-2 (page 253): Assume that the neutron density n inside U_{235} obeys the differential equation \nabla ^2 n+\lambda n =\frac{1}{\kappa } \frac{\partial n }{\partial t} (n=0 on surface). a)Find the critical radius R_0 such that the neutron density...

Hi, I am solving the diffusion equation using explicit finite difference to model the diffusion of an analyte through a membrane. I am interested in the concentration of the analyte on the other side vs time elapsed. On one side of the membrane is an initial concentration, which I am...

Hi, I'm trying to find an analytical solution (if one exists) to the 1d diffusion equation with variable diffusivity κ(x); \partial_t u(x,t) = \partial_x[\kappa(x) \partial_x u(x,t)] Could someone point me in the right direction to solve this if its possible to do so analytically. I've...

Homework Statement One face of a thick uniform layer is subject to a sinusoidal temperature variation of angular frequency ω. SHow that the damped sinusoidal temperature oscillation propagate into eh layer and give an expression for the decay length of the oscillation amplitude. A cellar...

Homework Statement Implement the non-linear de-noising algorithm of Perona-Malik. Consider a noisy image, u, with pixel values referenced by u(i,j). Non-linear de-noising can be achieved by solving the following non-linear diffusion equation: ∇ · (g(∇u)∇u) = 0 with g(s) = ((K^2)v) /...

Homework Statement A student working 3.0m away from you in a chemistry lab performs an experiment which creates a bad odor. It takes a while for the smell to get to you (assume air currents are negligible). You are able to move 2.0m further away from the source but the smell catches up with...

Homework Statement A student working 3.0 m away from you in the chemistry lab creates a bad odour. The odour takes a while to get to you (assume that air currents are negligible). You then move 2.0 m further away, but the odour catches up with you in another 60 seconds. What is the diffusion...

Suppose that a tracheae is 1.17 mm long with a cross-sectional area of 1.01 x 10-9m2. The concentration of oxygen in the air outside the insect is 0.659 kg/m3, and the diffusion constant is 1.99 x 10-5 m2/s. If the mass per second of oxygen is diffusing through a trachea is 1.50 x 10-12 kg/s...

Hi all: Now I have a question about the concept of diffusion coefficient in two cases: the diffusion equation (J=DdT/dx) and the random walk (tao^2=6Dt). My quesion is the two D in two equations are the same or different. If they are different, is there any relationship between them? Best Xu

Any one have online documents showing the complete derivation of the both with the numerical solution ?

Hey everyone, I was just wondering, in a PEM fuel cell the Hydrogen ion diffusion through the membrane is an important step. But don't these ions need to diffuse through the anode as well to reach the membrane? Also, if this is the case and the anode is a metal like Pt, wouldn't the diffusion...

EDIT: The subscripts in this question should all be superscripts! Homework Statement I'm trying to solve a temperature problem involving the diffusion equation, which has led me to the expression: X(x) = Cekx+De-kx Where U(x,y) = X(x)Y(y) and I am ignoring any expressions where...

Hello there! I am solving a heat diffusion problem which is described by the differential equation: θΤ/θt=a*(θ^2Τ/ΘΤ^2). I will apply two diffrent temperatures on the ends of a metal rod. Solving the equation i conclude, according to the boundary conditions of course, at the function...

Homework Statement For ordinary 1D diffusion show that the mean value of the square of the position is equal to 2Dt Homework Equations \left\langle {x^2 \left( t \right)} \right\rangle \equiv \int\limits_0^\infty {x^2 p\left( {x,t} \right)dx} \frac{\partial }{{\partial t}}p\left(...

why simple diffusion does not require a semi-permeable membrane?

Hi. I don't know if this is the correct place to ask this, but prefer you to suggest me where I should ask. I'm starting with numerical simulation and I've been playing with the finite differences method to solve the heat equation on 1D, 2D and 3D uniform grids. This was really simple. Now I...

What is Super Diffusion? I just came up with an article talking about "super diffusion", then I searched the net & came upon the wikipedia article on anomalous diffusion which was very short and not descriptive of the physics behind it... I will highly appreciate any enlightenment :)...

I am confused because I read that a selectively permeable membrane means that it becomes osmosis and that there can't be a selectively permeable membrane for diffusion. Or is osmosis just diffusion across a selectively permeable membrane?

I have a 1_D diffusion equation dc/dt = D*d^2c/dx^2-Lc where L,D = constants I am trying to solve the equation above by following b.c. by FTCS scheme -D*dc/dx = J0*delta(t); where delta(t)= dirac delta function ----(upper boundary) I have written the code for it but i just...

Hi, below, you will find an extract from a script. One sentence is: "Move these walkers according to the the Gaussian distribution ..." (you can find this on the second image) My question: Why is it obvious from formula (124) (the short time step proppagator) that we have to move the...

I'm trying to find an analytical solution (probably containing a convolution integral) to a 2D diffusion problem in the xy-plane, when the value h(t) at the origin is known for all times t>=0. The diffusion constant is the same everywhere. The last problem solved under the section...

Hello, Here is my problem: I need to turn my time dependent neutron diffusion equation into dimensionless one.. So, I have a couple of questions: 1. As neutron flux is a : "A measure of the intensity of neutron radiation in neutrons/cm2-sec" per definition, is "neutron" a unit? If yes, then...

Hi, How can I solve the diffusion equation in one dimension: u_t=ku_{xx} ; -\infty < t < \infty , 0<x<\infty With the boundary conditions: u(0,t)= T_0 +Acos(wt) u(x\rightarrow \infty,t) \rightarrow T_0 Thanks!

Hi, I'm new to the entire neutronics field. I've learned about adjoints as a physics student in undergrad and I'm doing nuclear engineering for my graduate studies. I understand how to derive the adjoint operator for the diffusion equation, but I'm a bit confused as to how to calculate the...

Water pressure in a filtration bed is given by the following diffusion equation: \frac{\partial p}{\partial t} = -k

The problem is as follows: \frac{\partial u}{\partial t}=k\frac{\partial^{2}u}{\partial x^{2}}+c\frac{\partial u}{\partial x}, -\infty<x<\infty u(x,0)=f(x) Fourier Transform is defined as: F(\omega)=\frac{1}{2\pi}\int_{-\infty}^{\infty}f(x)e^{i\omega x}dx So, I took the Fourier...

I'm having a little trouble understanding the Sherwood number, (Sh, mass transfer Nusselt number), which gives the ratio of convective to diffusive mass transfer. My question is: given a system that has a molecular diffusion coefficient of D, the effective diffusion coefficient is measured to De...

Hallo everyone, I am trying to find the way to solve the vertical diffusion equation for a spicies X in the atmosphere for steady state conditions (dc/dt=0). The equation has the form, dJ/dz -P+S=0 where J =(vs*C(z)) + rho*kz*d/dz(C(z)/rho(z)) is the flux of spicies X at height z...

Homework Statement at t=0, x=0, a schoolboy sets off a stink bomb halfway down a corridor that is long enough to be considered infinite. The dispersion of the particles obey the modified diffusion formula: \frac{\partial \rho (x,t)}{\partial t} - D\frac{\partial^2...