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

    Maximizing Oil-in-Water Separation: Tips for Efficient Drying Methods

    Try not to fly too far over my head if you answer this. I'm just an amateur chemist who spent three years in the chemistry department until I hit a wall (Calculus!) and ended up with a writing degree. So be gentle please. I'm trying to dry oil (vegetable oil) in a process (rather than a...
  2. M

    Young's Double Slit Experiment - Slit Separation Calculation

    Homework Statement Calculate the slit separation (d) given that: Wavelength = 650 nm (Plugged in 6.5*10^-7 m) m = 1 (plugged in 1) Distance to screen (D) = 37.5 cm (plugged in 0.375m) Distance between centre to side order (y) = 0.7 cm (pluged in 0.007m) Homework Equations We were only given...
  3. A

    Russell's Paradox and the Axiom Schema of Separation

    As everybody I have read or heard on the matter claims, the Axiom Schema of Separation was concocted to resolve a paradox that results from the Axiom of Unrestricted Comprehension. The Axiom Schema of Unrestricted Comprehension as I understand it is stated as follows (forgive my lack of...
  4. C

    Electric / thermal mineral separation.

    Hello my name is Colin Wilson and I am the inventor of a new mineral separation process. http://www.coldgold.rotoquad.com I am looking for help and/or a partnership in this endeavor. As a group I can not think of a better place to start. To test this new method of mineral recovery 3...
  5. A

    Finding charge with mass, length and separation

    I don't even know where to start.. Two styrofoam balls with the same mass (m=9.0x10^-8 kg) and the same positive charge Q are suspended from the same point by insulating threads of length (L=0.98 m). The separation of the balls is (d=0.020 m). What is the charge Q??
  6. E

    How do I solve this PDE using separation of variables?

    Homework Statement Solve the boundary value problem for a string of unit length, subject to the given conditions. f(x)=0.05sin \pi x, g(x)=0, c=\frac{1}{\pi} Homework Equations Model: u(x,t)=X(x)T(t) Which yields two separated equations by the one dimensional wave equation. X''-kX=0 and...
  7. B

    Separation of Multiple Universes?

    Assuming that theories regarding the existence of multiple universes are true, what would separate said universes? If multiple universes exist, it can be assumed that there is some form of separation between said universes. This could be in the form of a barrier, or a kind of "space" between the...
  8. A

    On the Physical Separation of Time

    We are considering a stationary curved spacetime fabric. Temporal separation[Physical]is given by: {T}_{2}{-}{T}_{1}{=}{\int \sqrt {g}_{00}{dt} [Limits of integration extending from t1 to t2which are of course the coordinate times] The above integral is path dependent,in the general...
  9. L

    Separation of variables on upper half-plane issue

    Given the Cauchy problem \begin{cases} u_{xx}+u_{yy}=0, & 0<y<\infty, x\in\mathbb{R} \\ u(x,0)=0 & \mbox{on }\{ x_2=0\}\\ \frac{\partial u}{\partial y}=\frac{1}{n}\sin (n y) & \mbox{on }\{ x_2=0\}\\ \end{cases} I am given that, by using using separation of variables, the solution ought...
  10. A

    Laplace DE separation of variables

    Homework Statement I'm supposed to find a nontrivial solution to tx'' + (t-2)x' + x = 0, x(0) = 0. You don't really need to know that but just in case. I got to this point: (s+1)X'(s) + 4X(s) = 0 Now I need to separate variables to find a solution but I've been working on this for two...
  11. S

    Repulsive central force, finding the minimum separation distance

    Homework Statement A particle of mass m is subject to a repulsive central force Am/r^{3} (A is a constant). At a large distance from the center of force, the particle has speed v_{0} and its impact parameter is b. Use conservation of energy and angular momentum to show that the closest m comes...
  12. S

    Charge separation in solar cells

    If there is a charge separation on macroscale in a solar cells (electrons flow in one direction and holes in another) why there is no high voltage build up similar to capacitors or piezoelectrics where also charge separation occur? There exist some glasses which become conducting when heated...
  13. R

    Separation of variables IVP, book wrong?

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  14. O

    Collision of Two Protons: Separation at Momentary Stop

    Two protons that are very far apart are hurled straight at each other, each with an initial kinetic energy of 0.15 MeV, where 1 mega electron volt is equal to 1x10^6 (1.6x10^-19) joules. What is the separation of the protons from each other when they momentarily come to a stop? i got 4.58e-13...
  15. M

    Using Separation of Variables to find potential inside of a sphere

    Homework Statement A cubical box (sides of length a) consists of five metal plates, which are welded together and grounded (Fig 3.23). The top is made of a separate sheet of metal, insulated from the others, and held at a constant potential V0. Find the potential inside the box...
  16. M

    Finding V for a 2D box using separation of variables.

    Homework Statement We have a 2-dimensional box with only one side at a potential V0. The other 3 sides are grounded. The box is a square with top and bottom at y=a/2 and –a/2 and sides at x=±a/2. Find V(x,y) (it should contain cos and sinh). Homework Equations The Attempt at a...
  17. M

    [tex]\Delta [/tex]Uand W, increasing the separation of capacitor, with V=const.?

    I expected it to be quite simple as it was without the battery, in which case \DeltaU = W, but now I am confused. with the separation increased from x to x+\Deltax, It is obvious that \DeltaU changes with 0.5[1/x - 1/(x+\Deltax)] since C changes with 1/r. (Without the common coefficient...
  18. arivero

    Exploring the Separation of Riemann Zeta and Dirichlet Eta Functions

    Consider the separation of the Riemann Zeta function in two terms \begin{flalign*} \zeta(s) &= 1^{-s} + 2^{-s} + 3^{-s} + 4^{-s} + 5^{-s} + 6^{-s} + ... = & \\ &=(1^{-s} + 3^{-s} + 5^{-s} + 7^{-s} + 9^{-s}+ ... ) + ( 2^{-s} + 4^{-s} + 6^{-s} + 8^{-s} + ...)&=& \\ &= (1 - 2^{-s}) \zeta(s) +...
  19. M

    Calculating Spatial Separation Using Lorentz Transforms: Homework Solution

    Homework Statement Two events occur at the same place in a certain inertial frame and are separated by a time interval of 4 seconds. What is the spatial separation between these two events in an inertial frame in which the events are separated by a time interval of 6 seconds? Homework...
  20. E

    Variable Separation and Partial Fractions

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  21. C

    Potential energy separation curve

    Here's my understanding of the Force /Separation graph, I'm open to criticism/ridicule if I've got it wrong: If the two atoms are pushed together, then there is a repulsive force between them of a positive magnitude. If they are separated by a distance r, then the two forces...
  22. I

    Sp^2 hybrid orbital lobe separation

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  23. E

    Variable Separation: Solving x^2y'=1-x^2+y^2-x^2y^2

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  24. T

    Understanding Lens Separation for Creating an Image at Infinity

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  25. F

    Separation of variables technique - When is valid? (and other questions)

    Hi. This is my first post in PF. I'm an undergraduate student of Electronics Engineering with strong interest in math & physics (and weak understanding of them :P). One of the things I always hate is when in some book (or some lectures) ODEs or PDEs are solved after the magic words "[...] and...
  26. B

    Separation of variables to solve DE

    Homework Statement y' + (2/x)y = 3/x^2 Homework Equations separation of variables The Attempt at a Solution First I turned it into dy/dx + (2/x)y = 3/x^2 dx then multiplied both sides by dx dy + (2/x)y = 3/x^2 dx I then tried to divide both sides by 2/x and got...
  27. G

    Heat equation - separation of variables

    Homework Statement du/dt=d2u/dx2, u(0,t)=0, u(pi,t)=0 u(x,0) = sin^2(x) 0<x<pi Find the solution Also find the solution to the initial condition: du/dt u(x,0) = sin^2(x) 0<x<pi The Attempt at a Solution From separation of variables I obtain u(x,t) = B.e^(-L^2t).sin(Lx)...
  28. D

    Separation of variables for second order DE

    Hi. I believe I understand separation of variables for a first order DE. But can anyone tell me how to use it on a second order DE? In particular I have been looking at this example http://en.wikipedia.org/wiki/Integrating_factor#General_use" where it is claimed that one can use separation of...
  29. M

    Need help testing vector separation.

    I'm writing code to check if polygons intersect, but I've ran into a problem. I have two "vectors." Each has an origin and x and y components. They are facing towards each other. I need to write code that determines if there's a perpendicular axis that separates them. Here's a picture of what...
  30. S

    Reduce to ODE using separation of varialbles

    Reduce the equation (equation is attached) to a set of ODEs by the method of separation of variables. kindly help me with the solution, i m unable to solve.
  31. Loren Booda

    Greatest degree of blood separation in humankind

    It is said that all humankind is at most six social relationships removed from each other. How many blood relationships at most currently remove every human from each other?
  32. S

    Angular separation between two wavelengths

    1. using differentiation,find the angular separation in arc minutes in second order for two wavelengths 589.0 and 589.6 nanometers 2. d sin(\theta)=m (\lambda) 3. i try to use D=\delta\theta/\delta\lambda by differentating d sin(\theta)=m (\lambda) i got d/m sec(thetha).this...
  33. K

    Find equilibrium bond potential, given energy as a function of atomic separation

    Homework Statement Given that the total cohesive energy, U, in an ionic crystal as a function of nearest neighbor distance, R, between two ions +e and -e is given by: U(R) = \frac{A}{R^n} - \frac{\alpha e^2}{4 \pi \epsilon R} show that at equilibrium: U(R) = \frac{\alpha e^2}{4 \pi...
  34. C

    How Does a Magnetic Field Influence Electron Energy Levels?

    Homework Statement Considering only orbital angular momentum, estimate the energy level separation between electron states in a magnetic field of 1 Tesla applied along the z direction. Homework Equations I am confused by how to even start this question! Isn't orbital angular momentum...
  35. B

    Separation of two wavelengths in a diffraction grating.

    Homework Statement Light with two wavelengths (510.0 nm and 525.6 nm) is spread by a diffraction grating. On a screen 4 meters behind the grating we observe that the diffrence between the two second order maximum is 1 cm. What is the grating constant (d) ?Homework Equations I think i only need...
  36. I

    Calculating energy separation between two states

    Homework Statement If the energy separation of two states is known for some atom, how can the same energy separation be calculated for the same two states for an ionized atom? i.e. if we know that the difference between the 1s^2 and the 1s2s states in Helium is something like 25eV, how could...
  37. J

    Determine the separation between the plates

    Homework Statement As shown in the circuit, a potential difference of 625 V is applied across an air-filled parallel plate capacitor having capacitance c1 = 2.36X10^-11 F and plate area A = 4X10^-3 m^2. the dielectric constanf of air is 1. consider the switch in the circuit to be opened as...
  38. M

    Speed of Separation between 2 masses?

    Homework Statement Outside the International Space Station, a 60 kg astronaut holding a 4.0 kg object (both initially at rest) throws the object at 10 m/s relative to the space station. A 50 kg astronaut, initially at rest, catches the object. What is the speed of separation of the two...
  39. C

    Integration using separation of parts

    Homework Statement evaluate the integral cos^-1 2x dx? Homework Equations The Attempt at a Solution let u = arc cos du = -1 / (sqrt 1-x^2) dv = 2x v= x^2 arc cos * x^2 - the integral of -x^2 / (sqrt 1-x^2) then i don't know what to do
  40. N

    Separation of Schrodinger Equation

    Homework Statement Show that the time-dependent Schrodinger equation is separable when V depends on time only and is uniform in space (i.e., V = V (t)). Homework Equations The Attempt at a Solution In the attached document
  41. B

    Calculating Rate Of Separation Between Two Arcs

    Homework Statement Is there a formula for calculating the rate of separation (per degree) for two planes beginning at a common point, traveling at the same speed, performing turns with two different turn radiuses? Homework Equations See linked image for better understanding...
  42. A

    Charge separation of neutral objects by rubbing

    How does rubbing separate positive and negative charge on neutral objects?
  43. V

    Solving Laplace Eqn by Separation of vbls

    Okay, I'm stumped at what seems like a very simple mathematical step I start with Then, the next step is I see what changed, but I don't understand exactly what happened. Can someone please explain? Thanks in advance!
  44. S

    Separation of variables / integrating factor problem

    Homework Statement Find the general solution for this differential equation. dy −2x^2 + y^2 + x dx = x yHomework Equations The Attempt at a Solution dy/dx = (−2x^2 + y^2 + x) / (x y) let y^2 = v dy/dx = v + x dv/dx v + x (dv/dx) = (-2x^2 + v^2 x^2 + x ) / v x^2 => x (dv/dx)...
  45. M

    Separation of Variable - What's REALLY going on?

    So I've always done simple ODEs by the method of separation of variables. You know, dy/dx = A*y dy/y = A*dx IndefiniteIntegral[1/y dy] = IndefiniteIntegral[A dx] ln(y) = A*x + Constant y = Constant*e^(A*x) It's easy to remember and it usually works. A lot of the PDEs I know how to do...
  46. L

    Need help with this differential equation using separation of variables.

    Homework Statement The differential equation I have is dy/dx = (xy + 2y - x - 2)/(xy - 3y + x - 3). I need help getting started. Neither the top nor the bottom can be factored, so I don't know what to do next. Can anyone give me a push? All I know is that I need to use separation of variables.
  47. C

    Separation of variables wave equation

    1. Solve the wave equation u_(tt) = 4u_(xx) on the interval [0, π] subject to the conditions u(x, 0) = cos x, u_t(x, 0) = 1, u(0, t) = 0 = u(π, t). Homework Equations 3. Hello. This appears to be a common separation of variables question. Only problem is after using...
  48. C

    Order of Initial Conditions in PDE Solutions: How to Determine?

    When solving a pde using this method how do you know what ORDER to use the initial/boundary conditions given to you? E.g. if you are asked to solve the wave equation given u(x,0), u'(x,0), u(0,t), u(l,t) how do you know what order to use these in (particularly the first two)
  49. F

    Nailing down charge separation due to a battery

    Hi all, I'm trying to nail very precisely the effects of a battery in terms of charge separation. In particular: when and what points are excess charges seen in a typical circuit powered by a battery. A. Prior to wires being attached to the battery, you just have the battery itself. My...
  50. R

    Parllel Plate Capcitor separation distance and voltage

    Hello, I'm studying for an exam tomorrow and am facing a question I can't for the life of me fathom. " A PP air capacitor is made by using to plates 16 cm squared, spaced 4.7 mm apart, connected to a 12V battery" Find Capacitance, charge on each plate, electric field between plated...
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