Diffusion Definition and 476 Threads

Homework Statement Homework Equations \[ \frac{{\partial c\left( {x,t} \right)}}{{\partial t}} = D\frac{{\partial ^2 c\left( {x,t} \right)}}{{\partial ^2 x}} \] The Attempt at a Solution First of all, I am not sure how to translate the given data to exact mathematical...

Hi, I'm looking for information on blood and neuron cells. Specifically I need to know how the membrane transport mechanism in blood and neuron cells work? I am aware of concepts such as active diffusion, facilitated diffusion, and simple diffusion. The task is to look at the membrane...

Something has been bothering me recently regarding a diffusion problem. Consider a source of particles in a box, diffusing outwards. Set the boundary conditions so that the density is zero at the edge of the box. We can solve this problem in "steady state" and we find essentially a parabolic...

Homework Statement http://img42.imageshack.us/img42/1082/clipboard01lx.jpg Homework Equations (see solution) The Attempt at a Solution I literary just spent 5 hours trying to apply those boundary conditions, trying exponentials, sines, cosines, hyperbolic function etc... I...

Homework Statement Constant for the diffusion of hydrogen through steel is D(steal) = 4 x 10^5 cm²/s. They try to improve steel tanks for hydrogen storage by applying the coating based on TiAlN alloys. What is the diffusion coefficient Dp of such coating, if the permeability of hydrogen is...

Homework Statement Constant for the diffusion of hydrogen through steel is D(steal) = 4 x 10^5 cm²/s. They try to improve steel tanks for hydrogen storage by applying the coating based on TiAlN alloys. What is the diffusion coefficient Dp of such coating, if the permeability of hydrogen is...

Homework Statement Solve the equation U{t}=kU{xx}+cU Hint:use an integrating factor Homework Equations The Attempt at a Solution

Homework Statement Hello, I have this project due for next Friday. I need help. Its on diffusion limited aggregation. A topic which is unfamiliar to me. I know exactly how to do the problem, but I don't know how to code it correctly. Basically I allow a seed particle to be in a location in a...

I am going to run an experiment where I have a laminar flow of water with a dye solvent. It is necessary that the velocity of the dye particles is mostly in the horisontal directions. Naturally particles will diffuse but my questions is how I can ascertain that this is kept below some...

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...

1. Hello, I got this project to show DLA on matlab. I have to write up the pseudocode, which is basically just a code explaining the bare bones of the solution. It contains no coding. I'm just wondering if I have enough information or if I'm running low. Its the first time I heard of DLA so I'm...

Hello, I got this project to show DLA on matlab. I have to write up the pseudocode, which is basically just a code explaining the bare bones of the solution. It contains no coding. I'm just wondering if I have enough information or if I'm running low. Its the first time I heard of DLA so I'm not...

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...

Homework Statement The Fourier method specifies that change of heat energy of = heat out from left boundary - heat in from right boundary segment in time Δt If vars such as c,p.. are constant in the equation, and T(-L,L) = T_a, does the the aforementioned Fourier method...

Homework Statement a material occupies -L < x < L and has uniform ambient temperature T_a. A chemical reaction begins within the body leading to the 1-d heat equation: pc \frac {\partial{T}}{\partial{t}} = k \frac {\partial^2{T}}{\partial{x^2}} + pQAe^\frac{-E}{RT} with BC and IC T(+/-...

Homework Statement a material occupies -L < x < L and has uniform ambient temperature T_a. A chemical reaction begins within the body leading to the 1-d heat equation: pc \frac {\partial{T}}{\partial{t}} = k \frac {\partial^2{T}}{\partial{x^2}} + pQAe^\frac{-E}{RT} with BC and IC T(+/-...

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 (Last one!) I think I filled out this table correctly, I just want someone to check over it for me, if you would :) Oxygen enters cells by simple diffusion, glucose enters most cells by carrier assisted (facilitated) diffusion, the sodium/potassium pump removes sodium...

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...

Hi all: I am confused about how far spin magnetic moment goes during a finite diffusion time (such as 100 ms). As we know, due to T2 relaxation mechanism in NMR, spin 1 and spin 2 can exchange magnetic moment but no energy transfer during this exchanging process due to dipole-dipole...

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?

Homework Statement You release a billion protein molecules at position x=0 in the middle of a narrow capillary test tube. The molecues' diffusion constant is 10^-6 cm^2s^-1. An electric field pulls the molecules to the right (larger x) with a drift velocity of 1 micrometer per second...

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 -...

Homework Statement I need help in solving a problem I was assigned from Numerical Methods for Physics, 2nd Ed., by Garcia. We are asked to create a solution, by hand, for the diffusion equation, using the method of images. In particular, we have a 1-dimensional bar, centered at x = 0, of...

the difference between the Heat and Diffusion equation ?! 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 Eq. 4.14: \zeta = 6 \pi \eta R (Stokes formula) 2. The attempt at a solution In my plot, collagen, hemoglobin and lactoglobulin give a straight line, while ribonuclease is a bit above the others. I don't know which diffusion law I'm supposed to use...

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...

Homework Statement http://img223.imagevenue.com/img.php?image=79777_Untitled_122_69lo.jpg So for this setup i understand that the light generates EHP in the semiconductor and creates a concentration gradient which causes the electrons and holes to diffuse to the other side, so if the light is...

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...