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. F

    Solving Question 2: Separation of Variables

    Homework Statement Not sure if you guys can get this link http://www.maths.uwa.edu.au/devsite/Units/math3341-s1-2008-crawley/assignments-solutions/Sheet%204 should be able to. Question is question two.Homework Equations Not many besides the general separation of solutions sort of thing but I...
  2. B

    Differential Equation- Separation of Variables

    Homework Statement y'=xsec^2(x^2) 2. The attempt at a solution dy/dx=xsec^2(x^2) dy=xsec^2(x^2)dx \intdy=\intxsec^2(x^2)dx lny= (here i'll do a u substitution) ---- u=x^2 du=1/3x^3dx ... and here's my problem. It seems like that creates a very difficult u-sub to try and manage...
  3. J

    Generalizing separation technique

    \left[\begin{array}{c} y'_1(x) \\ \vdots \\ y'_n(x) \\ \end{array}\right] = \left[\begin{array}{ccc} f_{11}(y) & \cdots & f_{1n}(y) \\ \vdots & & \vdots \\ f_{n1}(y) & \cdots & f_{nn}(y) \\ \end{array}\right] \left[\begin{array}{c} g_1(x) \\ \vdots \\ g_n(x) \\ \end{array}\right] If n=1, then...
  4. M

    Max Initial Separation for Meeting of Two Moving Bodies

    Homework Statement Two bodies move in a straight line towards each other at initial velocities v1 and v2 and with constant retardation a1 and a2 respectively at the initial instant. What is the max initial separation between the bodies for which they will meet during the motion? (sqr ->...
  5. C

    Separation Into Differential Equations

    I would use the entire template except this question is very simple and does not require all of it. Homework Statement How do I separate \frac{X''(x)}{X(x)}+\frac{Y''(y)}{Y(y)}=\sigma into ordinary differential equations when \sigma is a constant. Thanks for your help!
  6. T

    Hypothesis for the separation of variables method

    Hello ! I'm having a hard time finding the exact hypotheses which would allow me to use the separation of variables method for partial differential equations. I want a clear statement telling me 'when you have that very kind of partial differential equation (with precise boundary and...
  7. N

    Fourier seroes and separation of variables

    Homework Statement Sorry for the mis-spelled title - it's "series". Please take a look at http://www-solar.mcs.st-and.ac.uk/~alan/MT2003/PDE/node21.html In step 2.60, when he wants to find the coefficient B_n, the argument in the sine-function does not contain a "2". In my book, the...
  8. N

    Separation of variables and the separation constant

    Homework Statement Please take a look at: http://www-solar.mcs.st-and.ac.uk/~alan/MT2003/PDE/node21.html Look at step 2.53. Can you explain to me how c^2*T'/T = k becomes T' = k*T*c^2? The Attempt at a Solution I don't get it. What am I missing here?
  9. L

    Escaping to Infinity: Solving a Separable Differential Equation

    Homework Statement Using separation of variables determine if the solution escapes to infinity in finite time or infinite time? y'(t)=1+\frac{y(t)}{2} y(0)=.5 Homework Equations Knowing how to do separation of variables.The Attempt at a Solution Here is my attempt, but I get stuck...
  10. G

    MathCAD - separation of real and imaginary parts of a complex variable

    Hi guys, just wondering whether you could help. I've got a complex number in terms of a lot of variables, and need to separate it into its real and imaginary parts. How do I do that? I spent past hour trying to look for tutorials, unfortunately none tells you how to do it...
  11. F

    Space Shuttle SRB Cutoff and separation

    When a space shuttle launches, how is simultaneous SRB cutoff assured so as not to create an asymmetrical thrust situation? (assuming that SRB cutoff occurs prior to separation). Thanks, FRQ
  12. M

    Radio Wave Separation of H2O from Salt Water: Q&A

    Not sure if I'm in the right forum, but does anyone know anything about the mechanism behind using radio waves to disassociate hydrogen and oxygen atoms from salt water?
  13. H

    Capacitance vs. Distance of separation

    [SOLVED] Capacitance vs. Distance of separation Homework Statement Hi, I am suppose to make a capacitance vs (1/d) graph. I understand that the relationship between the capacitance and distance between the plates is inversely proportional and that it does not produce a straight line. My...
  14. Saladsamurai

    Finding Implicit and Explicit Solutions for Initial-Value Problems

    Homework Statement Find an implicit and explicit solution for the given initial-value problem \frac{dx}{dt}=4(x^2+1) for x(\frac{\pi}{4})=1 \frac{dx}{dt}=4(x^2+1) \Rightarrow \frac{dx}{x^2+1}=4dt \Rightarrow \tan^{-1}x+C=4t Now I am a little stuck. Usually I just plug in my...
  15. L

    Notation for separation of variables

    My book has a problem that requires you to separate variables (one side has all the y terms and one side has all of the x terms): \sin{xy'}=\cosx Equation after separation of variables: dy=\cot{x}dx My question is, how do you know that the y' is contained within the sine function or...
  16. L

    Understanding Separation of Variables in Derivatives and Integrals

    I do not understand the process of separating variables such as in derivatives. I thought that dy/dx is just the rate of change of y with respect to the independent variable x. Why can you physically move dx (like multiply it on both sides)?? What would "dy" be reffered to as then? Simply the...
  17. F

    Do equations in nature always have separate time and space derivatives?

    In pde, it seems to me all kinds of equations about nature phenomena have the property that time and space derivatives are separate. For example, u_t = u_xx, heat equation. So I wonder, is that always the case in nature? I mean, do you guys ever see equation describing real nature mechanism...
  18. S

    Understanding Entropy: Diffusion, Evaporation, Mixing, Melting, Separation

    entropy increases? entropy decreases ? no change in entropy? diffusion, evaporating, mixing, melting, separation i think diffusion - increase evaporation - increase mixing - increase melting - increase but what about separation :S? and if anyone thinks any others are...
  19. Q

    Laplace equation separation of variables

    u(r, θ) satisfies Laplace's equation inside a 90º sector of a circular annulus with a < r < b ; 0 < θ < π/2 . Use separation of variables to find the solution that satisfies the boundary conditions u(r, 0) = 0 u(r, π/2) = f(r) ; a < r < b u(a, θ) = 0 u(b, θ) = 0 ; 0 < θ < π/2 Consider all...
  20. 2

    Electron and proton separation in a hydrogen atom

    1) Hydrogen’s electron and proton are separated by 5.3x10-13 meters. What is the electrical force between them? 2) A charge moved .02 meters in an electric field of force 215 N/C. If the electric potential decreased by 6.9x10-19, what is the charge of the particle? 3) If a capacitor...
  21. H

    Mean Orbital Separation Question

    So it was basic to figure out the masses and such, but I'm not exactly sure what the "orbital separation" really is? Can someone enlighten me? Here is the question for reference: A moon with a mass one quarter that of its parent planet orbits that planet with a period of 12 days. The mass of...
  22. S

    How Do You Calculate Roller Separation for Elastic Recovery in Rolling Mills?

    No idea where to start with this one, any help is much appreciated... "A metal plate needs to be reduced to a thickness of 4 cm by involving a rolling mill. After rolling, the elastic properties of the material cause the plate to regain some thickness. Calculate the needed separation between...
  23. A

    Find separation between these two particles - kinematics

    Homework Statement Two particles A and B are projected from the same point O with angle speed 30degree from the horizontal. If A has the speed of projection equal to (7)^0.5m/s and B has twice the projection speed,find the separation between them,when their velocities are mutually perpendicular...
  24. H

    Navier Stokes, separation steady/non-steady

    Hello, I want, for obscur reasons which would lead us too far to explain, to split my flow into two component, one steady and another one non-steadyv = v_0 + v' I'm looking for a simple equation governing the evolution of this non steady components. The complete momentum equation gives...
  25. K

    Paritial Differential Equation separation of variables

    Homework Statement The temp. as a function of time of a metal rod obeys the following diff. eq. \alpha^2 \frac{\partial^2u(x,t)}{\partial x^2} = \frac{\partial u(x,t)}{\partial t} Use separation of variables to find u(x,t) in a rod of length 1 subject to the conditions u(0,t) = 0 ...
  26. Ivan Seeking

    Unlock Pet Separation Anxiety with "Puppy Prozac"

    http://www.abcnews.go.com/GMA/story?id=3063558&page=1 http://snltranscripts.jt.org/76/76gpuppyuppers.phtml Saturday Night Live Transcripts Season 2: Episode 7 76g: Dick Cavett / Ry Cooder Puppy Uppers/Doggie Downers Joy...Gilda Radner Jill...Laraine Newman
  27. R

    Separation of Variables / Boundary Conditions

    Homework Statement The edges of a square sheet of thermally conducting material are at x=0, x=L, y= -L/2 and y=L/2 The temperature of these edges are controlled to be: T = T0 at x = 0 and x = L T = T0 + T1sin(pi*x/L) at y = -L/2 and y = L/2 where T0 and T1 are constants...
  28. C

    Separation of variables and generalised fourier series

    Homework Statement if \nabla^2u = 0 in 0 \leq x \leq \pi, 0\leq y \leq \pi, boundary conditions u(0,y)=0, u(\pi,y)=cos^2y, u_y(x,0) = u_y(x,\pi)=0 Homework Equations I am required to show that u(x,y) = \frac{x}{2\pi} + \frac{cos2ysinh2x}{2sinh2\pi} The Attempt at a...
  29. R

    Separate Water from Carbon Tetrachloride by Fractional Distillation

    Can I separate water from Carbon tetrachloride by the method of fractional distillation? (I agree separating funnel is a better method)
  30. P

    Solving Conventional PDEs: Separation of Variables and Eigen Theory

    For conventional PDEs like diffusion, waves, it seems the standard way to solving them is in two steps. 1. Use separation of variables method to make them into ODEs 2. Use eigenvalues and eigenfunctions theory on ODEs to construct the final solution consisting of an infinite number of...
  31. J

    Light Speed Separation: How Long?

    If two objects move away from each other in opposite colinear directions at the speed of light. How long will it take for the light from one of the objects to reach the other? I think the answer is never, but not sure.
  32. D

    Use separation of variables to find particular solutions

    "Use separation of variables to find particular solutions of u_t-u_{xx}-2u_x=0, 1<x<2, 0<t, u(1,t)=u(2,t)=0 hint: change coordinates" I can't find the solution. The equation seems already separated, so all I need to do is to find a change of variables, I think. But I can't find one that...
  33. K

    Can the Separation of Variables Technique Solve This Integral Equation?

    Let be the integral equation: g(s)g(p)g(u)= \int_{0}^{\infty}dx\int_{0}^{\infty}dy\int_{0}^{\infty}dzK(sx)K(py)K(uz)f(x,y,z) then my question is if we could "seek" for a solution in the form: f(x,y,z)=A(x)A(y)A(z) where the function A satsify (for x y and z) the integral...
  34. P

    Can Separation of Variables Solve My Math Problems?

    http://album6.snapandshare.com/3936/45466/844588.jpg
  35. E

    Differential equations separation of variables

    xdv/dx=(1-4v^2)/3v I used separation of variables to get x/dx=(1-4v^2)/3v dv I'm not sure if that's even right. But if it is right, how do I integrate that?
  36. M

    Process design of vapor-liquid separation drums

    In Metric units: A vapor-liquid separator drum is a vertical vessel into which a liquid and vapor mixture (or a flashing liquid) is fed and wherein the liquid is separated by gravity, falls to the bottom of the vessel, and is withdrawn. The vapor travels upward at a design velocity which...
  37. V

    Boats A & B: Speed & Separation

    Two boats leave the shore at the same time and travel in the directions shown. If v_A\,=\,20\,\frac{ft}{s} and v_B\,=\,15\,\frac{ft}{s}, determine the speed of boat A with respect to boat B. How long after leaving the shore will the boats be 800 ft apart...
  38. K

    Separation of Isotopes by Laser Excitation

    Is this for real? http://www.smh.com.au/news/national/laser-enrichment-could-cut-cost-of-nuclear-power/2006/05/26/1148524888448.html
  39. D

    Can You Connect Mel Gibson and Pierce Brosnan in Just One Movie?

    I'm sure most people are familiar with the 6 degrees of Kevin bacon game. Here's something for folks to have fun with. The rules are: 1) You must name 2 relatively well known celebreties who have both appeared in at least one theatrical movie (i.e., not made for TV nor TV series). 2) You...
  40. O

    Help solving ODE using separation of variables

    Hello, Could someone please help me to simplify my solution to my ODE? Here is the solution I get when I check it using Maple 10, http://img524.imageshack.us/img524/415/ode2hx.jpg Here are my steps: \left( {1 + x^3 } \right)\frac{{dy}}{{dx}} - 3x^2 y = 0 \left( {1 + x^3...
  41. F

    How long does it take for air molecules to collide at STP?

    My text doesn't seem to talk about average separation of molecules, so I can only get so far with this problem. Help would be appreciated. The problem reads: From the average separation between air molecules at STP, and their mean speed, estimate how long it would take one molecule to move...
  42. S

    News Surprising Change in Government: Separation of Church & State

    I never thought I would see this day. Oh well. http://www.washingtonpost.com/wp-dyn/content/article/2006/03/21/AR2006032101723.html" Granted that previous administrations gave taxpayer money to organizations allied with them, atleast on social issues, it promoted the separation of the church...
  43. A

    Measuring Perception of Line Separation at Varying Distances and Light Levels

    ive done a test were, i get someone to try and distinguish to lines that are 0.25mm apart from varying distances. then I am going to do some kind of calculation to tell me somthing (hopefully) and i have done this experiement in different light levels, controlling the lux. and i have...
  44. V

    Diffusion equation & separation of variables

    hi i have been trying to solve the diffusion equation using separation of variables. i know the answer should turn out something like the normal probability density function but its just turns into a mess when i try it. i am given the following information: \frac{\partial p}{\partial...
  45. DaveC426913

    Exploring Separation of the Cord and Fetus in Animals

    1] Is the placenta and cord an extension of the fetus or of the host? We were talking about this, and have tentatively concluded that the DNA of placenta and cord would reflect the fetus rather than the host. This came up in a discussion about 'two vessel cord'. I was wondering if that would...
  46. M

    Separation of variables problem

    Hey, I need some guidance in this problem. Consider a rocket taking off vertically from rest in a gravitational field g, the equation of motion (which I had to derive in the previous part of this problem) is: m \dot{v} = -\dot{m}v_{ex} - mg where m is the mass of the rocket...
  47. S

    Solving a Separation of Variables Problem: $u(x,t)$

    Slve by separation of variables \frac{\partial u}{\partial t} - k \frac{\partial^2 u}{\partial x^2} = 0 for 0 <x < pi, t > 0 u(0,t) = u(\pi,t) = 0 u(x,0)= \Sin^2 x let u (x,t) = X(x) T(t) \frac{X''}{X} = \frac{T'}{T} = -\lambda = \mu^2 also lambda must be positive...
  48. S

    Solving Laplacian PDE with Separation of Variables

    we are given the laplacian: (d^2)u/(dx^2) + (d^2)u/(dy^2) = 0 where the derivatives are partial. we have the B.C's u=0 for (-1<y<1) on x=0 u=0 on the lines y=plus or minus 1 for x>0 u tends to zero as x tends to infinity. Using separation of variable I get the general solution u =...
  49. E

    PDE: separation of variables problem

    I am to reduce the following PDE to 2 ODEs and find only the particular solutions: u_tt - u_xx - u = 0; u_t(x,0) = 0; u(0,t) = u(1,t) = 0 I guess u = X(x)T(t), and plug u_tt, u_xx into PDE and divide by u to get: T''/T = X''/X + 1 = K I solve X'' + (1-K)X = 0 first. From...
  50. S

    Minimimum separation of to resolve 2 stars

    A telescope has an objective mirror of 6m. An astronomer uses it to determine if a certain object is a binary star, i.e. two stars in orbit around a common point. If the object is 25 light years away (a light year is the distance light travels in one year) what is the minimum separation of...
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