Lab 5: Mass Transfer and Flux in Brewing

Author

Gabriella Carlos

Published

February 23, 2026

Duration: 1.5 hours

Equipment and Materials

Equipment

  • Coffee grinder
  • Brush
  • Timer
  • Digital balance
  • Pour over carafe
  • Filter paper
  • Graduated cylinder
  • TDS meter or digital refractometer
  • Beaker
  • Electric kettle or Hot plate + Thermocouple

Materials

  • Roasted coffee beans (≥ 280 g per group)
  • Water (≥ 3 L per group)

Background

In chemical engineering, a crucial question one often has to consider if “How do we get the chemicals from over here to over there?” This question applies at large length scales (such as in large pipelines), but even more importantly at small molecular length scales. This consideration can be seen very clearly in the case of the coffee. Getting the organic flavor molecules and caffeine from the solid coffee grounds into the hot water is a pivotal step that determines the overall quality of the brewed coffee.

In this lab we will consider flux, the measurement of how much “stuff” is moving through a particular area per unit time. With regard to coffee, this concept has two key implication: (1) The more surface area of the solid particulates, the more area you have for flux, the more molecules you’ll get, and (2) The longer you expose it for, the more molecules you’ll get. We will directly compare grind size and extraction time on how much “coffee stuff” you extract into the water during brewing.

Another key idea is that the magnitude of the flux is proportional to the concentration difference, or \(Flux = k \times(C_s - C_b)\), where \(C_s\) is the concentration of some molecule (say caffeine) at the surface of the solid particulates (coffee grounds), and \(C_b\) is the concentration of that molecule in the bulk of the fluid. Recall from heat and mass transfer that the parameter k is the “mass transfer coefficient”, which will depend on temperature, and \((C_s - C_b)\) is the concentration difference, or the driving force for mass transfer.

Because there are so many different molecules in brewed coffee, it is challenging to measure the concentration of any specific molecule. Instead, we measure the cumulative concentration of all the different molecules that move from the coffee grounds to the liquid. This is known as the Total Dissolved Solids (TDS) and is often expressed as a mass percentage. In brewed coffee, a typical TDS is about 1%.

Usually when people refer qualitatively to how “strong” a particular cup of coffee is, they are responding to their perception of the TDS. However, the quality of the brew is also governed by the percent extraction (PE), which refers to the percent weight of solids originally in the coffee grounds that were transferred to the liquid phase. In other words, the PE is how much of the solid coffee mass is removed from the grounds to the water. The optimal range is usually within 18 to 22%.

There’s no easy way to measure PE, bur you can calculate it indirectly using mass balances. Looking at solids coming in and out, we know that \[m_{\text{dry grounds}} = m_{\text{spent grounds}} + m_{\text{coffee solids in brew}}\]. We’re obtaining the mass of coffee solids in the brew by measuring the TDS, so this equation becomes \[m_{\text{dry grounds}} = m_{\text{spent grounds}} + \frac{TDS}{100} \times m_{brew}\].

Next, the percent extraction is defined as “how much pf the original solids were removed into the liquid”, so we have \[ m_{\text{spent grounds}} = (1 - \frac{PE}{100}) \times m_{\text{dry grounds}}\]. Substituting this into our mass balance gives us our final expression, where \[ PE = TDS \times \frac{m_{brew}}{m_{\text{dry grounds}}}\].

Hopefully, this result is intuitive: the higher the TDS in the brew, the higher the extraction from the solid phase must have been. The important point is that measurement of the brew TDS, along with weighing the dry grounds and the brew, gives an estimate of the percent extraction, and a useful measure of whether you are under- or over-extracting your coffee.

Part 1: Brewing

1a: Surface Area

  1. Measure the TDS of plain tap water.
    A normal reading will be around 0.01% to about 0.05%.

    TDS of water: ____________________ g

  2. Perform three brews to assess the effects of varying surface area. Use the same brew ratio, water temperature (94 C), and extraction time (4 to 5 minutes), and compare 3 different grind sizes:

    i. Coarsely ground (as course as you can make it, or even whole bean)

    ii. Medium ground

    iii. Finely ground (as fine as you can make it)

  3. Measure.
    For each brew, measure the TDS and the mass of the brewed coffee. Remember to let your sample cool before measuring the TDS and wipe with a Kimwipe after each measurement.

1b: Temperature

  1. Measure the TDS of plain tap water.
    We will be getting three total measurements to get a standard deviation and make sure that the TDS meter is still calibrated properly.

    TDS of water: ____________________ g

  2. Perform two brews to assess the effects of varying temperature. Use the same brew ratio and extraction time as before, and a medium grind size. Compare 2 different temperatures:

    i. Moderate temperature (70 C)

    ii. Very hot temperature (99 C)

  3. Measure.
    For each brew, measure the TDS and the mass of the brewed coffee.

1c: Extraction Time

  1. Measure the TDS of plain tap water.

    TDS of water: ____________________ g

  2. Perform two brews to assess the effects of varying extraction time. Use the same brew ratio, medium grind size, and 94 C temperature. Compare 2 different extraction times:

    i. Short time (1 minute)

    ii. Long time (10 minutes, with small samples every minute)

  3. Measure.
    For each brew, measure the TDS and the mass of the brewed coffee. For the ten minute trial, give the carafe a gentle stir to mix, and dispense a very small sample into a paper cup or beaker once every minute.

Part 2: Analysis

You should create a report that includes the following:

  • A labeled column chart that shows the TDS value for each of the 7 brews
  • A labeled column chart that shows the PE for each of the 7 brews
  • A scatterplot of TDS vs extraction time

In your discussion, you should answer:

  • What is the TDS of tap water? Do you think the number you obtained is reasonable? Why or why not? What is the TDS in PPM?
  • Which variable had the most pronounced effect on TDS? Why do you think this is the case?
  • Likewise, which variable had the most pronounced effect on PE? Did you see any differences in trends with PE when compared to the trends in TDS? If so, what might account for these differences?
  • Recall that the ideal extraction is typically considered to be about 20%, with a TDS near 1.3%. Which brew was closest to these ideals? What is the TDS of this brew in PPM?
  • Describe how the TDS varied with extraction time. Why do you think it behaved like this? What do you think would’ve happened to the TDS and PE if you let it brew for 20 minutes?