Diffusion Definition and 399 Threads

I have to write a FD expilicit method, for temp dist on 2D plane. I am trying to mod the 1D solver to 2D solver, the code below is a 1D solver. Any possible suggestions how it can be done? I initially, derived u(i,j+1) for 2D for in that derivation i,j corresponds to x,y... where as in 1D...

Hi all: Does anyone explain why we call diffusion as the second rank tensor variable? I understand Based on the tensor definition, we know tensor expresses the relationship between input vector and output vector. How about diffusion? what is its input vector? what is its output vector? thanks...

Technically speaking, this is not a homework problem; it is something extra that I want to explore using data from my biomedical engineering class. We recently finished a lab involving testing the design of a micromixer; now comes the analysis of the data. No where in the lab are we instructed...

Hello everyone, I got some questions about diffusion. My note says that diffusion is affected by 1. Solubilty of solute- What do they mean by this. Does solubility increase or decrease the rate. Since water is the major liquid found inside the body. Are they referring to solubilty in...

Hi there, as the title already suggests, I'm currently a phd student focusing on molecular simulation of diffusion phenomena. I took this position, because I'm very interested in the application and development of simulation methods in general. However, for my taste there is simply way to...

Hi there, I'm trying to wrap my head around Fick's first law of diffusion (for one dimension): J_{x} = -D \frac{\partial \phi}{\partial x} I understand that \phi is the concentration in units amount/volume and that x is position on the gradient in units length. What I don't understand...

Homework Statement Show that concentration of a substance obeys the diffusion equation if the rate at which substance leaves a region is proportional to the concentration gradient. Homework Equations Diffusion equation: \nabla2\phi = (1/a) (d(phi)/dt) where Phi is a function of r, t...

Homework Statement Explain why facilitated diffusion, unlike simple diffusion, is both specific and saturable. (Short essay, 4 points) Homework Equations -------------------------- The Attempt at a Solution Is this a good beginning to an answer? I feel like I can never...

I have been asked to solve a diffusion equation with a source term using finite differences method. I need to numerically integrate the following equation either in MATLAB or C++. The equation is dT/dt = d2T/dx2 + S(x) The form of S(x) is some function given by a Gaussian profile...

help w/ diffusion equation on semi-infinite domain 0<x<infinity Woo! First post! And I'm trying out/learning the latex code which is really neato! Okay, so... please help! I'm trying to solve \frac{\partial^{2}T}{\partial x^{2}} + \frac{1}{x}\frac{\partial T}{\partial x} =...

Hello, I would like to know how the lattice diffusion is done & why is it temperature dependent? I have tried googling Lattice diffusion several times, but I couldn't find any complete online reading/video... Your contributions will be highly appreciated.

Hi I am trying to solve the following diffusion problem using crank Nicholson method, but having trouble on how to proceed with the tridiagonal matrix and boundary conditions. dy/dt = k* d^2y/dx^2 K = increases with x My initial condition is y(x,0)=0; Boundary conditions are...

Does anyone know figures for Diffusivity (diffusion coefficients) for two gases at different temperatures. Such as air - Hydrogen or air-methane. For example the diffusivity of hydrogen into air when the hydrogen is at 300C and the air at 100C. Please don't point me to Fick's laws...

Hi! I'm a student and I have a project to do. It's about the diffusion's path. My problem is that I can't find a definiction of diffusion path. Could anybody be able to tell my where to look, or what is that?

Does anyone know how to write the diffusion tensor (coefficient) for a isotropic media? It should be a matrix but I can't find it in the literature. Maybe you guys know it or can help. Jackson doesn't have it. Cheers

Homework Statement The Attempt at a Solution I'm really at a loss on this question, which is why i have achieved so little on it so far. I think i more or less understand what a Fourier transform does (transpose amplitude vs time to amplitude vs frequency, ie the Fourier transform...

Hello, I am trying to (numerically) solve the following reaction-diffusion equation for the probability density of the a pair, \rho (\vec{r}_1,\vec{r}_2): \dot{\rho} (\vec{r}_1,\vec{r}_2,t) = D_1 \nabla^2_1 \rho (\vec{r}_1,\vec{r}_2,t) + D_2 \nabla^2_2 \rho (\vec{r}_1,\vec{r}_2,t) - k...

Hi, I have seen the solution to the diffusion equation written as C=(N/sqrt(4PiDt))exp(-x^2/4Dt). Hoever, as I understand it, this is for an instant input of N material. I want to express the concentration of substance at a point x away from the source for an arbitrary input signal. Is there...

What is the main physical difference behind these two theories? 1) I understand that the thermionic emission theory is applied in metal-semiconductor contacts and heterostructures where the energy band off-sets are large. Whereas the diffusion theory is applied in a simple homojunction, of...

N particles diffuse in one dimension in the potential U(x) = ax^2, with a > 0. Find steady-state concentration, c0(x). No idea how to solve this. Any equations?

The diff. eq. F'(t) / [1 - F(t)] = p + q F(t) or F'(t) = [p + q F(t)][1 - F(t)] has the solution F(t) = [1 - exp(-bt)]/[1 + a exp(-bt)] where a = q / p and b = p + q. How can I write the system of equations with the solution {F1(t), F2(t)} = { [1 - exp(-b*t)]/[1 + a exp(-b*t)] , [1 -...

the difference between the Heat and Diffusion equation ?! [FONT="Arial"][SIZE="5"]Please: What is the difference between the Heat and Diffusion equation ?! thank you.

Homework Statement Consider a traveling wave u(x,t) =f(x - at) where f is a given function of one variable. (a) If it is a solution of the wave equation, show that the speed must be a = \pm c (unless f is a linear function). (b) If it is a solution of the diffusion equation, find f and show...

Homework Statement Apologies if this doesn't come through properly. The question states Use a change of time variable to show that the equation c(\tau) \frac{\partial u}{\partial \tau} = \frac{\partial^2 u}{\partial x^2} can be reduced to the diffusion equation. The...

Homework Statement 2. The attempt at a solution a) The steady state concentration is the concentration when t --> infitine, right? How can I find that when I don't know c(x, 0)?

If the gas particles in a box are uniformly distributed in the y and z directions, and linearly distributed in the x direction, is it true that the concentration won't change with time, according to the diffusion equation? I find this very unintuitive.

Phosphatidylcholine is a lipid that can be found in egg yolk. When phosphatidylcholine is mixed with water it will form micelles – spherical particles. Molecular weight (Mw) for the particles is 97*000 g/mole Density for the particles is 1.018 g/cm3 The temperature is 25°C a) What is the...

I am attempting to solve a second order differential, but I am have never done anything like this. I was told that it was a good Idea to think about Fourier transforms. \frac{d^{2}q}{dx^{2}}=\frac{dq}{dt} Boundary Conditions: q(+/-\infty,t)=0 q(x,0)=S_{0}\delta(x) Apparently the final...

Greetings, I'm trying to get an intuitive understanding about a process involving an ion mobility that (I'm told) has D = 9.3 x 10-5 cm2/s. I'm assuming that D is a diffusion coefficient. I'd like to know approximately how long it takes for the ion to travel about 10 cm. Would this be...

Hi this is my first post and so I hope it will be good one for you physicists to solve for me! In angling anglers use small round balls called boilies.Say for instance you make 2 round boilies of 14mm in diameter.When these are prepared they are boilied in water to make a tough skin.They will...

Hi, I've decided to make my own meter for measuring laser power to around 10% accuracy if possible. Optical power meters are way too expensive for me though. One building block I've decided to use is a phototransistor, because I've found one which has very good linear response - when measuring...

Homework Statement A cylindrical wire of thermal conductivity k, radius a and resistivity p uniformly carries a current I. The temperature of its surface is fixed at T0 using water cooling. Show that the temperature T(r) inside the wire at radius r is given by T(r) = T0 + p(I^2)(a^2 -...

Homework Statement diffusion thru a semipermeable membrane. Homework Equations section 1 of the lab LAB - dialysis tubing containing distilled water and the beaker containing glucose and starch .. put it in water. Leave it over night and jot the changes, it goes through osmosis but...

a theoretical qstn.. the diffusion constant D, represents the avg. rate of unit displacement by a fluid particle. should D increase or decrease in time? and should D increase or decrease if length (lets say length of the capillary through with its travelling) increases? - m

Does anyone know of any good Diffusion (ie. Fick's laws, interstitial jumps, etc) online resources? Thanks!

Homework Statement Considering the periodic boundary conditions (given below) I am supposed to find the solution T(x,t) with the initial condition T(x,0)=\delta(x) Also I am limited to use method of images so I can't use separation of variables unfortunately. Homework Equations The boundary...

Hello everyone, a wave propagates at a speed (group of phase speed), less than the speed of light, no matter what type of wave we are dealing with (electromagnetic, mechanical,...). Why is infinite velocity characteristic of a diffusion process? What does that mean? For something to...

Hi, I am not sure if this is the right place to post a COMSOL question. If not I apologise, could you point me to the right place. I have a 3D geometry in COMSOL shape like a "T" where I want to model flow using navier stokes and a chemical diffusion using convection and diffusion. Both...

VERY URGENT: Please help with Diffusion Question and Membrane Protein question Proteins associated with the plasma membrane can be classified as either integral membrane proteins or peripheral membrane proteins. For the following types of proteins, please specify whether they would be integral...

I'm wondering if anyone is aware of any computational/theoretical work on solving the problem of describing the motion of a biological macromolecule in a cellular microdomain? This would have to mean setting up and solving a stochastic partial differential equation with boundary conditions...

i know that idea would seem a bit weird but, let us suppose we have a surface or volume in d- dimension, here d can be any real number (fractional dimension) the question is that we do not know what value 'd' is \frac{\partial \phi}{\partial t} = D\,\Delta \phi D is a diffusion...

isotropic equation, so k, ρ, and c are constant, where k is thermal conductivity, c is specific heat, and ρ is the density of the body. the equation boils down to \left( \frac{c\rho}{k}\right) \left(\frac{\partial u}{\partial t}\right) - \left(\frac{\partial^{2} u}{\partial...

Please provide me Diffusion coefficients of following ions in water at different temparatures (25 deg celcius, 75, 125, 300 etc) 1. Fe2+ 2. H2O 3. Fe(OH)+ 4. Fe(OH)2(aq) 5. H+ 6. OH- 7. CO3-2 8. H2CO3 9. HCO3- 10. Na+ 11. Cl-...

Hi. I've thought for some time about a problem that I'm not able to solve (to my own surprise). We have closed container, say a relatively high cylinder, placed vertically. In it are two gases of different density enclosed. Obviously the lighter one will 'fleet' and stay on top of the...

Homework Statement Since the problem involved formulas I have posted it as an attachment. Please check the attachment first. (I have not scanned this problem, just wrote it in word and posted it) The Attempt at a Solution My approach on this problem is to start with separation of variables...

I do not understand the difference between diffusion and migration is case of anion/cations. Thank you!

Hello everybody, I don't know if this is the right place to post this question. Sorry for that. I have the following system: small particles (I don't know exactly the composition) in a batch stilled tank reactor in which i add some hydrochloric acid. How I evaluate the concentration of...

which gas would diffuse the quickest? the slowest? A. methane B. oxygen C. nitrogen D. C2H6 (need to show work to verify!)

I have trying solving this PDE for some random boundary values, and were wondering if someone could verify my calculations? \[ \begin{array}{l} T_t = DT_{xx} \\ T\left( {0,t} \right) = 0,T(\pi ,t) = 0,T(x,0) = \frac{1}{4}\left( {\left( {x - \frac{\pi }{2}} \right)^2 + \frac{{\pi ^2...

Hey all, I'm wondering if someone can help me understand how to apply the boundary conditions to the diffusion equation in one dimension. Diffusion equation is: \frac{\partial u}{\partial t}=D*\frac{(\partial)^{2}u}{\partial x^{2}} The initial condition is: u(x,0)=0 And the boundary...