Diffusion Definition and 399 Threads

Disclaimer: This is a homework problem I need to analytically solve the diffusion equation for a 1d 1 group slab with width a, and source distribution Se^(-k(x+a/2)) I've gone through the math, and come up with my homogeneous and particular solution and attempted to apply the boundary...

Homework Statement Hello, I don't understand the solution of an exercise Let P(x) be a continuous function such that |P(x)|≤Ceax² . Show that formula (8) for the solution of the diffusion equation makes sense for 0 < t < 1/(4ak), but not necessarily for larger t. Homework Equations Equation...

Hello Everyone, I have a question regarding the diffusion of a gas (or mixture of gases) into an evacuated space. The situation I am picturing is one where you have two vessels of equal volume, one contains a gas at room temperature, some known pressure (say ~760torr), and the other at static...

I am running a general circulation model (EPIC, which uses isentropic vertical coordinate system, potential temperature) and need to add vertical diffusion to the zonal velocity U. The vertical coordinate is theta (Θ, potential temperature) and there is no vertical height coordinate in z but I...

Homework Statement Consider the diffusion of a drop of ink in a water vase. The density of the ink is ## \rho (\vec{r}, t) ##, and the probability ##P(\vec{r}, t)## obeys the diffusion equation. What is the relationship between ##\rho (\vec{r}, t)## and ##P(\vec{r}, t)##? Homework...

Hi guys, I have functioning MATLAB code for my solution of the 3D Diffusion equation (using a 3D Fourier transform and Crank-Nicolsen) that runs just from the command window and automatically plots the results. However, it seems like my solution just decays to zero regardless of what initial...

Hello. I have some questions regarding the equation: k\frac{\partial}{\partial x}\left( u\frac{\partial (u-r(x,t))}{\partial x} \right) = \kappa \frac{\partial u}{\partial t}. u is positive. r(x,t) is given as an input. I have implemented this non-linear diffusion equation using backward Euler...

Homework Statement Exercise: Hexachlorobenzene (C6Cl6) is a highly toxic waste product of pesticide manufacturing. It is resistant to biodegradation. Sediments at the bottom of a reservoir in the Upper Mississippi River catchment have been found to contain high C6Cl6 concentrations. The...

I want to model the diffusion-controlled combustion of a small carbon particle. The system I want to model is similar to this one However, I'm not going to use the stagnant gas film model as shown in the figure, since I lack data for the film thickness, and I want to evaluate the problem...

Homework Statement Is the oxygen required by the single-celled organisms obtained by diffusion or osmosis through the surface membrane of the cell? Homework Equations The Attempt at a Solution I'm thinking osmosis since there's a membrane through which the oxygen passes. But I've been...

Hi, PF! I recently solved a problem from BSL which asked to analyze the following system used for determining the diffusivity of a binary mixture of gases. The left portion of the system, from the left bulb up to the stopcock at the middle of the tube, is filled with gas A. The right portion...

Homework Statement Problem 18B.13 from Transport Phenomena, BSL. Tarnishing of metal surfaces. In the oxidation of most metals the volume of oxide produced is greater than that of the metal consumed. This oxide thus tends to form a compact film, effectively insulating the oxygen and metal from...

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Homework Statement A (spherical) rubbery balloon of 20 cm in diameter is filed with helium. The rubber balloon wall has a thickness of 0.05 cm and diffusivity of 0.1x10-10 cm2 /s for helium. When the balloon is left in the air at 25°C, helium leaks into the air by diffusion through the rubbery...

At Earth's 1g, is the rate of diffusion equal to the rate of sedimentation for cellular molecules (or proteins)? The diffusion rate is higher, correct? Thanks.

OK the atmosphere by definition envelopes the earth.The force keeping it here is solely gravity. The "force" opposing this is diffusion across a pressure gradient into the vacuum of space. Assuming that is correct how could I prove this other than looking out the window. Newton's law of...

Homework Statement What is the difference between diffusion and osmosis? Homework Equations 3. The Attempt at a Solution I am guessing that diffusion means that particles spread out. And osmosis is when particles spred out in a cell membrane. [/B] Osmosis can be "diffusional" but...

This is my attempt at the solution. I have been told that the given function is a solution. I just need to prove it. As you can see that I am stuck. What am I doing wrong?

I'm right now working with modelling a system, where atoms diffuse along a coordinate z until they reach a certain point z=z0 at which they are taken out of the system. The diffusion equation is: ∂n/∂t = D∂2n/∂z2 The question is now what boundary conditions to use for the concentration profile...

Hello, I am trying to solve the following simple diffusion equation using the method of lines: du/dt=D(du2/dx2)function k=func1() k = [0, 0, 0, 0, 0, 0, 0.4380, 0, 1e5]; %k(9) initial value of the molecules end %k(7) D/dx2 function...

Hello all, I have a Varian M4 diffusion pump that has a 6 inch diameter opening at the top, is it okay for me to connect that to a reduced size opening like just 2 or 3 inches diameter so that I can use a smaller valve? I am only trying to pump down a cubic foot or two sized chamber. I am...

1. A sheet (with a thickness of 0.05 cm) of MgO lies in between layers of Ni and Ta to avoid reaction between these two metals . At 1400 ºC, ions of Ni are created and diffuse through the ceramic MgO to the Ta. Find the number of ions that go through the MgO per second, knowing that the...

Hello everyone, I have a question concerning the following: There is a relationship for diffusion concerning the RMS: <x^2>= 2\cdot D \cdot T for one dimension and there is also Fick's 2nd Law. When does the above formula apply? What I don't understand is that in the RMS formula there is...

We solved a simple looking heat diffusion problem because it describes an apparatus used in an NIH sponsored research project. It resembles problems discussed in textbooks and in many papers on the web. A textbook method solves all those problems but a straight forward application of that...

Hi, I'm just an average guy here, mostly self educated, and am looking for experts to verify my theories on developing revolutionary impact protection. If I disrupt direct impact to the head using a highly elastic layer of material, does that create an inelastic impact interruption? A helmet...

I'm trying to understand how a diode works and for this I've used(among other resources) the book written by Albert Malvino, Electronic Principles. Everywhere I read about this topic, it says that when the N-type and P-type semiconductors are joined together, the free electrons from the N-type...

The diffusion distance for a Brownian particle is given as x^2 = 2Dt D: diffusion coeficient, t: time However, not all textbooks include the factor 2 (i.e. they just write x^2=DT). Is there a difference or are they just beeing sloppy? I run into trouble when I want to calculate the length of a...

Homework Statement A slab of radioactive material of thickness L lies in the x-y plane surrounded by a material that can be thought of as extending to +/- infinity from -L/2 and +L/2. The system is in steady. Find the general solution for the diffusion equations in each region(ok). Find the...

I am trying to understand about glucose metabolism! I have been researching this stuff forever! X( Would you see if my explanations are right, and if not, tell my why? Thank you SO much! That would be a HUGE help! Is it true that uptake and release of gas/nutrients only occur in the...

Homework Statement The goal is to derive the heat equation with convection, ut=α2uxx-vux but for the case where u(x,t) instead models concentration changes by diffusion and convection. The idea is to use conservation of mass to do this. Homework Equations We are given: Change of mass inside...

Hello, The diffusion current in a semiconductor is caused by difference in concentration of holes and electrons. My question is it related to Coulomb's law (electric force due to electric field) ? Thank you

Show by direct calculation that Eqs. (4-134) and (4-137) in the textbook by Duderstadt and Hamilton hold, i.e.:(a) ∫ dΩΩiΩj= 4π/3 δij; i,j = x,y,z; 4π(b) ∫ dΩΩxΩyΩz = 0, if l, m, or n is odd. 4π The integrals are over 4π. This is part of the derivation of the diffusion equation...

Can I make diffusion pumps from aluminum? I am going to create parallel connected diffusion pumps for many UHV purposes. I see that aluminum that is treated to prevent outgassing is used for UHV valves, chambers, and reactors. I'd like to know what temperature diffusion pumps boil their...

Hi, I understand that an exciton must reach the D/A interface within the Exciton diffusion length to prevent recombination, however, what are the factors during device fabrication that can affect the Exciton diffusion length of a P3HT:PCBM BHJ OSC?

Hello everybody. I should solve a modified version of second Fick's law in nondimensional spherical coordinates; t is the time and rho [0,1] the nondimensional radius. In this equation the diffusion coefficient is vraiable with t and rho. The equation is the following: dC/dt =...

Hey, I have a question for evaporation--What is the real driving reason for evaporation? I usually believe that it is a pure diffusion process: the saturated pressure of liquid at the liquid vapor interface is higher than the partial pressure of vapor in the ambient, and this pressure difference...

Hi all, This is the situation: Solution A with 200 Osm urea, solution B with 200 Osm KCl, separated by a semipermeable membrane that is permeable to urea but impermeable to KCl. Each solution is in 1 L water. Calculate the equilibrium concentrations of urea and KCl. The numerical answer...

I'm looking for a proof of the following statement at a level an early undergrad would understand: ##J=D \vec{\nabla} \vec{n}## where ##D=\frac{v_{th}l}{3}## with ##l## being the mean free path and ##v_{th}## the thermal agitation velocity, ##J## is the particle current density. I really did...

Homework Statement Find the solution for: ({\partial{}_t}^2 -D \Delta^2)G(\vec{r},t;\vec{r}_o,t_o)=\delta(\vec{r}-\vec{r}_o)\delta(t-t_o) In two dimensions. Homework EquationsThe Attempt at a Solution Am I supposed to use bessel eqs? I'm kind of stuck in starting the problem :L

1. Homework Statement Question This is an experiment on a dilute isotopic mixture of helium gas. A spherical vessel of diameter 1 m is first filled with 4He gas to one atmosphere pressure. Then a small amount of 3He gas is introduced through a valve on one side of the vessel. Make a rough...

Hello, I just began learning mass transfer, and I am trying to use analogies from heat transfer to help me solve problems. For example, if you have one dimensional heat transfer through a plane wall, I would start with a general energy balance. $$\frac {dE}{dt} = \dot Q_{x} - \dot Q_{x + \Delta...

If we have a hole in a container with pressure equal to the pressure outside it and the concentration of gas inside the container is more than that outside will the gas effuse out?

[SIZE=14px][FONT=Lato]So the rate of diffusion is dependent upon the speed of the molecules and the existence of a concentration gradient. What about the concentration of the particles themselves? Diffusion is dependent upon mean free path and concentration is inversely proportional to mean...

I am going to do a numerical simulation of diffusion in matlab. The diffusion coefficient is concentration dependant, and i use an array operation to calculate D(x), so it is known. Based on Fick's second equation: $$ \frac{\partial C}{\partial t} = \frac{\partial}{\partial x} D \frac{\partial...

Dear scientists, For my thesis I am searching for a hydrogel that limits the diffusion of calciumions. The objective of this is to get the calciumconcentration in the hydrogel within a certain measurable (with fluorescent Cameleon) range. Unfortunately I don't know where to start looking, do...

Homework Statement i) At rest a 70 kg person with an area of 1.7 m2 consumes around 14 litres of oxygen per hour. Around 2% of this is provided by diffusion through their skin. Calculate the diffusion rate for oxygen through human skin, in millilitres per second per square metre. ii) What...

Hey guys, I have a problem that is giving me trouble. Homework Statement I have to solve time dependent diffusion equation ##D\nabla^2 T(r,t)=\frac{\partial T}{\partial t}## (##D## is diffusion constant and ##T(r,t)## is temperature function) for a spherical shell of radii ##r_1## and ##r_2##...

Hi, I want to solve the following diffusion equation: (d/dt) C(r,z,t)=D*∇^2 C(r,z,t) where C is the concentartion and D is the coefficient of diffusivity (constant) with initial condition C(r,z,0)=C0 (constant) and boundary condition dc/dr=0 at r=0; (dc/dz) at z=-L equal to (dc/dz)...

Homework Statement Plot the transient conduction of a material with k = 210 w/m K, Cp = 350 J/kg K, ρ = 6530 kg/m3 Where the material is a cylinder, with constant cross sectional area and is well insulated. The boundary conditions for the cylinder: T(0,t) = 330K T(l,t) = 299K...

Homework Statement Would appreciate any help quite confused on this topic. If a type of ion has a diffusion coefficient of 10^-8 m^2/s in water. What is average distance traveled after 30 mins? What sort of graph should you plot in order to easily test validity of r=squarer root-2Dt. How...