What is Mixing: Definition and 296 Discussions

In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, industrial mixing, etc.
The concept appears in ergodic theory—the study of stochastic processes and measure-preserving dynamical systems. Several different definitions for mixing exist, including strong mixing, weak mixing and topological mixing, with the last not requiring a measure to be defined. Some of the different definitions of mixing can be arranged in a hierarchical order; thus, strong mixing implies weak mixing. Furthermore, weak mixing (and thus also strong mixing) implies ergodicity: that is, every system that is weakly mixing is also ergodic (and so one says that mixing is a "stronger" notion than ergodicity).

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  1. chocopanda

    Mixing two gases in an isolated system and calculating final p and T

    Hey everyone, I have an attempt at fully solving this problem (my final pressure is ##p_f = 5373,64 hPa##, final temp. is ##T_f = 303,15K = 30C##), but this exercise confuses me very much. First, I have not used the masses in my calculations and I'm pretty sure my prof. accidentally copypasted...
  2. chocopanda

    Mixing two ideal gases with different V, T at constant pressure

    To be honest, thermodynamics is really not my strong suit and I get confused when and how to apply formulas. My thought process is as follows: - there are two ideal gases (ideal gas law applies) - the pressure remains constant (isobaric process), so p1= p2 = p - I imagine there being two...
  3. jaumzaum

    I Mixing two different gases

    Consider that I have 2 adiabatic containers, one with a monoatomic gas at pressure P1, volume V1 and temperature T1 and another with pressure P2, volume V2, temperature T2. If I open a valvule and mix the two gases, how do I calculate the equilibrium pressure and temperature? I know the final...
  4. James1238765

    I Evaluating the quark neutrino mixing matrix

    The mixing of the 3 generations of fermions are tabulated into the CKM matrix for quarks: $$ \begin{bmatrix} c_{12}c_{13} & s_{12}c_{13} & s_{13}e^{-i\sigma_{13}} \\ -s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\sigma_{12}} & c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\sigma_{13}} & s_{23}c_{13} \\...
  5. S

    B Graphical representation of the weak mixing angle

    The graphical pattern of particles in the weak hypercharge and weak isospin plane, visible in this wiki page, shows the mixing angle between the Yw and Q axes. Actually , from the weak hypercharge (-2) of a right-handed electron and its electric charge (-1), one obtains an angle Pi/3, not the...
  6. T

    I Temperature change due to mixing liquids, heating and heat losses

    Hello, I am stuck how to proceed with the equations below. The problem: A tank containing ##m_0## mass, with a temperature of ##T_0##, is to be filled with a total mass of ##m_1##, with the constant mass flow rate ##G## and temperature ##T_1## during ##t_p## seconds. ##T_0>T_1##. Other than the...
  7. J

    I Exploring Entanglement Through Laser Light Mixing Experiments

    https://quantum.phys.lsu.edu/old-website/seminars/abstracts/Kaushik10.pdf I have discovered an experiment in the link above where you get NOON entangled states by mixing classical laser light with quantum light from SPDC. But I cannot understand the mathematics behind it. Can you explain it to...
  8. Pythagorean

    Mixing between Neolithic Farmers and Mesolithic Hunter-Gatherers

    I watching this YouTube video about Göbekli Tepe which suggests that hunter-gatherers may have been more capable of creating civilizations than we presumed and it got me wondering what hunter-gatherer / farmer relations were like. Apparently they were good...
  9. gggnano

    Can I make a rocket by mixing aluminum + iodine (+ water catalyst)?

    Basically it's a well known reaction, many kids on youtube make it for the views: I am thinking, since AlI3 sublimes can it be put in say tungsten bottle (is this even a thing??) and then used as a rocket the same way Na+H2O or HCL+Al rockets are used - the gas escapes? This phase...
  10. R

    Looking for basic theory on mixing of gases

    Hi, In my situation, I am dealing with two ideal gases traveling down a pipe at the same bulk velocities. I am only considering a 1-D treatment at the moment and I would like to find out at which point the two gases should be considered a well mixed, homogeneous mixture. Would anyone know...
  11. gggnano

    Is it possible to have an "Eternal reaction" by mixing the products?

    So this is a very simple concept but I am not explaining it well: Let's say you have 4 reactants in 2 different reactions (apologies: the symbols I am using do NOT exist, other than the "C" symbol, I just can't find real elements so that I am using just alphabet symbols as an allegory to show...
  12. J

    My first time mixing Kroll's reagent

    I am going to etch some titanium and need to mix up a 100ml batch of Kroll's reagent ( 92ml distilled water, 6ml nitric acid and 2ml hydrofluoric acid. Do I add the nitric acid to the water first and then add the hydrofluoric or vice-versa?
  13. maistral

    Departure enthelpy for mixture EOS = enthelpy of mixing?

    Hi. I am well aware that if say, there are two components A and B, the ideal mixing enthalpy between those two components are: (1) hmix = zA hA + zB hB. If I want to get the real behavior of a pure component, I am also aware that; say for example, liquid enthalpy: (2) hL = Href + ∫CpigdT (from...
  14. A

    Solving a mixing problem with a differential equation

    Hello! First I tried modelling it like most mixing problems. $$ \frac{dA}{dt} = rate coming in - rate coming out $$ where dA is the volume and dt is the time rate coming in/out can be describe as; contrencation * flow rate. Now if we plug that all on $$ \frac{dA}{dt} = 35 * 0 -...
  15. TonyCross

    Mixing Newton's law with Adiabatic Process

    I have attached an image showing the perimeters of the problem. I have included what I think is the solution, could someone please take a look and tell me if I am on the correct path, in the solution I am taking Joules as a common term to attempt to solve the question. The gas I have used is N...
  16. Will26040

    How do I get the Convection Coefficient for steam in a jacketed vessel?

    Please could someone point me in the direction of an equation/ book I can use to obtain the convection coefficient for steam in a heating jacket. Steam is at 1 bar pressure. I think I need to use a dimensionless number. Thanks
  17. Z

    Why does mixing blue and yellow create green?

    I am curious about how mixing paints works. If I mix an ideal paint A and an ideal paint B what is the product mixture C? Is it (Option 1) a mixture absorbs all the range A absorbs and absorbs all the range B absorbs OR is it (Option 2) a mixture with original A and B pigments therefore some...
  18. M

    I What is the purpose of the Prandtl Mixing Length for turbulent flow?

    Hi, I was recently learning about turbulent boundary layers and came across the 'Prandtl mixing length'. I am struggling to understand what the concept is and what its purpose is. I would appreciate any help or guidance of where I can look to gain a better understanding. The information I...
  19. maistral

    Helmholtz free energy for mixing?

    Hi, I have been reading a few literature regarding excess Helmholtz energy and I encountered this definition from the paper of Wong and Sandler (apparently, from the mixing rule used in a EOS): In particular, the ones in the red boxes. How did these equations come into being? I tried to look...
  20. Philip Koeck

    I Experimental test of the Mixing Paradox

    Can anybody point to an experiment that shows that the total entropy increases if two different gas mix at constant pressure and temperature, whereas if two volumes of identical gases mix the total entropy doesn't change?
  21. R

    Gibbs "Paradox" and the Entropy of mixing

    (not a paradox nowadays, but it was an issue for years) https://en.m.wikipedia.org/wiki/Gibbs_paradox It's not a question about a formula. I don't understand the motivation in physics to claim Gibbs mixing "paradox", the discontinuity point. What bothers the physicist to ask for a continuous...
  22. sneakycooky

    Chemistry What precipitates form by mixing 2 saturated solutions?

    At first I thought it was C. A few sources agree with me. The book says D is correct. Here was my reasoning for C: With both salts having a formula of MX3, their [OH-]'s can be compared according to their Ksp values. Tl(OH)3 has a smaller Ksp, so it has a smaller [OH-] at saturation than...
  23. kunalvanjare

    Controlling two valves with different flow-rates to achieve mixing

    Guys, I hope you guys are keeping well. I have been working on developing a Compact Dispensing Station for my CNC Machine & Parts Washer where coolant is mixed with water in different concentrations & volumes as per the requirement which will vary on a day-to-day basis (not the concentration...
  24. E

    Mixing of two polymer particles heated above Tg

    I am wondering if two polymer particles, of same kind, heated above Tg can be mixed, over time, if they are squeezed together. By mixing I mean that the surfaces of the two particles will mix into one after they are squeezed together. For simplicity let's assume that the polymer particles are...
  25. caffeinemachine

    MHB Regarding mixing time of a Markov chain

    Let $X=X_0, X_1, X_2, \ldots$ be a Markov chain on a finite state space $S$, and let $P$ denote the transition matrix. Assume that there is an $\varepsilon>0$ such that whenever $\mu_0$ and $\nu_o$ are point distributions on $S$ (in other words, $\mu_0$ and $\nu_0$ are Direac masses) we have...
  26. Muskyboi

    [Differential equations] Mixing problem.

    v(t)=600+(9-6)t =600+3t 1500=600+3t therefore t=300 hrs when tank is full Cin=1/5(1 + cost) ds/dt=Rate in - rate out = CinRin - Cout*S(t)/V(t) =1/5(1 + cost)*9 - 6*S(t)/(600+3t) S(0)=5 ib Solving the first order linear ODE we get: https://www.desmos.com/calculator/l7iixzgyll therefore...
  27. K

    Gibbs' theorem and partial molar volume

    In the chemical engineering text of Smith, VanNess, and Abbott, there is a section on partial molar volume. It states that Gibbs theorem applies to any partial molar property with the exception of volume. Why is volume different? In other words, when evaluating the partial molar volume of a...
  28. kunalvanjare

    How can I achieve homogeneous in-line mixing of a Coolant with water?

    Hello guys, This is for a new product I am designing, which involves topping-up or refilling the liquid into a CNC Machine or Part Washer. I have to mix about a Litre of the chemical (alkaline.. pH in the range of 8-12) with about 50 Litres of water. The water will be fed under gravity through...
  29. entropy1

    B Mixing two discrete audio signals

    Suppose I have two audiofiles in 16 bit PCM, both recorded on a level that, except for the noise and distortion, is maximally recorded, or that the maximum recording level results in the maximum PCM level. So, the signal is recorded on the maximum level such that there is no clipping. If we...
  30. L

    Mixing Substances: Engineering Solutions for Dilution Challenges by Lee

    Hello, my name is Lee. I am a design and electrical engineer and I am involved in a project where I have developed a piece of equipment that mixes substances, primarily two liquids. My equipment is a rotational shaking machine. The liquids are put into a vessel which is then shook over a number...
  31. S

    Mixing Fluids in Flow: How to Achieve a Fixed Concentration | Sanatan

    Hello, I am trying to mix two fluids which are in flow. To be exact, I am trying to mix a concentrated mineral solution to an outlet of my RO filter. Is there a method to mix the two fluids to get a fixed concentration of the mixed solution ? Regards, Sanatan
  32. DaveC426913

    B Can He be used as a safer alternative to H in blimps?

    Saw the saddest thing in the world today: party balloons peeking out over the top of a dumpster. I started thinking about the buoyancy of H versus its flammability. H is 6-7 times more buoyant than He. It would be more more economical to use H if we could eliminate the explody bit. If you can...
  33. T

    Change in entropy when mixing cold and hot water

    I tried following: $$ dS_{\text{total}} = |\frac{dQ}{T_c}| |\frac{dQ}{T_H}| $$ where ## T_h ## is temperature of hot water and ## T_c ## is temperature of cold water. Coefficient for water wasn't provided in the assignment so i used following value c = 4190 J/kgK. $$ dS_{\text{total}} =...
  34. A

    Simplified SUSY models with different mixing cases

    Hi Probably a bit technical, but here it is. I am trying to construct some simplfied SUSY models (that is, you only tune the masses of the core process, while all the rest are decoupled), and I would like to play with different mixing scenarios for the neutralino and charginos, so to get a...
  35. i_hate_math

    Quantum Gases - Mixing of 3He and 4He

    Homework Statement Consider a solution in which 99% of the atoms are 4He and 1% are 3He. Assuming that the 3He atoms behave as an ideal gas of spin-1/2 particles determine the Fermi energy of the 3He atoms. You may assume that one mole of 4He occupies a volume of 28 cm3.Homework Equations EF =...
  36. C

    How does the phase noise of the LO effect IF accuracy?

    Hi, I have a roughly 1.1 GHz signal to be downconverted to 100 MHz by mixing it with a 1 GHz local oscillator. I am not sure how to choose the performance of the LO. In particular: let's assume the LO has a jitter of 100 fs rms. At 1 GHz this corresponds to a frequency error of 100 kHz. Does...
  37. K

    B Additive colour theory and "traditional" colour mixing

    Hi folks. I am trying to reconcile the additive colour theory of light with more traditional grade school colour mixing. For example, we all know that blue paint plus yellow paint makes green paint. How do we explain this from the perspective of light? So the yellow paint appears yellow because...
  38. EastWindBreaks

    Do we assume the mixing chamber has an outlet?

    Homework Statement Hot and cold streams of a fluid are mixed in a rigid mixing chamber. The hot fluid flows into the chamber at a mass flow rate of 5 kg/s with an energy in the amount of 150 kJ/kg. The cold fluid flows into the chamber with a mass flow rate of 15 kg/s and carries energy in the...
  39. G

    Chemistry Convert a number concentration of 15 X 10^12 molecule/cm3 into volume mixing ratio

    Homework Statement Convert a number concentration of 15 X 10^12 molecule/cm3 into volume mixing ratio at: a) 1 atm pressure, and 20 C temperature. b) 500 mbar pressure, and 253 K temperature. Using the Ideal Gas Law, calculate: a) Loshmidt’s number (# of molecules/cm3 of air, at standard...
  40. runningman19

    Measuring Torque on the Impeller Shaft of a Stirred Tank

    Hi Everyone, I am working on a project which requires me to determine the torque on the impeller shaft of stirred tank. Currently as I see it, there are 2 viable options: To measure the torque in the shaft using a torque transducer such as this one. This is by far the most accurate means of...
  41. C

    Practical Fluid Mechanics: inversions & mixing

    I'm trying to think through a situation, and develop some confidence I've got it right. The situation is a apartment building, about 60'/20m high, with a courtyard in the middle about 60'/20m square. In the middle of the courtyard, is an low exhaust stack, about 8' high and around 8' square...
  42. stockzahn

    I Mixing of regatta competitors

    Dear all, we are organizing a regatta, there are 12 competing crews and we have six boats. Therefore the regatta is organized in so-called fleets, each consisting of two races at which six crews (using the six available boats) are participating. We assume to be able to race 10 to 15 fleets...
  43. HumanistEngineer

    A 1D Convection Diffusion Equation - Inlet Mixing Effect

    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...
  44. L

    Solving Entropy of Mixing Problem in Physics

    Hi again Physics Forums! Last time I was here, I was an undergrad student. Now I almost finished a PhD in quantum information and became a high school teacher. I've never properly learned thermodynamics. I'm now trying to get it on the same level, that I understand the other topics in classical...
  45. M

    MHB Mixing with Common Drain: Mass of Salt in Two Tanks #46 Nagle

    Mixing with a Common Drain. Two tanks, each holding 1 L of liquid, are connected by a pipe through which liquid flows from tank A into tank B at a rate of 3-a L/min (0<a<3). The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 3 L/min. Solution flows out of...
  46. Jezza

    I Quark mixing and energy conservation

    We've recently been looking at the hadronic decays of the W boson. In this one example, we looked at possible decays for the W boson being produced near its resonance peak, meaning the centre of mass energy is sufficient to produce u,d,c,s & b quarks. However, because we're below the mass of...
  47. V

    Mixing CP asymmetry calculation

    Homework Statement Consider decay ##\bar{B^0_s}\rightarrow D^+_s \pi^-## and calculate its mixing-induces CP asymmetry. Homework Equations $$\xi_f^{s}=e^{i\theta_{M_{12}}} \frac{A(\bar{B^0_q}\rightarrow f)}{A(B^0_q \rightarrow f)}=\pm e^{-i\phi_s}\frac{...
  48. Irl495

    Rotating magnetic field effect on aqueous mixing (opinions?)

    This is question that can't really get a precise answer without significant modeling or experimentation, but I'm wondering what folks' intuition might be on an answer to the following setup + question: Suppose there is a steel tank made of steel pipe with walls about 0.25 cm thick, internal...
  49. M

    Rushton Turbine Torque Calculation - D, H, Viscosity, RPM

    Hi; In one of my projects I need a Rushton impeller to be used for mixing applications. However, these kinds of impellers are quite expensive(400$ for a 2inch impeller) if bought from laboratories equipment manufacturers. The price tag would be fine with me if only one blade was needed, but this...
  50. C

    Measurable consequences of entropy of mixing

    Most textbooks include an example of entropy of mixing that involves removing a partition between two (in principle) distinguishable gases, and compare this to the case where the two gases are indistinguishable. What I’ve not yet been able to figure out is what the consequences of this...