# 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. ### 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. ### 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. ### 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...

15. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### [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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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...

48. ### 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. ### 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. ### 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...