Part-2: Determining Solvent Evaporation Rates Faster with Science based Tool

TAGS:  Science-based Formulation 

In Part 1, we looked at how the formulator might go about choosing the right balance of solvent evaporation properties using basic parameters such as:

• Flash Point
• Relative Evaporation Rate (RER)
• Boiling Point
• Vapor Pressure

These properties have to be balanced against other factors such as toxicity, green credentials, odor and the all-important solubility behavior encoded in Hansen Solubility Parameters, HSP.

Here we look at ways in which things become complicated – and what we can do about it. Surprisingly, HSP turn out to be a helpful pragmatic tool for dealing with the complications.

It’s not ideal

A good way to create a real-world solvent for a specific application is to create a blend of two solvents that can deliver properties neither can deliver on their own. For example, HSP shows that you can take two rather poor solvents for a given solute and create a good solvent via a smart blend. This is because the HSP of the mix is the weighted average of the individual components.

This means that a solvent with parameters that are too large can be offset with another solvent with parameters that are too small. In the extreme, two bad solvents can create a good one, as indicated in the diagram where each solvent is far from the center that defines the HSP of the solute, but a 50:50 blend would be perfectly in the middle.



Via the simple evaporation theory discussed in Part 1 we can readily estimate how the blend will evaporate. The one with the higher RER will evaporate faster, meaning that the HSP of the blend will change with time. An app shows this well:



We start with a 50:50 blend of heptane:cyclohexanone. The red line shows the overall % solvent over time. The heptane evaporates faster than the cyclohexanone and from the yellow and blue lines, you can see how the original 50:50 blend quickly becomes 100% cyclohexanone.

The Ra value, in green, describes how far the solvent blend is in HSP terms from the polymer. The original distance is 5.7, not very good but adequate. Because cyclohexanone is closer in HSP space as the heptane disappears, the Ra decreases to ~3, i.e. solubility increases.

There’s a problem with this simulation. Heptane and cyclohexanone are rather dissimilar, so their mix is non-ideal. This means that when heptane is in a minority in the solution it is uncomfortable being near cyclohexanone, so its vapor pressure will be higher than expected. This non-ideal behavior is expressed as an activity coefficient.

Another app (based on UNIFAC theory, not shown) tells us that heptane’s activity coefficient is in the 1.2-1.3 range when at a lower concentration in cyclohexanone, so the evaporation will be 20-30% faster than expected from the simple evaporation app.

We can also get non-ideal behavior with respect to the solute, so the activity coefficient might be somewhat larger again. And in some cases, the solvent interactions are sufficient to create an azeotrope where the evaporation is at constant composition.

What should we do about non-ideality?

Given that activity coefficients are complicated and that most of us don’t have access to evaporation models that incorporate their effects, what should we do about non-ideality? The answer is rather straightforward: check how far apart in HSP space the two solvents (and maybe the solute) are then making a rough estimate of the non-ideal effects.

Then make a judgment about how significant these effects will be in your formulation. For the above example, a 20% faster removal of heptane isn’t of much significance. But if the faster-evaporating solvent is the better solvent, then this might be enough to cause the formulation to crash out of solution rather faster than you might like.

This sounds rather poor advice. But let’s think of the alternatives. You can either get hold of an accurate evaporative model which takes into account non-ideal effects (I’m the author of one such model, built in to the TopCoat software, but I don’t recommend it for anyone other than serious formulators), or you can formulate in the hope that non-ideal effects will not be significant. Hope is not a strategy. By having a feel for the likely size of the non-ideal effects, you will be better placed to make a judgment about whether there might be odd effects during drying and to do something about them.

Blocked!

Entering the diffusion-limited zone

The other, more important, the effect is apparent if you carefully monitor the overall solvent content during drying. For a while, evaporation takes place at the pace predicted by the simple model, then suddenly slows down dramatically. We have transitioned from the state where removal of the solvent is governed by how fast the airflow can remove it, to the state where the speed at which solvent comes to the surface is the controlling factor. We have entered the diffusion-limited zone.



The diagram shows an extreme form of diffusion limitation where the wet liquid is constrained by dry skin. Hopefully, you never reach this drastic situation, but it does happen. If you turn up the temperature to speed up drying, you might exceed the boiling point of the trapped solvent and it will start to boil - rupturing the skin to form a blister.

Modeling the diffusion-limiting rate

It turns out to be rather easy to model the diffusion-limiting rate and, therefore, when the evaporation will swap to diffusion-limited mode. Three parameters describe the situation:

• The first is a diffusion coefficient
• The second is the exponential dependence of that coefficient on temperature, and
• The third is the exponential dependence on concentration

The TopCoat model mentioned above can do these calculations effortlessly. The only problem is that none of us knows, or has the time and equipment to measure, the three parameters.

So, we are in the same position as with non-ideal solvents. We can pretend the situation doesn’t exist, or, we can use two sensible approximations.

The second approximation takes us back to HSP. Let’s use a solvent blend. If the faster-evaporating solvent is relatively poor, then the formulation will tend to stay nicely in solution during evaporation and this will tend to keep an open structure for longer - allowing most of the solvent to evaporate quickly before (as inevitably happens) diffusion limitation kicks in. Don’t do it the other way round where the good solvent evaporates quickly, causing the formulation to crash out early near the surface and create a skin.

We all know that “adding a high boiler” often helps with drying formulations. But we need to be more precise – we have to add the best possible solvent with the lowest acceptable evaporation rate, and “best” is found via a small HSP distance to the solute.

Conclusion

Readers who know my passion for Science-Based Formulation (SBF) may be surprised that I’m recommending that most formulators should ignore full models of non-ideal behavior, or avoid trying to get the parameters for calculations of diffusion-limited evaporation. But there’s a meta-science to SBF which says:



If you are working on many different formulations, there will never be the time necessary to get into all the details, so use those tools such as HSP and simple evaporation models to give you 80% of the benefit for 20% of the work. Those who are working on the optimization of a few large processes really should invest the time to get the benefits of deeper theories.

In other words, SBF is a good friend, not a harsh dictator.