What is Separation: Definition and 475 Discussions

A separation process is a method that converts a mixture or solution of chemical substances into two or more distinct product mixtures. At least one of results of the separation is enriched in one or more of the source mixture's constituents. In some cases, a separation may fully divide the mixture into pure constituents. Separations exploit differences in chemical properties or physical properties (such as size, shape, mass, density, or chemical affinity) between the constituents of a mixture.
Processes are often classified according to the particular differences they use to achieve separation. If no single difference can be used to accomplish the desired separation, multiple operations can often be combined to achieve the desired end.
With a few exceptions, elements or compounds exist in nature in an impure state. Often these raw materials must go through a separation before they can be put to productive use, making separation techniques essential for the modern industrial economy.
The purpose of separation may be analytical, can be used as a lie component in the original mixture without any attempt to save the fractions, or maybe preparative, i.e. to "prepare" fractions or samples of the components that can be saved. The separation can be done on a small scale, effectively a laboratory scale for analytical or preparative purposes, or on a large scale, effectively an industrial scale for preparative purposes, or on some intermediate scale.

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  1. J

    MHB Separation of Variables/ODE

    The temperature distribution u(x, t), at time t > 0, along a homogeneous metal rod can be obtained by solving the 1d heat equation; ut = kuxx (1) where k = 2 is a constant. The length of the rod is 1m and the temperature at either end of the rod is zero for all time, so that the boundary...
  2. beep300

    I General topology: Countability and separation axioms

    I need some help understanding the countability and separation axioms in general topology, and how they give rise to first-countable and second-countable spaces, T1 spaces, Hausdorff spaces, etc. I more or less get the formal definition, but I can't quite grasp the intuition behind them. Any...
  3. N

    Solving for electric potential using separation of variables

    Homework Statement Given two two grounded concentric spherical shells with radii a,b (a<b) and a point charge q between them at a<r=R<b find: 1.The surface charge density of the point charge using the delta function, assume the charge is on the z axis 2.By using the separation of variables...
  4. MotoMike

    Payload accelerate after rocket separation?

    The USN used to shoot ASROC from box launchers. It was a torpedo with a rocket motor on the back. it was ballistic. The rocket fired and then separated mid flight. the torpedo continued on, a chute was deployed to slow and I think stabilize the water entry after which the torpedo went on...
  5. B

    Exploring NV(-) Separation with a to r Transformation

    reading a Nature paper tonight, I read that the NV(-) separation is ~ 1.7Angstroms. There was no equation to show how they arrived at this. Any insight into how this was determined? I don't think there is a direct equation, but perhaps using a to r?
  6. I

    How to calculate slit separation?

    Homework Statement Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the fourth order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separation of the two slits? Homework Equations d * sin(theta) = m * lambda The Attempt...
  7. sa1988

    Solve PDE by separation of variables

    Homework Statement Solve ∇2T(x, y) = 0 with boundary conditions T(0, y) = T(L, y) = T0 T(x, L/2) = T(x, -L/2) = T0 + T1sin(πx/L) Homework EquationsThe Attempt at a Solution Set T(x, y) = X(x)Y(y) Then ∇2T(x,y) = (∂2X/∂x2) Y + (∂2Y/∂y2) X = 0 Rearrange to find two separate ODEs: d2X/dx2 =...
  8. Z

    Separate Variable Homework: Solutions & Equations

    Homework Statement m1v1=m1v1'cosa+m1/2v2'cosB 0=m1v1'sina-(m1v2'sinB/2) m1v1^2=m1v1'^2+(m1v2'^2)/4 Homework Equations The solution in my book is v2'=2v1sqrt(3) The Attempt at a Solution I thought to separate v1' at the firts and put it at the second, but I don't know how to change sin and cos then.
  9. Konte

    Variable separation - Schrödinger equation

    Hello everybody, My question is about variable separation applied in the solution of general time-independent Schrodinger equation, expressed with spherical coordinates as: \hat{H} \psi (r,\theta,\phi) = E \psi (r,\theta,\phi) Is it always possible (theoretically) to seek a solution such as...
  10. F

    Spacelike separation. Finding a specific frame.

    1. The problem: If the Sun blows up at some instant and four minutes later we on Earth sit down to eat lunch, these two events are separated by a spacelike interval. The explosion of the sun cannot have influenced us at the time we sat down because it takes 8 minutes for light to reach us from...
  11. CivilSigma

    Separation of Particles in a fluid flow?

    Hello, I'm doing some online research on fluid flow in waste water treatment. One of the problem I'm trying to find information about is how can visible particulate matter be separated within a liquid. I saw the following picture: What fluid concepts are going here that allow the grit to...
  12. wolram

    What has happened to gender separation?

    I have noticed that women don't seem to make them self's up so much as 20yrs ago, and they wear things like raggety jeans, i know i am going to get killed for this but i am being honest, some girls look like boys and some boys look like girls, what has happened to gender separation? mod note...
  13. 24forChromium

    Is Electrostatic Ion Separation Possible for Industrial Element Separation?

    This is probably painfully obvious, but I keeping getting the impression that aqueous ions can be separated spatially via electrostatic force. For example, dissolve some sodium chloride in water, and then put the container in an electric field. Wouldn't the sodium ions migrate to the negative...
  14. W

    How to Create a Charge Separation to Migrate Ions in Solution

    Howdy, I am working in a research lab at The Ohio State University. I need to separate positively charged ions that are intramolecularly bound to negative counterions. I was hoping to use use static electricity to do this. Any suggestions on the power supply/control to do this?Lucas
  15. B

    Smallest Angular Separation

    Homework Statement For an eye in which the pupil has a radius of 3.0 mm, what is the smallest angular separation that can be resolved when two violet (λ = 400 nm) objects are placed side by side? Homework Equations theta_r = sin(theta_r) = 1.22(wavelength/d) The Attempt at a Solution theta_r...
  16. T

    Maintaining Charge Separation: The Role of EMF in Electrochemical Cells

    Hello, I have a question concerning electrochemical cells or batteries. It is said that when the battery is at open circuit, it has small charge separation on its electrodes thus having a potential difference equal to the emf of the battery. When the battery is connected to a circuit, the emf of...
  17. moenste

    Young's slit: find wavelenght, double slit separation

    Homework Statement 1. The distance between the 1st bright fringle and the 21st bright fringe in a Young's double slit arrangement was found to be 2.7 mm. The slit separation was 1 mm and the distance from the slits to the plane of the fringes was 25 cm. What was the wavelength of the light...
  18. W

    Solve PDE with separation of variables

    Homework Statement The wave equation for ψ(t, x) in 3D is ##\frac{\partial ^2 \psi}{\partial t^2}## - Δ ##\psi =0## Let ϒ(x) satisfy Δϒ = λϒ where λ<0. The x is in bold presumably to indicate it is in 3D, so represents also y and z? Show there is a solution of the form ψ(t, x) = sin(ωt)ϒ(x)...
  19. W

    How to Separate the Wave Equation into Three ODEs Using Separation of Variables?

    Homework Statement The wave equation for ψ=ψ(t,x,y) is given by ##\frac{\partial ^2 \phi}{\partial t^2} - \frac{\partial ^2 \phi}{\partial x^2} - \frac{\partial ^2 \phi}{\partial y^2}## Use separation of variables to separate the equation into 3 ODEs for T, X and Y. Use the separation...
  20. W

    Can All Differential Equations Be Separated?

    I just wanted to check something. The equation ∂2φ / ∂x2 + ∂2φ / ∂y2 = sin(xy) Was given as an example of a separable equation. I can't separate it, and I found online that to use separation of variables the equation should be linear, which this isn't? Is there a way of separating this?
  21. S

    Separation of variables and potential

    Homework Statement A potential satisfies ##\nabla^2 Φ = 0## in the 2d slab ## -\inf < x < \inf ##, ##-b < y < b ##, with boundary conditions ## Φ(x, +b) = +V_s(x)## on the top and ##Φ(x, b) = -V_s(x)## on the bottom, where[/B] ##V_s (x)= -V_0 for -a<x<0## ##V_s (x)=+V_0 for 0<x<a## (a) what...
  22. Isaac0427

    News The candidates' views on the separation of church and state

    Hi all! As a republican (libertarian to be exact) I would only consider voting for 10 out of the 17 candidates (I mean, if I were voting age). The 7 I would never vote for are in that place because of their lack of understanding of the separation of church and state. I just don't understand how...
  23. S

    Separation of Variables Problem

    Homework Statement A square is made up of four plates with a potential of zero on the top and bottom plates at (x,L/2) and (x,-L/2), and a potential of cos(πy/L)+cos(3πy/L). Find the potential and electric fields inside the square. The Attempt at a Solution I start with...
  24. D

    Simultaneous events, space-like separation & QFT

    First of all, sorry if this is in the wrong forum, wasn't quite sure which one to post it in given the question. My question is, given two space-time points ##x^{\mu}## and ##y^{\mu}##, if the events that occur at these points are simultaneous, i.e. ##x^{0}=y^{0}##, are the two events...
  25. K

    Wing flaps: Increase/decrease flow separation at low speeds?

    Hi all, I was just reading about airplane flaps. From I what I understood, they increase lift and drag (at lower speeds) to help land the aircraft. Do flaps also reduce the tendency of flow separation at lower speeds? Let's say we have an airplane wing with no flaps (Case I) and airplane wing...
  26. P

    Double slit - slit separation

    About how far apart can the slits get, in the double slit experiment, and still show the interference pattern?
  27. VintageGuy

    Advanced Dirac field propagator (spacelike separation)

    Homework Statement [/B] I'm supposed to calculate the advanced propagator for the Dirac field, and I have no problem with that. Then I'm supposed to show it vanishes for spacelike separation (that is (x-y)^2<0). Homework Equations For the advanced propagator I get something like: S_A =...
  28. P

    Explaining the Solution for Separation of Variables PDE with Initial Condition

    Homework Statement Homework EquationsThe Attempt at a Solution I managed to do the first part of the question. But I'm not sure how to find u(x,t) with that initial condition. The solution says; "since ##u(x,0) = \sum_{n=1}^\infty a_{n}\sin{(n\lambda x)}## Then it follows by linearity that...
  29. S

    Angular separation between moons

    Please help I am not sure of how to work this out The angular separation between Styx and Nix 28 days after they are in line with each other on the same side of Pluto. Mass of Nix = 5*10^16 Kg Orbital Radius of Nix = 48675 Km Orbital period of Styx = 20 Earth days
  30. H

    Separation of Variables in PDEs

    I am using the text by Farlow to study elementary methods of solving PDEs, and there is a point in his illustration of separation of variables where I am not seeing something. I am clear on everything that comes after and before this point, but after having returned to a certain step a few times...
  31. W

    Induced EMF in Coaxial Loops: Calculating Separation Distance

    1. A very large loop of metal wire with radius 1meter is driven with a linearly increasing current at a rate of 200amps/second . A very small metal wire loop with radius 5centimeter is positioned a small distance away with its center on the same axis (the loops are coaxial). The small loop...
  32. V

    Bond energy - (Force/ potential E vs interatomic separation)

    Hey guys, So, I was in my materials lecture today and something the lecturers and the tutors said was slightly confusing. We were talking about the repulsion and attraction force between atoms. This is all good as I can understand how if two atoms will repel each other if they get really close...
  33. Jon Richfield

    Disposition of Spent Fuel - Separation option

    But nikkkom, that makes no sense. 1: Vitrification is not cheap; I doubt that even superficially it is significantly cheaper than reprocessing; you know perfectly well that one does not simply dunk spent fuel rods in molten glass and bobsyouruncle. You first have to get the relevant materials...
  34. kini.Amith

    Separation of variables to solve Schrodinger equation

    How do we know that separable solutions of Schrodinger equation (in 3d) form a complete basis? I understand that the SE is a linear PDE and therefore every linear combination of the separable solutions will also be a solution , but how do we know that the converse, i.e 'every solution can be...
  35. H

    Maximum separation between blocks on spring

    Homework Statement Two blocks, each of mass m, are connected on a frictionless horizontal table by a spring of force constant k and equilibrium length L. Find the maximum and minimum separation between the two blocks in terms of their maximum speed, vmax, relative to the table. (The two blocks...
  36. microsansfil

    Spin-Charge separation seem to have been experimented

    Hello, There this article "http://www.nature.com/nphys/journal/v11/n1/full/nphys3172.html". High-energy experiments have shown that the electron is a point-like particle with spin-1/2 and electric charge -e. In highly correlated condensed matter systems these two properties can decouple in the...
  37. E

    Why Velocity Same at Min Separation? | Conservation of Momentum

    Homework Statement Why is the velocity the same at minimum separation? For example, two positively charged pucks are traveling towards each other. Find the minimum separation. They oppose each other so they should slow down and reach minimum separation when their velocities are 0. It does not...
  38. N

    Separation of subatomic particles within a capacitor

    I've recently taken to understanding capacitors and capacitance. If I understand them correctly they are what store electrical charge or electrical energy. I don't quite understand their purpose though, do they keep the breadboards from overloading with power but keeping little pockets of...
  39. S

    Gas separation in solar splitting of water

    I saw recently a new article about some kind of PEC cell immersed in water which could separate water into hydrogen and oxygen. (It was news because they found a way to protect the cell from immediate corrosion damage) It seemed that somehow the scientists had designed a cell that could put the...
  40. C

    Separation of Variables Spherical Coordinates

    Homework Statement So I'm doing a question from one of my past exams as attached, there are no copy right issues with this document that I know of and have asked my lecturer who wrote the exam and he said I am welcome to upload it. The question is 1)b)iv), my attempt is attached. I end up with...
  41. P

    Separation of variables technique

    If $$u=\frac{1}{2} E^2$$ and $$v=\frac{1}{2}B^2$$ and we have that $$\frac{\partial L}{\partial u} \frac{\partial L}{\partial v} = -1$$ The author says: to obtain explicit solution of the above, one must resort to techniques such as separation of variables in particular coordinate systems. For...
  42. J

    Chemical/Paint DIY ion exchange? Purifying glycerol, removing salt/lye/h2o

    My challenge is to provide a low-tech (DIY) way to purify the glycerol produced from soapmaking or biodiesel production. Simple distillation is out because the boiling point for glycerol is above its smoke point. Vacuum distillation and electrolysis do not count as low-tech. :) The input...
  43. G

    Diffraction gratings and angular separation

    Hello everyone, I came across the following when I was reviewing diffraction gratings: "The condition for maximum intensity is the same as that for a double slit. However, angular separation of the maxima is generally much greater because the slit spacing is so small for a diffraction grating."...
  44. M

    4 slit interference, unequal separation

    Hi all I can't find any guidance on this on the internet, so hopefully someone here can help! Basically, I want to work out the intensity profile produced by a multiple slit experiment, with 4 slits. No problem there, but I need the separation between slits to be unequal! I've found mention of...
  45. S

    Energy separation between two states?

    Homework Statement The wavelength of the radiation emitted when the outermost electron of Al (Aluminum) falls from the 4s state to the ground state is about 395 nm. Calculate the energy separation (in joules) between these two states in the Al atom. Draw an energy level diagram of the states...
  46. Eric Williams

    An Explosive separation of two carts already in motion

    Homework Statement An assembled system consists of cart A of inertia mA, cart B of inertia mB, and a spring of negligible inertia, clamped together so that the fully compressed spring is aligned between the front end of cart B and the back end of cart A. The internal energy of the system...
  47. H

    Exploring How Heating & Pressure Affect Distillation Separation

    I'm having trouble understanding why 1) Heating a solution more slowly would increase separation in a distillation and why 2) Lowering the pressure above the solution, i.e. with a vacuum, would decrease separation. Distillation depends on you collecting one component before the second...
  48. B

    Separation of Variables in 2 Dimensions: A Laplace Equation Primer

    So I'm currently taking electricity and magnetism and I'm expected to know how to perform a separation of variables on laplace equation in 2 dimensions.I have taken Zero differntial equations courses and I literally have no freaking idea what's going on. The book I use doesn't spend any time...
  49. S

    Separation of Variables to Calculate Potential Inside Box

    My friends and I are in our first senior-level physics course at the University of Alabama in Huntsville, Introductory E&M. At the moment, we're working on using separation of variables to calculate electric potentials inside different objects given certain boundary conditions. One, however, is...
  50. B

    Scalar propagator for lightlike separation

    Hello everybody. I have a free scalar in two dimensions. I know that its propagator will diverge for lightlike separations, that is t= ±x. I have to find the prefactor for this delta function, and I don't know how to do this. How do I see from, for example, \int \frac{dk}{\sqrt{k^2+m^2}} e^{i k...
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