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(#54) The Complex Physics of Industrial Mixing · Mechanical Engineering Made Simple

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  Welcome back, design junkies, to Mechanical Engineering Made
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  simple. Today we're doing a deep dive
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  into the literal and often unseen physics that govern how
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  almost everything is made. If you've ever wondered how a
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  huge batch of, say, pharmaceutical powder or a VAT
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  of polymer can be identical every single time, well, that's
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  the core challenge of mixing engineering.
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  It really is. We've pulled our material today
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  from some advanced handbooks on the topic and we're going to get
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  into blending, sampling, heat transfer, and even chemical
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  reactions. And the big picture here is that
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  mixing sounds simple, but it's not.
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  Not at all achieving true molecular level homogeneity.
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  That's where the physics gets incredibly complex.
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  The real headache for engineers is making sure that what worked
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  in a small lab beaker still works in a massive silo every
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  single time. OK, so let's unpack that,
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  starting with what seems simplest, mixing dry powders.
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  You've got these theoretical states of what a mixture can be,
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  and honestly, a couple of them are pretty counterintuitive.
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  Right, the first one is what is purely theoretical.
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  It's called the perfect mixture. Like a crystal lattice.
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  Exactly. Imagine particles alternating
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  perfectly, one of A, one of B, and so on.
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  Every single sample you could possibly take would be
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  identical, but you know unless you're placing each particle by
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  hand, you're never going to get. There.
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  So the best we can actually hope for is what's called a random
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  mixture. That's the practical goal for
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  most free flowing powders. It's purely statistical.
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  The particle here doesn't care if its neighbor is the same or
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  different. You end up using a binomial
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  distribution to describe the quality.
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  But then there's this third state, the ordered mixture,
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  which can actually be better than random.
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  How does that work? If random is the best
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  statistical average, how can non random be an improvement?
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  Because the physics changes, this happens in cohesive systems
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  where surface forces take over. Think of very fine small guest
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  particles, literally coding larger host particles.
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  Oh, so they're stuck together? Precisely.
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  The unit you're actually mixing is no longer particle A and
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  particle B. It's this new composite, this
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  coded host particle. And since that unit is uniform,
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  you're just mixing a collection of identical things.
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  So your samples become incredibly consistent.
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  They can be even more homogeneous than a perfect
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  random mix of the original components would allow.
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  That sounds amazing. So why isn't every fine chemical
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  blend made this way? What's the catch?
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  The catch is that it relies on those surface forces being
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  stable. It works great on a small scale,
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  but when you scale up to industrial equipment, the huge
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  shear forces just RIP those bonds apart and the whole thing
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  can collapse back into a segregated mess.
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  Segregation. OK, So even if we get a great
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  blend, the next hurdle is just figuring out what we have.
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  This is the sampling trap, right?
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  It's the Achilles heel of solids blending.
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  You can't see inside the mixer and powders just love to demix
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  on their own, so you have to rely on sampling and almost
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  every tool you use introduces some kind of bias.
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  Let's talk about the thief samplers.
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  I was shocked at how flawed the standard site sampling thief is.
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  It's a huge problem. You stick it in a slot, opens
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  and powder flows in. But first, just putting it in
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  disturbs the bed and 2nd, it relies on passive flow.
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  Meaning the easy flowing stuff gets over represented.
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  Exactly the smallest, most free flowing particles just pour
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  right in. Your sample might be almost
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  entirely the fine component, which is completely wrong.
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  And the fix for that? The unsampling thief just
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  created a different problem. It did.
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  It forces material and as you push, which reduces that flow
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  bias. But the tool itself is bulkier,
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  so it disturbs and entrains even more material on the way down.
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  You're often just creating 1 error for another, and it
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  frequently makes the mixture look better than it actually is.
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  So for a real accurate picture you need a core sampler.
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  That's as close to a gold standard as we get.
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  It pulls out a continuous, unbroken core of material.
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  It minimizes all those disturbances and lets you see
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  the differences between layers. Which is why you can't just rely
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  on an average concentration for the whole batch.
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  No, an average tells you nothing about where the problem is.
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  We use axial variance to see differences between, say, the
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  front and back of the blender, and then radial variance tells
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  you about the consistency within one of those locations.
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  You need both to diagnose what's going wrong.
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  The way these grains flow, it feels so different from fluids.
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  You said they have to dilate. Yeah, that's the key.
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  Liquids can just cheer smoothly, but for a pile of grains to
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  flow, the individual particles have to physically move apart a
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  little. To expand, they have to dilate.
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  So you can have different states of matter all at once.
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  In a way, yes. You can have a static solid like
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  region sitting right next to a flowing fluid like region, and
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  maybe even a gas like region near the surface.
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  It's so complex that our computational models for
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  granular flow are still way behind fluid dynamics.
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  And that complexity leads to two main types of equipment tumbling
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  blenders. Right.
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  Things like V blenders, they rely on gravity.
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  The mixing really only happens on the top surface as it
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  tumbles. They're gentle, but finds can
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  easily segregate into a core in the middle.
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  Versus convective blenders which are more aggressive.
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  Much more. A ribbon blender, for example,
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  uses an impeller to physically move material all over the
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  place. It's great at fighting
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  segregation, but all that action creates high shear.
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  Which can grind your particles down or create a lot of.
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  Heat. Exactly.
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  It's always a trade off. OK, let's make that transition
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  now from dry powders to, well, the really heavy sticky stuff,
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  viscous fluids. We're talking paste polymers
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  things over 10 Pascal seconds. And suddenly all the rules
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  change. You completely lose the gift of
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  turbulence. No more eddies to do the work
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  for you. None.
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  And molecular diffusion is incredibly slow, so all your
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  mixing, 100% of it has to come from direct mechanical action.
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  You are physically forcing it to mix.
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  And this forces engineers to think about two very different
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  kinds of mixing. That's the key distinction.
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  First, you have distributive mixing.
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  It's all about spatial uniformity.
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  You stretch and fold the fluid, creating thinner and thinner
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  layers. Like a Baker folding dough.
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  You're just trying to spread everything out.
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  And the other is dispersive mixing.
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  That's the intensive part. It's about applying high
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  mechanical stress to break things up.
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  Lumps, agglomerates, droplets of another liquid.
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  It's the brute force. So.
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  You need both. You need to break the lumps and
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  then you need to spread the pieces.
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  Almost always, yes. You need intensive dispersion
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  and extensive distribution. What I.
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  Found really wild in the material was this hard limit
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  when you're mixing 2 admissible fluids, the viscosity ratio.
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  It's a fundamental physical barrier.
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  If the viscosity of the droplet you're trying to break up is
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  about four times higher than the surrounding fluid, more or more
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  simple shear flow cannot break it.
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  It's physically impossible. The forces just aren't there.
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  Wait, so no matter how fast I spin my mixer, if the oil I'm
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  adding is just a bit too thick, the droplets will never break
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  up? Not with simple shear.
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  You hit a wall. To get past that, the mixer has
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  to generate what we call elongational flow, a true
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  stretching and pulling action. It requires very different
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  specialized equipment design. All this mechanical work,
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  forcing things to stretch and shear, that creates a massive
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  heat problem, doesn't it? A huge one.
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  It's a double edged sword. All that power you put in
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  becomes heat through viscous dissipation, and at the same
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  time these thick fluids are terrible at transferring that
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  heat out through the vessel walls.
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  So you have a machine that's great at making heat and a fluid
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  that's terrible at getting rid of it.
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  Exactly. And here's the paradox you have
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  to remember, if you think I'll just speed up the agitator to
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  mix better and improve heat transfer, you could actually
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  make things worse because the power you're adding goes up
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  exponentially with speed, dumping in way more heat.
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  But the improvement in the heat transfer coefficient is modest
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  at best. You can get to a point where
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  spinning faster actually just cooks your product faster.
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  Wow, so there's an optimal speed for cooling and going past it is
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  counterproductive? There is.
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  It's a critical constraint. It's why you see specialized
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  equipment like helical ribbons that have very small clearances
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  to the wall. They have to physically scrape
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  the fluid off the wall to force heat transfer and make sure
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  nothing stagnates. And that heat problem is the
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  main reason for the scale up dilemma, right?
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  Why bigger mixers run slower? It's the absolute driving force.
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  When you go from a small reactor to a huge one, your volume
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  increases much faster than your surface area for cooling.
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  So to avoid scorching the product on the walls, you have
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  to slow down the blades and reduce the power per unit
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  volume. Which means mixing takes longer
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  on the large scale. Significantly longer you trade
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  time for thermal safety. OK, finally, let's connect this
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  to chemistry. We're talking about mixing
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  sensitive reactions. This isn't just about being
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  uniform anymore. It can determine if you make the
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  right product at all. Absolutely.
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  This is common in pharma and specialty chemicals.
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  A reaction is mixing sensitive. If it's so fast that it starts
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  to happen before your reagents are even fully mixed at the
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  molecular level, we call that micro mixing.
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  So the molecules are reacting with whatever is closest, not
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  necessarily what they're supposed to.
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  What does that do to the final product?
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  It can be catastrophic for your selectivity.
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  If reagent A&B are supposed to react, but you have a local spot
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  with not enough A, then B might start reacting with itself or
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  decomposing. Your yield of the desired
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  product just plummets. And this isn't just for liquids,
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  the same problem happens in multi phase systems because of
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  mass transfer limits. Right, there's a classic example
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  with an antibiotic synthesis. The reaction creates
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  hydrochloric acid as a by product which is toxic to the
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  main product so. You have to get it away fast.
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  Instantly, even if the overall pH in the reactor is fine, the
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  local concentration of HCL right at the surface of the particle
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  can be high enough to destroy the product as it's being made.
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  The solution wasn't just a stir harder.
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  What was it? It was a more elegant solution
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  using things like powdered molecular sieves that could get
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  in there and scavenge the HCL locally right where it was
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  formed before it did any damage. That leads us to what you said
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  is one of the hardest operations to scale crystallization.
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  Because mixing effects everything.
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  Take nucleation, the creation of new crystals.
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  It's highly dependent on impacts either crystal on crystal or
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  crystal on impeller. If you mix too hard, you get way
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  too many nuclei. And that's bad because?
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  Because the final crystasize you can achieve is exponentially
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  related to how many nuclei you start with.
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  Too many nuclei means you end up with tiny fine powder instead of
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  the large crystals you want it. It sounds like you're trying to
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  juggle glass balls. You need to move them around for
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  them to grow, but you can't let them hit each other too hard.
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  That is the perfect analogy. It's the ultimate tradeoff.
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  You need enough circulation for mass transfer and to blend
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  everything, but you need low enough shear to prevent over
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  nucleation and breakage. Nailing that balance is
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  everything. And just quickly, how do
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  continuous mixers handle this? They have a different problem,
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  right? Feed fluctuations.
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  They do. They use what's called axial
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  mixing to smooth out or dampen any variance in the feed
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  streams. It's measured by something
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  called the Variance Reduction Ratio, or VRR.
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  But high axial mixing has a downside.
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  A big one. It broadens the residence time
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  distribution. That means some particles fly
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  right through the mixer, while others hang around for a long
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  time. If the mixer is also a dryer or
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  a reactor, that's a disaster. Some product is under processed
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  and some is over processed. So when we put all this
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  together, the real art here is so much more than just stirring
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  something in a pot. Oh, it's about controlling
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  things at a molecular level, managing these brutal formal
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  constraints, and balancing these delicate, conflicting
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  requirements, especially in sensitive processes like
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  crystallization. It's a field where honestly
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  experience and testing still rule because the models just
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  aren't all the way there yet. It really changes how you think
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  about the word blending. If knowledge is power, then
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  industrial blending is the ultimate power application.
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  Considering that increasing the agitator speed to mix of viscous
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  fluid faster might actually prevent you from cooling it.
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  Where else in your world do your solutions inadvertently become
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  part of the problem? We'll leave you with that
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  thought for the week. Until next time, keep digging
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  deeper.