Caking of powders - how to deal with it...

A number of years ago, I visited a company that supplied cocoa mixes for McDonald's. McDonald's was unhappy because its bags of cocoa had lumps that plugged up its milkshake making equipment. I was psyched. I Googled caking and agglomeration, and the first hit was the Chemical Engineering magazine article that I wrote with my friend Scott Clement! (https://www.chemengonline.com/solids-processing-prevent-caking-and-unintended-agglomeration/) When I refined my search to include cocoa, I found several good chocolate cake recipes.

You already know that a frequent cause of caking is moisture, either in the powder or in the surrounding air. Quantifying caking can be challenging and time consuming. After all, the likelihood of caking is not always evident. The powder may be free-flowing when it is packaged, but days later, your warehouse may be full of pallets with stacks of 50-lb bricks. Worse yet, the bricks may be in your customers' warehouses.

If caking is indeed moisture-induced, an investigator can gleam a lot of information from a powder's moisture sorption isotherm. An isotherm is the relationship between a powder's moisture content and its water activity. The water activity is equal to the relative humidity (RH) of the interstitial air at equilibrium with the powder divided by one hundred. One thing that differentiates chemical engineers like myself from normal people is that we had to take a course in chemical thermodynamics. Think of activity as the escaping tendency of moisture in a powder. If it has high activity, a lot of water will want to be in the vapor phase even when its moisture content is very low; hence the interstitial air of a powder with a high water activity will be very swampy.

A powder's moisture isotherm is measured by placing a small sample of powder in a chamber and then, after a drying step, measuring the uptake in moisture after the relative humidity of the air in the chamber has been changed stepwise. Typically, the RH is raised from 0 to 95 percent in 5 percent increments, and then lowered back to zero percent humidity stepping in reverse. Sorption takes place when the RH is increased; desorption takes place when the RH is decreased. For some powders, the equilibrium moisture content is different for sorption and desorption, that is, the isotherm exhibits a hysteresis. Occasionally, the final mass may be greater or less than the starting mass after completing the sorption and desorption cycles, which means water may have been chemically adsorbed or hydrated water may have been released. Again, a lot of information can be gleamed from a powder's isothgtrtrerm.

There are many testing labs that will measure moisture isotherms for you. If you are miserly, you can always create your own RH chamber using saturated salt solutions. A list of equilibrium relative humidities for various salts can be found at https://www.omega.com/temperature/z/pdf/z103.pdf.

Isotherms come in many styles. Two common isotherms are shown here. The leftmost Type II isotherm has a sigmoidal shape with three regions. The first is at low relative humidity where the moisture isotherm is linear. In this region, water molecules are adsorbed until a monolayer is formed.  As relative humidity increases, multilayer adsorption takes place as a result of hydrogen bonding. In this second region, the slope of the isotherm is initially shallow but steepens with increasing relative humidity. The third region occurs at high RH, where the equilibrium moisture content increases dramatically. In this region, most of the incremental condensation takes place at the contact points between particles. This phenomenon is known as capillary condensation or liquid bridging, which results in strong forces between particles. The moisture content at this inflection point on the isotherm is sometimes called the critical moisture content, and its corresponding equilibrium relative humidity is the critical relative humidity or ERH. The ERH also happens to be the ratio of the water vapor pressure over a saturated solution of the solid to the saturation water vapor pressure, times 100. Exceeding the critical moisture content or ERH likely will result in caking, and über caking if the solid is at least partially soluble in water because solid bridges will form if the moisture evaporates.

The Type III isotherm shown on the right is concave upward from the get go. Type III isotherms are often characteristic of powders that are readily soluble in water. Moisture not only adsorbs onto the surface; it also readily penetrates inside. The moisture content or RH at which caking can be expected may not be obvious.

Water is a universal plasticizer. An increase in a powder's moisture content or activity or an increase in the relative humidity of the interstitial and surrounding air can lower the material's glass transition temperature or Tg, which is the temperature at which a solid becomes rubbery. The glass transition temperature as a function of relative humidity can be determined by inverse gas chromatography or IGC. Very quickly, a sample of powder is placed in a chromatography column, and a probe gas and water vapor are injected. By some magic P-chem principle, the glass transition temperature can be determined from IGC retention volume data, and by conducting IGC runs over a range of RH, the relationship between RH and Tg can be determined. Results should look something like the figures shown below. Sometime I wished I stayed awake during my P-Chem class.

Inverse gas chromatography tells us the effect of interstitial gas RH on the glass transition temperature. The powder's moisture isotherm tells us the relationship between moisture content and equilibrium relative humidity. Materials soften significantly at temperatures higher than Tg, and conditions that cause particles to deform often lead to caking. Therefore, from IGC and moisture sorption tests, we ought to be able to figure out what moisture content not to exceed if we don't want to make bricks.

By the way, there are other types of isotherms. The Type II is frequently modeled by the Guggenheim, Anderson, and de Boer equation and Type III is often described by Flory-Huggins. Other models, such as one derived by Valdez, Paredes, Vargas-López, and Hernández, can be used describe complex isotherms. I no longer have JMP on my computer, but I'm fairly certain that there is a correlation between the number of authors of a model and the number of empirical parameters. Some parameters have a fundamental basis, so it may be tempting to include an Arrhenius temperature term if sorption behavior varies significantly with temperature. Don't bother. Unless you have a lot of data, it's best just to interpolate linearly. What is the difference between a physicist and an engineer? A physicist will say E = mc^2 while an engineer will say E = α mc^2 + β where α and β are empirical constants. Choose the right regression, and I can get an R-squared of 1.

If caking is indeed moisture induced, we ought to be able to determine a spec or condition for avoiding caking just by scrutinize a powder's moisture isotherm. We might not even need shear cell or uniaxial compaction tests to determine if strength actually increases with time, but it's probably a good idea to perform a limited number of them to confirm that moisture is indeed the culprit. Unfortunately, it takes time to conduct time tests, and sometimes, we just don't have enough time.

There is one more complication. When defining a specification, we need to worry about moisture migration. Moisture migration takes place when a temperature gradient exists during packaging or storage. The mechanism of caking due to moisture migration is as follows:

?      The relative humidity of the interstitial air at a warm boundary decreases.

?      As a consequence, moisture desorbs from the warmer solids, as the solids and interstitial air are no longer in equilibrium.

?      The absolute humidity of the interstitial air increases.

?      The driving force in the gas phase leads to moisture migration toward a colder region, which has a lower absolute humidity.

?      The relative humidity of the cooler interstitial air increases.

?      Moisture adsorbs onto solids in the interior in an effort to re-establish equilibrium.

Moisture migration is illustrated below:

And so over time, if there are temperature gradients, moisture will become higher in a cooler region of a container of or a vessel filled with a powder. If the ERH or critical moisture content is exceeded, caking may occur. If the moisture content is high enough that the temperature locally exceeds Tg, caking will likely occur.

If you want to complicate things, you can refer to numerous studies by investigators who model the kinetics of moisture migration. In most cases, diffusion is described by Fick's Law:

where N, D, and c are the flux, diffusivity, and concentration of species i, and z is the spacial coordinate. Of course, in a bed of powder, the water molecules must take a serpentine route to respond to the difference in humidity. Therefore, most investigators cheat and define an effective diffusivity as:

where the subscript eff denotes effective, ε is the powder's porosity, and τ is its tortuosity, which purportedly describes the twisted path that the water molecule must follow to diffuse through a porous material. Don't you think it's odd that diffusivity is frequently reported to several significant figures but the tortuosity seems to nearly always be a factor of 0.1? Engineers love effective parameters because it saves us a lot of work.

I suggest that you instead perform as simple steady-state analysis that determines the moisture distribution in a bulk solid that will result if a temperature gradient were imposed. The temperature gradient is assumed to remain constant. Since this is not true, the analysis gives a conservative view of possible conditions that can exist if temperature differences were to remain for an extended time. The advantage is that it is a slick way to come up with a moisture spec. The disadvantage is that you won't be able to imbed any fancy COMSOL plots into your PowerPoint presentations.

The analysis is as follows. If a bulk solid is exposed to a warm surface (temperature = TH) on one side and a cool surface (temperature = TC) on the other, the temperature profile at steady state would be given by:

where z is the normalized ratio of the distance from the cold surface to the width between the hot and cold surfaces. At steady state, the concentration of water in the interstitial air Cw, is constant. The vapor phase moisture concentration is the product of the absolute humidity H and the dry air density ρa:

The relative humidity RH is related to absolute humidity by

where Pt and Pwsat are the total pressure and saturation pressure of pure water, respectively.  (Oh, and 18 and 29 are the molecular weights of air and water, respectively.) Due to the temperature gradient, the relative humidity of the interstitial air will vary. As a result, the amount of moisture in or on the solid that is in equilibrium with the interstitial air will also vary. The relationship between the solid’s equilibrium moisture content X and the relative humidity of the interstitial air is given by the material’s isotherm. Since the amount of moisture in the gas phase is negligible compared to that in the solid, the total amount of moisture in the solid after migration can be assumed to be equal to the initial solid moisture content X0, i.e.,

A specification for a bulk material’s moisture content that, if exceeded, causes caking can be determined by finding the value of Cw that satisfies the above system of equations and the material’s moisture isotherm. Now if this seems familiar, I copied it from the article on caking that I wrote for Chemical Engineering Progress (https://www.aiche.org/resources/publications/cep/2016/april/prevent-caking-bulk-solids). I word-smithed it a bit, but it's not plagiarism is you copy your own work, right?

Knowing the pack-out temperature of his or her (or xer) powder, an engineer can determine the moisture content spec that should not be exceeded to avoid caking; the warehouse manager can advocate a spec that will minimize caking in an uncontrolled warehouse; and the marketing department can recommend storage conditions at its customers' facilities.

For example, if you are packaging lactose that has the moisture isotherm given below, a possible water activity spec as a function of the pack-out temperature or the maximum expected temperature in your warehouse is shown in the adjacent figure.

It looks like moisture induced caking will occur if its water activity is circa 0.7 as that is where the isotherm become dramatic and liquid bridging will occur. If you expect your warehouse to reach 100°F (38° Canadian), then you'd better shoot for a water activity spec of about 0.22 to prevent the water activity from reaching 0.7. I prefer using water activity as a target rather than moisture content. For materials like lactose, the moisture content is very low and I doubt if you'll be able to measure it by weight loss. Get yourself a water activity meter. They are essentially RH meters for powders. The QC department will love you and you won't have to bribe anyone to get a result quickly.

Oh, and the analysis assumes that your packaging is impermeable to moisture. To check, try this simple experiment. Take an RH meter and measure the relative humidity of the room. Then punch it through the bag and measure the RH of the interstitial air of the powder inside the bag. If the RH readings are about the same, then you'd better invest in some tighter bags, throw in some desiccant, or switch to drums or other water-tight containers. Or you better make damned sure that the warehouse relative humidity remains below your powder's ERH or move to a drier climate.

BTW --- about the cocoa mix. If you take two powders that have the same moisture content but different water activities, moisture is gonna migrate. And if moisture leaving one powder had some soluble matter in it before it migrated to the lower-activity powder, it will probably leave behind some solid bridges, which will P.O. your customers who use it to make milkshakes.

P.S., if you like my article, please "like" it or share it. Check out my previous posts:

When measuring powder flowability, don't forget about wall friction!

Why liquids and bulk solids give me different levels of stress...

Optimizing pharmaceutical formulations for flow.

Hopper Design Cliff Notes

Greg Mehos; [email protected]; 978-799-7311