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# Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

## Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

(OP)
I'm planning a lab / pilot plant to test a flow reactor which has two immiscible liquids reacting. To keep them well mixed a static mixer is one option.

What I cannot seem to figure out is whether there's a certain minimum flow rate (I suppose there must be) for the mixer to be effective. Any correlations about this? Would it suffice to, say, keep the Renyolds No. at 4000 and hence the turbulent regime based on nominal pipe dia.?

Another question: When a static mixer gets inserted inside a pipe what's the typical void fraction? Of course, the exact value will depend on the particular model but right now I'm looking for ball park estimates.

Context: There's a two phase reaction I'm planning on testing which needs a 15 minute residence time. The flow rates I'm thinking of are 5 ml/min (organic phase) and 15 ml/min(aqueous phase). Both are water-like low viscosity liquids.

The degree of freedom I have is in choosing the right pipe diameter. Any tips?

The reaction is only mildly exothermic so heat transfer should not be a concern.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

The point of a static mixer is to permit mixing even in the laminar regime. You can easily find literature which will show you highly viscous pastes being mixed, merely by dividing the streams and rotating the split streams by 90 degrees.

Obviously you're fighting density differences and surface tension in your situation rather than just trying to produce mixing. Your goal is to generate interfacial surface area which requires energy input to generate and maintain, so you can't go infinitely large- but if you're even verging on turbulent you're likely going to be OK.

That said, most liquid-liquid contacting isn't done in static mixers, particularly if long times are required. Mixer/settlers and packed pulse columns are more typical, but of course they're going to give you mixed flow rather than PFR behavior. The reaction engineering of two-phase systems like this is pretty complex though, so you'll need to have a close look in Levenspiel's Omnibook to figure out whether you really need 15 minutes of residence time, or more, assuming you're getting your RT requirement from a mechanically mixed batch reactor.

The void fraction of the mixing elements depends greatly on the tube diameter. At small diameters it could be 50%- at larger diameters the elements occupy a smaller fraction of the internal volume.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

I am puzzled by using the term "void fraction" when mixing liquids. Void fraction is for two phase streams and is the fraction that is gas.

There are different types of static mixtures. The least expensive type is the twisted ribbon. It is for Reynolds number below 2500.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

What the OP meant by "void fraction" was the fraction of the static mixer tube ID not occupied by the metal of the mixer ribbon, for the purposes of calculating an internal liquid volume per unit length and hence a residence time.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

(OP)
@moltenmetal

Exactly right, re. the "void fraction"

@srfish

My residence time will be based on the empty volume inside the flow reactor. So I need to start with the nominal volume of the tube & correct it by the void fraction to get the true residence time.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

This is not a simple topic. Static mixing is very dependent on the two different fluid's properties. Viscous fluids can be mixed at low Reynolds numbers by using a folding together of the two streams. Oil and water require High Reynolds number to provide the high shear required to break droplets into smaller ones and to prevent gravity from separating the two fluids.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

(OP)
@Compositepro

Totally agree that it isn't simple. That's what I suspected.

But how do I make inroads on this. I see very little correlations etc. to go by so far.

My fluids themselves are very well characterized. Viscosity, density etc. are all known. What I need to figure is what's the best dispersion I can achieve and under what conditions and using what type of mixer.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

For low viscosity fluids a centrifugal pump is often all you need for mixing. If you have any flow variations in in the two streams being combined a static or in-line mixer cannot fix this. That is why tanks are often used for mixing, even in continuous- flow processes.

Contact static mixer manufacturers for data they have on fluids that are similar to yours.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

Again, if you read my post, I've given you plenty of good information there. Mixer-settlers and pulse columns are typically used for liquid-liquid transfer operations. An aggressive mixer like a pump may be adequate or may generate a terrible, intractable emulsion, and will be of limited use to you if what you really need is continuous generation of new phase contact area AND time for a reaction to occur.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

(OP)
@moltenmetal

Thanks! Your ideas are indeed sound. A mixer settles / CSTR cascade or a Rotating Disc Contactor / Schiebel Column will be great here.

The point is, they are relatively complex pieces of moving equipment, high on Capex & maintenance. Especially because I will need an exotic MOC since corrosives are involved.

Hence the desire to see if a static mixer can be made to work somehow, even if the pumping cost via a pressure drop is high. In other words, I want some quantitative metric / heuristic that lets me estimate the relative degree of mixing / dispersopm of my static mixer vs (say) a mixer settler.

You got to the crux of the point: Its a tradeoff between true PFR behavior (e.g. long static mixer) and high droplet dispersion (e.g. pulse column or mixer settler) Since I need complete conversion (since subsequent separation and recycle of unconverted reactants is not feasible) achieving true PFR-like behavior is essential.

@compositepro

A cfg pump won't work here. It will mix the fluids well but they will segregate into separate layers pretty fast due to the density differences involved.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

If you have strong density differences, a static mixer is going to need substantial velocity to generate enough pressure drop to do the work required to continually re-form the liquid-liquid interfacial area you need.

A static mixer actually has lots of expensive metallic material if you're worried about corrosives. A pulse column is often made of glass, and a mixer-settler is usually made of reinforced plastics with plastic-coated agitators when corrosives are involved i.e. in the mining industry. There are issues associated with flammability required in the design but they are manageable.

Another method is the fibre-film contactor made by Merichem:

http://www.merichem.com/FIBER-FILM

A bundle of fibres which are either hydrophilic or hydrophobic (depending on which phase you wish to be continuous and which dispersed) are essentially coated with the phase they love, while the phase they hate is recirculated by the resulting coated fibres. What you get is effectively a shell and tube liquid-liquid mass transfer unit without the shear that causes the emulsification. At the end of the fibres, the dispersed phase coalesces and drips off into a liquid/liquid separator at the bottom. I think this technology has applications far beyond what Merichem is currently using it for. No idea if it will work for you.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

Have you thought of trying a high shear mixer, like Greerco, Silverson, and numerous others? I understand they will loan out lab and small production scale models. It may be worth a shot.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

(OP)
@Latexman

That's a great idea. I will try a high shear mixer.

One question: Suppose you took an immiscible pair like water / toluene through such a mixer any idea how long the dispersion takes to coalasce? i.e. How would my design look like? Would I have a high shear mixer followed by a residence time leg & recirculation?

Or is it possible to keep a relatively large tank, say 15 kL constantly in a state of fine dispersion with a high shear mixer?

Reason I ask is I've only seen them used in applications where once dispersed a stable dispersion was formed.

### RE: Static Mixer Typical Reynolds Number to be effective for Liq Liq mixing

If your goal is to generate a stable emulsion, you'll need to add an emulsifier, but then you'll have to demulsify to separate the phases again.

If your goal is a phase transfer reaction or other liquid-liquid extraction process, you need to CONTINUALLY add energy to keep breaking up the liquids and re-forming liquid/liquid interface, or you need to stabilize the liquid/liquid interface in some way to minimize coalescence which is what the fibre film contactor attempts to do. You can't just grind the liquids up into a fine dispersion and then hope it will remain dispersed for 15 minutes for your reaction to take place.

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