Validating the DiFluid R2 Extract

Introduction

A little while back, DiFluid sent me a pre-production version of their R2 Extract refractometer. Since then, these units have gone to production, and DiFluid kindly sent me one of the production units as well.

One of the things I like most about the R2 Extract is that it displays temperature and refractive index as well as the usual measurement of total dissolved solids (TDS). Speaking with a representative from DiFluid, I confirmed that the refractive index reported by the R2 Extract has been adjusted to nD20—that is, it is an estimate of the value measured at the sodium D line (589.3 nm wavelength) and at 20 °C.

I’d like to use this refractive index measurement in an upcoming post, so I wanted to check it using reference solutions. The easiest reference solution to prepare is a solution of sucrose—that is, refined table sugar—so that’s what I decided to use.

I’ve also wanted to try validating TDS measurements using instant coffee for a while, so I decided to try that at the same time.

As always, raw data and analysis have been uploaded to GitHub. In particular, I’ve uploaded raw data for this experiment as well as a collection of references for refractive index measurements.

Drying

To prepare the reference solutions, I will be mixing a measured amount of solute (sugar or instant coffee) into distilled water. In order for these solutions to be accurate, we need to make sure there is no moisture in the solute.

The Sigma-Aldrich datasheet indicates that sucrose can absorb up to 1% moisture, and that this moisture can be removed by heating to 90 °C. Dittmar et al. indicate that the moisture content of sucrose could be greater than 1% in high humidity conditions.

Federal regulations in Canada specify a maximum moisture content of 4.25% for agglomerated instant coffee.

For this reason, I split each solute into two batches, and dried one batch in the oven at 100 °C for 24 hours.

Equipment and materials

The following equipment was used for this experiment:

• A 0.01 g scale similar to this one
• A 0.001 g scale similar to this one
• A pre-production DiFluid R2 Extract refractometer
• A production DiFluid R2 Extract refractometer
• Rogers fine white granulated sugar
• Maxwell House Original Roast instant coffee

One of the main differences I noticed between the pre-production R2 Extract and the production unit is the colour of the light used to make the measurement:

In this image, the pre-production unit is shown on the left and the production unit is shown on the right. The pre-production unit used a green light, whereas the production unit used an amber light. This is a good change, I think, since the sodium D line is close to the colour used by the production unit. I believe this means we are less likely to see errors due to the wavelength dependence of refractive index.

Method

For this experiment, I prepared and measured reference solutions of sucrose and instant coffee, both in dried and undried form. Five reference solutions were prepared for each solute, with TDS of approximately 10%, 8%, 6%, 4%, and 2%.

Each reference solution was prepared using the following procedure:

1. Check the calibration of the 0.001 g scale using a 10 g weight.
2. Check the calibration of the 0.01 g scale using a 50 g weight.
3. Put a sample boat on the 0.001 g scale and tare.
4. Measure the dry sample into the sample boat.
5. Put a clean and dry cup on the 0.01 g scale and tare.
6. Add the weighed dry sample to the cup.
7. For coffee samples, weigh the sample boat after transferring the dry sample to the cup and subtract from the measured weight of the sample to get the weight transferred to the cup.
8. Add room temperature distilled water to the cup to get the desired solution weight.
9. Stir the solution until no solid remains.

Once the reference solution was prepared, I checked zero on both refractometers using distilled water then dried them. Then the following measurement procedure was repeated three times:

1. Stir the solution a few times.
2. Flush the pipette 3 times with the reference solution.
3. Transfer a sample of the reference solution to each refractometer, filling the sample area to about 80%.
4. Immediately start a measurement on both refractometers.
5. Record the refractometer measurements.
6. Clean and dry both refractometers.

Finally, the spoon and pipette were cleaned and dried, then the next reference solution was prepared.

Results and analysis

Sucrose solution

First, let’s look at refractive index vs. prepared TDS for sucrose samples. To evaluate the accuracy of the refractometer measurements, we can compare them against published measurements of refractive index for sucrose in aqueous solution.

I was able to find two reference data sets which seem to come from undergrad lab manuals:

• Weber State University
• UCLA

We can zoom in on each cluster of points to get a better idea of how well these measurements agree.

There is some disagreement between the reference curves at 10% TDS, and the pre-production R2 Extract generated one erroneous measurement, but otherwise our measurements are very close to the reference curves. The error in refractive index seems to be less than about ±0.00005. At a TDS of 10%, this would correspond with an accuracy of about ±0.03% TDS.

There is no clear difference between the two refractometers, or between the dried and undried solutes, which suggests that the moisture content of the sucrose is negligible.

Instant coffee solution

For the instant coffee samples, it will be more instructive to look at residual TDS, rather than refractive index. Residual TDS is the difference between TDS reported by the refractometer and TDS calculated from the measured weights. The following plot shows residual TDS vs. prepared TDS.

We immediately see a couple of differences compared to the sucrose measurements:

• There is much more variation between measurements for a single solution.
• Despite this variation, we can see a clear difference between the two refractometers, and between the dried and undried solutes.

We can fit a straight line to each solute to quantify the differences between them.

We should be careful about taking these fits too seriously, since the underlying data has quite a lot of variation. However, I think we can draw two conclusions from these fits:

• The result for the dried coffee is about 4% higher than the result for the undried coffee.
• The result given by the production R2 Extract is about 1% lower than the result given by the pre-production unit.

The first statement implies a moisture content of about 4% for undried instant coffee.

Given that we saw no significant difference between the two refractometers when measuring sucrose solutions, the second statement suggests that there is some difference in the way the two refractometers process the raw sensor data. This would be particularly noticeable in the case of unfiltered solutions, where undissolved solids can make measurement more difficult.

It is also worth noting that both refractometers gave increasing TDS results with repeated measurements for instant coffee solutions. For solutions with high TDS, both refractometers would eventually report an error. Again, it seems likely this is due to undissolved solids precipitating out of the sample.

Discussion and conclusions

When calibrated using distilled water, the DiFluid R2 Extract seems to measure refractive index of sucrose solutions with an accuracy of about ±0.00005. At a TDS of 10%, this would correspond roughly with an accuracy of ±0.03% TDS.

I was not able to get a clean result using Maxwell House Original Roast instant coffee. However, I think this part of the experiment offers two lessons:

First, if calibrating with instant coffee, care must be taken to dry the coffee first. However, drying the coffee may introduce other sources of error. Liang et al. suggest that about 2.5% of coffee solid mass is volatilized during 24 hours of drying at 100 °C. This means dried coffee has a different composition than undried coffee, and a refractometer which is calibrated for undried coffee might not give an accurate result for dried coffee.

Second, the accuracy of refractometer measurements is affected significantly by undissolved solids in the sample. Filtering the sample should fix the problem, but again this changes the composition of the sample, so that what we’re really measuring isn’t the coffee we’re drinking, but rather a filtered version of it.