Diffusion Definition and 476 Threads

Dear all, I would like to perform numerical simulations of the heat transfer/temperature field in a static bath of superfluid helium. The heat conduction in superfluid helium can be modeled in two regimes depending on the heat flux. For low heat fluxes ##\dot{q}##, the temperature gradient...

Recently, I've been told I was wrong concerning the nature of stationary states and diffusion being related. Even though I pointed out to the people involved that I was merely paraphrasing Max Born, who was apparently quoting the same idea as Linus Pauling. No one has been able to tell me...

I see in most newer syllabus textbooks it says that diffusion is the mixing of fluids and diffusion cannot occur in solids But when is search the web I see lectures and books written on the title diffusion in solids and when I studied I was taught that diffusion occurs in solids but at very very...

I have recently been curious about heat diffusion. If there is space in one dimension with any kind of temperature dispersed throughout, then the heat equation states that the derivative of the temperature with respect to time at any point equals some constant (k) multiplied by the second...

I have studied that mass transfer is of two types Molecular mass transfer(diffusion) Eddy diffusion then in later portion of the book I found that there is convective mass transfer too, I wanted to ask if both convective mass transfer and eddy diffusion are same ? I read this equation N_i =...

Homework Statement The evolution of the density in a system of attractive spheres can be described by the following dynamic equation. $$\frac{\partial}{\partial t} \rho (r,t) = D_o [\nabla^2 \rho (r,t) + \beta \nabla \rho (r,t) \int dr' [\nabla V (|r-r'|)] \rho (r',t) g(r,r',t)]$$ a)...

I understand that diffusion is the movement of molecules from a region where concentration is high to one where it is lower. This happens due to the molecular agitation which leads to frequent collisions and hence scattering of molecules. But I do not know what is effusion. Any help? Thanks

Diffusion of A through Non-diffusing B Dry air is required for burning of sulphur in a sulphuric acid plant. Moisture (A) diffuses through a film or layer of air (B), reaches the acid and gets absorbed in it. But air being virtually insoluble in sulphuric acid will not diffuse. So air is...

Homework Statement [1] is the one-speed steady-state neutron diffusion equation, where D is the diffusion coefficient, Φ is the neutron flux, Σa is the neutron absorption cross-section, and S is an external neutron source. Solving this equation using a 'homogeneous' material allows D to be...

Consider this Ito proces: $$dX_t = \mu(X_t,t)dt+\sigma(X_t,t)dW_t$$ with W_t being a wiener process. My question: What is the diffusion coefficient of X? My motivation for asking: A lot if financial literature refer to "diffusion coefficient" and I haven't understood by googling it, because...

Homework Statement Hi I am doing an assignment and this question is actually really simple in a way, but I am not sure where I am getting this wrong. Which of the following statements about diffusion is false? Choose All That Apply Diffusion depends on the intrinsic kinetic energy of...

Homework Statement Hi guys. So for my biology class, we were doing a water chemistry experiment. We placed potato cells into beakers of different [sucrose] (dissolved in water). The goal was to plot the change in mass % on a graph, make a linear trendline, and see which solution was isotonic...

I have a working Matlab code solving the 1D convection-diffusion equation to model sensible stratified storage tank by use of Crank-Nicolson scheme (without εeff in the below equation). As indicated by Zurigat et al; there is an additional mixing effect having a hyperbolic decaying form...

In context of heat transfer, are conduction and diffusion same process?

Well, I was solving the 3D diffusion equation: ##\displaystyle \frac{1}{c}\frac{\partial \phi(\mathbf{r},t)}{\partial t}-D\nabla^2 \phi(\mathbf{r},t)=q(\mathbf{r},t)##. I wrote a program to do this. The problem concerns the diffusion of light. However, all this time I've been working with...

So I want to write a short code to solve the diffusion equation and I want to be lazy and use the gradient function for the spatial differences, so for the second order derivative: \frac{f(i+1)-2*f(i)+f(i-1)}{h^{2}}=\textrm{gradient}(\textrm{gradient}(f,h),h) So the code I wold use is...

Homework Statement I am trying to solve the axisymmetric diffusion equation for vorticity by Fourier transformation. Homework Equations $$ \frac{\partial \omega}{\partial t} = \nu \Big( \frac{1}{r}\frac{\partial \omega}{\partial r} + \frac{\partial^2 \omega}{\partial r^2} \Big). $$ The...

I have a question about osmosis that goes a bit deeper than most basic textbooks so I cannot find the answer.Here's the problem: Imagine an animal cell, say a red blood cell, in a slightly hypotonic solution. The water starts to flow in osmotically. The concentration of solute in the cell...

Hello everybody! For my water in nanoscaled-pores simulations with SPH I need a value for the characteristic velocity. My planned approach is to estimate this value by attaining the propagation speed of a diffusion wave. But I have problems with understanding this process since I find some...

Homework Statement The activation energy of vacany formation in Zinc is 72kj per mole. What is the vacancy concentration at 687k Homework Equations Nv=Nexp(-Q/kt) N=p(Na/A) The Attempt at a Solution Seems very straight forward. Although I keep getting zero for the exponent term...

Homework Statement Gas with thermal conductivity κ fills the space between two coaxial cylinders (inner cylinder radius a, outer cylinder inner radius b). A current I is passed through the inner cylinder, which has resistivity ρ. Derive an expression for the equilibrium temperature of the inner...

Hi guys! My question is about the diffusion coefficient of the mixture of gases. Consider two gases in thermal equilibrium (Maxwell velocity distribution) having different densities n1 and n2. Let's suppose that the molecules are rigid spheres with diameters d1 and d2 and masses M and m...

Let's suppose an electrochemical system with given coordinates: We are interested in diffusion motion of ion ##i## in the direction of ##y## axis. Concentration ##c_i## is a function of both ##x## and ##y##. Concentration ##c_i## at ##y=0## is zero. The system is steady thus ##\frac{\partial...

I recently bought an old diffusion pump from eBay which I'm fixing up, and need 100cc of Santovac-5 oil (polyphenyl ether) for it. Does anyone have an idea where I can get a small amount (~100cc) of it to a reasonable price? What I've found isn't either shipped to Ireland or too expensive...

Imagine attaching electrodes to a complex sample, e.g. a semi-conductor or a single chemical molecule, leading to some electric current. Can we decompose this electron flow into local flows? - like locally attaching amperometer and counting what fraction of electrons flow directly between given...

I'm tinkering with the Convection Diffusion Equation (a second order differential equation) to model a temperature behavior in proximity to a heat source in a water bath. Just to get going I solved the system for some arbitrarily chosen boundary conditions. The result is that the temperature at...

The following lines of codes implements 1D diffusion equation on 10 m long rod with fixed temperature at right boundary and right boundary temperature varying with time. xsize = 10; % Model size, m xnum = 10; % Number of nodes xstp =...

The Eurodif gaseous diffusion plant required so much electricity that three of the four 955 megawatt nuclear reactors at Tricastin were allocated to meet to its power demands. In fact the Eurodif plant was such a large industrial consumer that the reactors were were built close by to minimize...

Consider the conceptual model presented in the attached image, of heat conduction in a bar. There is a heat source at left side and heat is observed at point Ho after a distance L from the source. If we consider only heat transfer through conduction then this problem can be modeled by...

Say I have a small solid polymer container filled with gas A. The walls of the container are semi-permeable, so gas A on inside can't get through/out. On the outside, gas B at atmospheric pressure, which can migrate through the membranes of container. Pressure inside the container is 0,6 bar...

Homework Statement I am trying to understand the derivation of the diffusion equation from the Master equation for a 1D chain. We have an endless 1D discrete chain. State from ##n## can jump to ##n+1## and ##n-1## with equal probabilities. The distance between chain links is ##a##. Homework...

Hi there. I was trying to solve the time dependent diffusion equation in only one dimension. I derived a explicit scheme using a finite difference in the time variable. The equation I am trying to solve is: ##\displaystyle \frac{1}{c} \frac{\partial \phi(x,t)}{\partial t} -...

Hi. I have this problem in trying to solve this PDE analytically. The PDE is represented by this diagram: Basically this is solving the Laplace equation with those insulated boundaries except it has that point diffusing its value across the plane. I know how to solve the Laplace equation...

I was reading this paper on rectifying properties of mangese oxide films, and came across this mention of diffusion voltage. Can anyone explain please what it is? Here's the context: In this piece of work, we successfully constructed heterojunctions by growing a manganite...

Homework Statement We let a dye diffuses into an environment of dimension L. We inject that dye into a box by one face, at t = 0 on x = 0. The linear density c follows that equation : with the conditions : Homework Equations / questions[/B] a. nondimensionalize the equations and the...

Homework Statement You dope an $n$-type substrate at time ##t=0## with electrons and holes around the points: ##\vec{r}_{0,c}## and ##\vec{r}_{0,v}## respectively. The initial densities' distributions are: $$\Delta n (\vec{r},t=0) = \frac{\Delta N_0}{(2\pi...

I have been preforming experiments to study the diffusion of Hydrogen through Molybdenum. According to Sievert's law diatomic molecules would diffuse as atoms. But according to my experiments I notice that the flux of hydrogen is directly proportional to the pressure of hydrogen and not to the...

Homework Statement This problem belongs to the Intermediate Physics for Medicine and Biology, Hobbie Chapter 4. The heat flow equation in one dimension $$ j_H=-\kappa \partial_x T $$ where ## \kappa ## is the termal conductivity in ## Wm^{-1}K^{-1}##. One often finds an equation for the...

Hi, I'm a second year undergrad and we've covered the heat equation, \begin{equation} ∇^{2}\Psi = \frac{1}{c^{2}}\frac{\partial^2 \Psi}{\partial t^2} \end{equation} and the wave equation, \begin{equation} D∇^{2}u= \frac{\partial u}{\partial t} \end{equation} in our differential equations...

I am trying to come up with an analytical solution (even as a infinite series etc.) for the following diffusion-convection problem. A thin layer of gel (assumed rectangular) is in direct contact with a liquid layer (perfusate) flowing with velocity v in the x direction (left to right) just...

Hi all. I've been working on this for two days and I feel embarrassed that I haven't been able to figure it out. I'm dealing with the following cocurrent diffusion situation between an aqueous and gaseous flow moving at the same velocity: X% of the liquid is removed and replaced with fresh...

In a fluid moving at constant velocity V, a concentration will undergo diffusion and convection $$U_t=\alpha^2 U_{xx}+VU_x$$ I understand that in this situation you can transform to a moving coordinate system and the convection term will disappear and you can solve for diffusion alone and...

Hello Physics Forums I’m doing some numerical studies on diffusion. I began with monte carlo simulations on gas diffusion, and more recently I’ve started to dabble in carrier diffusion inside semiconductors. It looks like diffusion in semiconductors is a lot more amenable to experimental study...

Hello physicsforums, I was wondering in the case of CO2 exchange in the capillary and alveolar system, if there is less CO2 in the alveolar, I understand that CO2 will move in the direction to the alveolar from the capillary through diffusion. My question is, if we are looking at brownian...

Hello, I have a project (model reaction diffusion brusselator 2d) ∂u/∂t=A+u^2v-(B−1)u+D1((∂^2)u/∂(x^2)+(∂^2)u/∂(y^2)) ∂v/∂t=Bu−u^2v+D2((∂^2)v/∂(x^2)+(∂^2)v/∂(y^2)) initial conditions: u(x,y,0) = 0.5 + y, v(x,y,0) = 1 + 5x. boundary conditions: ∂u/∂n = 0, ∂v/∂t = 0 n-external normal to the...

I saw the DAPL news story about the oil pipeline and I realized I have no idea how to analyze the problem of a fluid flowing from a boundary into granular material (or however you would classify soil). Does anyone know of any book or website that discuss the governing (or approximate) equations...

Ignoring cross-diffusion, diffusive mass fluxes down chemical potential gradients can be described by the equation (I am working from de Groot and Mazur's 1984 text on non-equilibrium thermodynamics): \frac{\partial C_k}{\partial t} = L_{kk}\frac{\partial (\mu_k-\mu_n)}{\partial x} where C_k...

Hello, I 'm trying to perform alloy of FeCr (Iron-Chrom) with calculate self diffusion iron depend with chromium composition. My work result that chromium doesn't give linier function with self diffusion iron in the alloy of FeCr. Maybe, anyone can tell me what's happened with my work. I'm so...

Homework Statement An initial particle distribution n(r, t) is distributed along an infinite line along the z-axis in a coordinate system. The particle distribution is let go and spreads out from this line. a) How likely is it to find a particle on a circle with distance r from the z-axis at...

Homework Statement The problem requires me to find the entropy of a diffusion constant as a function of time (I guess in terms of diffusion coefficient) Homework Equations Perhaps Heat / Diffusion kernel S = k p lnp The Attempt at a Solution I assume it was a delta initial condition then...