How can you measure the humidity of coffee, rice, beans, yerba mate, flour, oatmeal, polenta, wood, clay, concrete, soil, plastics, and so on?
The measurement techniques described in Trellis-coded buttons to run a whole keyboard off two microcontroller pins can be applied to humidity measurement, but there are additional issues.
On Earth, humidity is a crucially important property for many purposes.
Dried food stored with too much moisture can grow mold, and in particular mold on improperly stored legumes is one of the major causes of human liver cancer in the world, by way of aflatoxin contamination in the food eaten by the humans. Also, extra moisture in food represents extra weight that must be stored and sometimes moved, and food is often sold by weight, so standards of marketability impose maximum humidity contents on foods.
Deep freeze talks a bit about moisture content of marketed dry food (11% or less for marketed soybeans, for example). Food storage talks a bit about moisture as a factor in food decay.
Wood expands and contracts considerably according to humidity, and so must be dried to roughly the proper humidity before being made into things, so that it doesn’t expand or contract too much after being assembled; also, ever since the development of lignolytic enzymes such as lignin peroxidase (probably at the end of the Carboniferous), already-installed wood is subject to attack by fungus if it’s humid.
Additionally, humidity in installed wood can indicate the presence of termites, which will destroy the wood, or a water leak, which may destroy things in contact with the wood, as well as permitting fungal growth, as above.
Wood products like fiberboard and particle board are similar to wood in this way, but some of them additionally suffer direct degradation from being wetted. Most varieties of MDF expand about 60% in the cross-grain direction when they get wet, losing most of their already rather pitiful strength in the process, and the adhesives used in in particle board are also often degraded by getting wet, even if the moisture doesn’t last long enough to permit mold attack.
Dry wood and wood products also provide substantial insulation values, while their wet versions do not.
A design sketch of an air conditioner powered by solar thermal power talks a bit about various organic hygroscopic substances, including wood, and how much water they can absorb: dry wood contains about 12% moisture, while wood in equilibrium with a humid atmosphere can contain up to 25% to 30% humidity.
The physical properties of a clay body† prepared for pottery-making depend sensitively on its moisture content. In a couple of percent near 20% water by weight, it transitions from brittle “dry” clay, which is still cool to the touch because of the heat-pipe effect as water evaporates from near the humans’ fingers, to flexible “leather-hard” clay, which can still be broken, to fully plastic clay which can be deformed arbitrarily as long as it’s kept in compression. (Like ductile iron, it still eventually reaches brittle fracture under sufficient tensile deformation.) A fully plastic clay body is a fucking amazing material for forming: it requires very little force to deform it, and because its elastic deformation is so small as to be very difficult to measure, which means that once you form it into a shape, it has very little springback as you remove the forming tool.
There’s a further humidity reduction from “dry” to “bone-dry”, at which point the object no longer feels cool to the touch, and is ready for firing. Bone-dry clay is still brittle, but considerably stronger than merely “dry” clay.
The precise moisture percentages at which the clay body transitions between these states vary fairly widely depending on the types of clay involved and the other ingredients.
As the clay body dries, it contracts, which sets up stresses in the object, which can deform it, and provokes some dimensional imprecision — the contraction is typically anisotropic due to not only anisotropic orientation of clay grains but also because of external forces present during the contraction process, so the shrinkage is somewhat unpredictable. Nearly all of this contraction is between the “fully plastic” state and the “leather-hard” state; there is dramatically less contraction from “leather-hard” to “dry”, and none from “dry” to “bone-dry”, and almost none from “bone-dry” to bisque-fired (sintered) ceramic. (Glaze-firing densifies the ceramic further, producing further contraction.)
In the plastic state, the clay is sticky and tends to adhere to whatever you use to form it, pulling it out of shape as the forming contact ends; once it is leather-hard, it is no longer sticky. Plastic clay in a dry atmosphere forms a thin leather-hard layer at the surface which can serve to ameliorate this stickiness.
So, if you form clay in the fully plastic state, you get substantial contraction and consequent imprecision upon drying to leather-dry. If you form the clay in the leather-hard state, you can get near-net shapes, but you are very limited in the deformations you can achieve. You can also cut leather-hard clay with a blade, getting glassy-smooth surfaces, although these do not survive bisque firing. Once the clay is dry, it can be further cut to shape with abrasive processes, at the risk of shattering the brittle piece.
So, precise measurements of clay moisture content, down to a fraction of a percent, are very useful for controlling manufacturing processes, particularly automated manufacturing processes. The humidity at each of these transition regions depends on the precise contents of the clay body, but if you’re using a well-controlled clay body, you can calibrate your humidity levels to that clay body and get reproducible manufacturing results.
† For making pottery, we mix clays with other materials, including of course water, but also sand, other “tempers” such as grog (powdered fired clay), flocculants, deflocculants, and organic gums, in order to balance the properties of plasticity, green strength, contraction, firing temperature, and strength after firing; this mixture is called a “clay body”, although sometimes in the above I’ve sloppily called it “clay”. Pure clay contracts on drying considerably more than commonly-used clay bodies do, and its green strength and even fired strength are much lower.
Concrete needs water to harden, but I think that if it’s too wet, atmospheric carbon dioxide can’t penetrate, which slows the hardening process. If it dries out before hardening fully, it can become crumbly and impossible to harden. So, during hardening, it’s potentially beneficial to monitor the moisture.
Also, continued exposure to water can degrade concrete, particularly if the water contains high concentrations of, for example, chloride or hydronium ions. And, as with wood, moisture in concrete can be a sign of water leakage, which can eventually result in damage to other objects if it continues. If the moisture is sufficient to saturate the surface of the concrete, it usually becomes very visible to the humans by darkening the concrete, but if the surface is kept somewhat dry by exposure to air, moisture in concrete can be entirely invisible.
So, monitoring moisture in concrete is useful both during hardening and long afterwards.
Soil moisture is crucially important for plant growth, because if there isn’t enough moisture in the soil, plants can’t suck it out of the soil, so they stop growing and eventually die. Also, if the moisture levels are too high, you get two kinds of fungal problems and a bacterial problem: too much water can suffocate symbiotic mycorrhizal fungi, which are extremely beneficial to land plants (although some land plants can survive without mycorrhiza); too much moisture can help non-symbiotic fungi to eat the plants; and, without access to nitrogen from air, rhizobial bacteria cannot fix nitrogen.
However, the particular level of soil moisture needed for plant growth depends on the salinity of the soil; roots have a harder time pulling moisture out of saline soils due to higher osmotic pressure.
Many common plastics, notably including PET, nylon 6, and PLA, are hygroscopic; they absorb water from the air. In ordinary use, this is rarely a problem, or is even beneficial, but it has a couple of important effects on melting or hot-forming the plastics.
First, the absorbed water affects the plastics’ specific heat, generally increasing it, so the plastic heats up more slowly. Second, although these plastics are relatively stable in the presence of water at ordinary temperatures, they hydrolyze at the temperatures used for forming or melting them. (Also, PLA in particular, if kept wet, hydrolyzes to lactate over several months at body temperature, and several years at room temperature.) So they must be dried before molding, which is done by heating them to a lower temperature for several hours.
Electric charge produces an electric field according to Gauss’s law, ∇·E = ρ/ε₀, where ρ is the charge density and ε₀ is about 8.8541878 × 10⁻¹² A² s⁴ / kg m³. But, here on Earth, the electric field we observe is always lower than this prediction — usually about 0.06% lower in air, almost 5 times lower in glass, and almost 90 times lower in pure water. That is, to get a given field, we need about 0.06% more charge than this law would predict, or about 5 times as much charge if the region of interest is mostly filled with glass, or almost 90 times as much charge underwater. (Of course, unless our water is very pure, the charge will leak away over time through electrolytic currents, but we can do this measurement pretty quickly, in much less than a nanosecond, so the leakage is small.)
We explain this by a phenomenon called “electric susceptibility”: we suppose that the molecules of the substance have their own electric fields, and they interact with the applied field. For example, in water, the two hydrogen atoms are kind of on the same side of the oxygen, and they have a small positive charge, while the oxygen has a small negative charge, less than an electron. So if we put a negative charge on the left of it, it attracts the hydrogens and repels the oxygen. Because water is a liquid, the water molecule is free to turn around, it tends to turn so that its hydrogens are on the left and the oxygen is on the right (“dipole relaxation”). So then the water molecule’s own tiny electric field is subtracted from the electric field of the negative charge we put to its left, and in fact it cancels almost 99% of it under ordinary conditions. So we need 90 times as much charge to get the same electric field as we would predict from Gauss’s law.
There are a few different ways that charges can move around inside the substance (“polarize”) in response to the applied electric field. For example, in addition to molecules turning around, ions can move around (“ionic conduction”); crystal structures can deform (“ionic polarization”); electrical charge can flow to different parts of a molecule, especially a conjugated compound; and so on. As a general principle, though, because opposite charges attract each other, all of these effects cancel the field somewhat; they never make it stronger. The cancellation is never complete, either, because as it approaches completeness, the leftover field’s influence on the charges approaches zero, so other influences on them are more important, like thermal motion. So we would expect that usually heat would make this susceptibility go down, and in fact we do see this with water: at 100°, we only need about 55 times as much charge as Gauss’s law predicts, instead of the 88 times as much charge we need at 0°.
So usually when we apply Gauss’s law, we apply it in the form ∇·E = ρ/ε, where the ε is a “permittivity” which is ε₀ multiplied by a “relative permittivity” or “dielectric constant” that includes the susceptibility of the medium, as well as the inherent “vacuum permittivity” ε₀. So, for water at 0°, we say the relative permittivity is 88, and for water at 100°, we say it is 55.
(This effect is also the main reason light travels at different speeds through different substances, which is why transparent substances both refract and reflect light at their surfaces. Rutile — titanium dioxide — refracts light so strongly because its permittivity is even higher than water’s, even though it’s solid.)
Porous, dry organic materials like paper, wood, coffee, beans, and rice have relative permittivities around 4, which is much smaller than water’s permittivity of 88. By coincidence, quartz sand’s relative permittivity is also about 4 (it’s 3.9) and so is concrete’s (it’s 4.5). So, if these materials absorb water, their permittivity goes up substantially.
Consider the polarization of water again, though. It happens by turning the water molecules around so that their hydrogens are predominantly on the side toward the negative charge and their oxygens are on the side toward the positive charge. It happens that this effect is close to linear under normal circumstances: slowly applied fields that are quite small compared to the enormous electric fields inside the molecule. But, as you can imagine, this linearity breaks down under other circumstances.
One aspect of this is that it takes a certain amount of time for the molecules to come into this alignment, and some of the energy of the applied field is lost in the process — the molecules in liquid water are shaking around under the influences of one another’s fields, and so if you apply a rapid enough jolt of electrical field, they won’t respond fast enough. So as the time we’re considering goes to zero, or frequency goes to infinity, the susceptibility also goes to zero.
(In optics, this variation of permittivity with frequency is called “chromatic aberration” or more generally “material dispersion”.)
So you could imagine rapidly bringing some charge into proximity with some water, over a short time period, like an attosecond. At first you would observe the whole field predicted by Gauss’s law in its pure form, the ε₀ form, but then if you left the charge there for a while, gradually the field would decay down to its usual level of about 1% of its original value. Most of the energy has gone out of the field. Where did it go?
And of course the answer is that it went into heating up the water molecules: as they rotated around to come into alignment with this sudden jolt of electrical field, they jostled against each other and gained some kinetic energy. And this is how we heat up water in a microwave oven, by applying an electrical field that goes the other direction every 210 picoseconds or so. This loss of electrical energy to heat is called a “dielectric loss”. The dielectric loss is often combined with the dielectric constant into a single complex number called the “complex permittivity”.
A thing to note there is that the different susceptibility mechanisms operate on different time scales. Ionic conduction is a great deal slower than dipole relaxation, for example, and water always contains some ions; water absorbed by organic matter or soil usually contains an enormous quantity of ions. It happens that ions become more mobile when the temperature is higher, so the low-frequency permittivity of moist organic matter is dominated by ionic conduction, and so its permittivity goes up when it gets hot, instead of down like pure water’s, at least until it’s close to boiling. But, for the same reason, the permittivity of water with lots of ions drops sharply with frequency, much more sharply than pure water’s, and above a few tens of megahertz, its permittivity becomes dominated by dipole relaxation and drops with temperature, for the reason explained above.
So, for example, carrots contain so many solvated ions that, at low frequencies, they have a relative permittivity of about 600 at 25°, which increases to about 850 at 45°, but around 100 MHz the permittivity of carrots is nearly invariant with temperature. Navel oranges, which contain many fewer ions, only have a relative permittivity of about 200 at 25°, which increases to 250 at 45°, and the point at which their permittivity becomes insensitive to temperature is about 40 MHz. (All of this is according to Nelson’s 2006 paper, “Agricultural applications of dielectric measurements.”)
(I am somewhat skeptical of the precision of these numbers; theoretical considerations suggest that they come from Maxwell–Wagner–Sillars polarization, which can give you arbitrarily large permittivities because the charges can be separated by arbitrarily large distances.)
Not only the permittivity but also the dielectric loss varies with frequency; the dielectric loss, too, falls with frequency in the limit, but may locally rise over some frequency range.
Another way this linear approximation can fail is with very strong fields. At the macroscopic field strengths we usually observe, the linear approximation is very good, but you can easily see that once, for example, all the water molecules are all pretty well lined up with the applied field, they can’t align themselves any further to cancel an even stronger applied field; any further electrical susceptibility must be due to other effects such as the molecules bending, or charge moving around on them, or ions moving through the water, which are much weaker effects. So at high enough field strengths, the relative permittivity of any substance drops back to almost 1, just like its relative magnetic permeability. In optics these deviations from linearity are called the “Kerr effect”, and they are one of a few ways to get nonlinear interactions between light beams or to electrically control light beams at subnanosecond timescales. (At even higher field strengths, though, the applied field is stronger than the fields that hold the molecules together and the substance will ionize. This alters its electrical and optical properties more radically.)
This nonlinearity is also very important in practice with ceramic capacitors; among the highest-dielectric-constant materials available are the piezoelectric ceramics barium titanate and lead zirconate titanate, which can have relative permittivities (dielectric constants) in the thousands, and they make possible high-capacitance chip capacitors. But when fully charged to their rated voltage, the capacitance of these capacitors can drop by almost half — the field is almost high enough to cause avalanche breakdown of the perovskite structure, and the permittivity of the dielectric drops dramatically at such high fields.
However, I don’t think these strong-field effects are important to the moisture-measurement problem.
Another direction in which the linear approximation fails — for some substances — is in the limit of long time periods. The energy stored in a capacitor at a given field strength is proportional to the permittivity of the capacitor’s dielectric; by using a higher-permittivity dielectric, you can store more energy in the same space. So why don’t we use water-dielectric capacitors for everything except cases where miniaturization is paramount, since water is so much cheaper than lead zirconate titanate? It turns out that, in the limit of large times, water will always break down in a constant electric field, although the time it takes extends exponentially as the field is reduced. So water-dielectric capacitors do work, and they are used for some systems that need to release an enormous amount of energy very quickly, but they cannot hold their charge for a long time.
A third direction in which this approximation fails has to do with anisotropic materials, which can have greater permittivity in some directions than in others.
So, suppose you have some ground coffee, and you want to know how much moisture it contains. The most straightforward thing to do is to place an insulated metal plate in contact with the coffee — for example, a copper pour on a printed circuit board, covered with solder mask — and charge the plate up to a given voltage, like 3.3 volts. The amount of charge needed for this will depend on the permittivity of the coffee. To measure the charge, you can allow the plate to discharge through a known, or at least constant, resistance, and measure the time constant of the decay curve. This gives you a measurement which depends on the moisture content of the coffee.
(For a sensor that isn’t connected to earth ground, you might actually need two equal-size metal plates, one treated as “ground”, to reduce variation due to the floating voltage of the instrument.)
The problem with this is that, as explained above, the measurement depends not only on the moisture, but also on the temperature. It also depends on how tightly packed the coffee is, because if there’s more air mixed in with the coffee, that will lower the measured permittivity. And in situations where the measurement is being taken by placing some kind of handheld sensor against the coffee (or wood or whatever), rather than dumping the coffee into the sensor, you have the additional variables of the size of the air gap between the sensor and the coffee, and the percentage of the plate that is in contact with the coffee.
(I suspect, but am not certain, that all three of density, contact area, and air gap size will have essentially the same effect, in which case we can lump them together into a single unknown, “quantity of material”.)
In an alternative arrangement, you run a sinusoidal AC voltage at a controlled frequency into the sensor plate (or plates) and measure the AC current that ensues, thus giving you a measure of capacitance, which varies linearly with permittivity; the phase shift between the voltage and the current tells you how large the dielectric losses are. If you know enough about the substance whose humidity you’re measuring, you can choose the frequency where its permittivity doesn’t vary with temperature, only with density and humidity, and then you can use the dielectric losses to determine how much of the substance you’re measuring.
More generally, at that point, it’s just a matter of estimating two unknowns (moisture content and quantity of material) from two measurements (capacitance and loss factor).
By sweeping the frequency over a wide range, you can obtain a whole spectrum of complex permittivities at different frequencies, which in theory can provide you with an arbitrarily large number of possibly independent measurements. This could allow you to estimate a larger number of unknowns, such as temperature, moisture content, density, air gap size, and contact area, and perhaps even to distinguish between, for example, coffee, human flesh, and rice.
Another possibility is to use an array of smaller “pixel” contacts; for example, a 16×16 array of 4 mm × 4 mm contact areas separated by 1-mm gaps would enable an independent permittivity measurement on each pixel. This would reduce the problem of unknown contact area (where an unknown fraction of the sensor plate is in contact with the material being measured) and also permit the generation of images.
In the cases of soil and concrete, an important additional unknown is salinity. In soil in particular, higher salinity increases permittivity and conductivity, but makes water less available to plants, while higher moisture increases permittivity and conductivity, while making water more available to plants. So if we want to measure the soil’s need for irrigation, but don’t know the salinity, a simple permittivity measurement is insufficient — we need to estimate both the moisture content and the salinity, and probably the density and temperature as well. For irrigation measurements in particular, it may be feasible to supplement the permittivity measurements with resistivity measurements and thermometer measurements, if you’re leaving the sensor embedded in the soil long enough to measure its temperature to some degree of precision.
An alternative approach to controlling for temperature effects is to intentionally heat the material being measured during the sensing process. The dielectric losses being measured will deposit a small and approximately known amount of heat into the substance being measured; since some of the temperature coefficients of permittivity we’re talking about above are as high as 2% per degree (20000 ppm/K), even small temperature shiffts might be detectable, and might provide a much-needed additional dimension of variation. That is, you can map the complex permittivity of the sample not just at many frequencies but at many frequencies at many temperatures.
If you’re generating the stimulus signal from something like an AVR Arduino, the signals you can generate are somewhat limited — the AVR can easily generate square waves of up to about 4 MHz, and I think that by hacking the SPI you can generate a somewhat noisy 8-MHz square wave. More modern cheap microcontrollers like the STM32L0 and STMF0 lines (see Notes on the STM32 microcontroller family) can easily generate square waves and pulse trains at a few tens of MHz. However, as mentioned earlier, the permittivity of moist organic material has important variations up to and above 100 MHz — in particular, you often have to go that high for the dipole-relaxation mechanism to be the dominant contributor to the dielectric constant.
However, an 8-MHz square wave has significant harmonics at 24 MHz, 40 MHz, 56 MHz, and 72 MHz. Perhaps a small amount of analog circuitry connected to the outside of the microcontroller could filter out a particular harmonic for later conversion.
However, if you’re doing that, maybe you should just offload the whole oscillation and demodulation task onto analog electronics, reserving the microcontroller for just control.