What Affects Brew Time

[Edit October 23, 2019: Kevin Moroney pointed out to me that the slurry getting concentrated as it passes through the coffee bed also makes it more viscous as it reaches the bottom layers in a V60. This is indeed a very valid point, so I added a paragraph about this in the viscosity discussion below. In practice, this effect depends on the more direct variables of (1) brew recipe, (2) dripper geometry, and (3) the type of coffee, so it doesn’t change the final list of directly controllable variables that affect brew time. I still thought it is valuable to discuss it. ]

If you are used to pulling shots of espresso, measuring shot time might be a tool you use often to determine whether your grind size was dialed in appropriately for that coffee and set-up. This may lead you to believe that total brew time is also a very useful concept in the context of pour over filter coffee, for example to communicate your preferred grind size.

I think that this is really not the case, and I’d like to lay down the reasons why. I’m even slightly skeptical that shot time in the context of espresso is that useful especially when communicated online to different baristas that live in different conditions, but I don’t have any strong opinion about espresso making, because my lifetime cumulated number of shots pulled is currently a grand total of 1. So, at least for now, let’s focus on pour over coffee, as I usually do.

The reason why I think brew time is not that useful is simple: I think there are way too many variables that affect it, several of which are almost never measured, and some of which would be hard to always measure accurately. I’m personally striving at eventually measuring all of them such as to make my brews as repeatable as I can, but I’m not even sure yet whether that’s a realistic goal at all.

If we want to understand what affects drawdown time, it’s very useful to turn to Darcy’s law; this is an empirical equation that describes how a liquid percolates through a porous solid medium. In other words, it was originally deduced directly from observations and experiments rather than from fundamental concepts of physics. We now know enough about the physics of hydrodynamics that it can be derived from more fundamental principles, but it is only valid under some specific conditions which are almost always respected in coffee brewing, and more generally in daily life.

For the more mathematically inclined, let’s have a look at Darcy’s law applied to a liquid flowing down through a cylindrical medium, and then I’ll explain it with words:

In the equation above, Q represents the discharge, which is the volume of water coming out from the percolation medium in units of volume per time (e.g., mL/s). k is the permeability of the porous medium, which can also be though of as the inverse of its resistance. A more permeable medium will let more water pass through in a fixed amount of time; the physical unit of k is a surface (e.g., m²). A is just the surface area of the medium (remember we are applying Darcy’s law in a cylindrical geometry, so A is the same at all depths). μ is the dynamic viscosity of the liquid; it is low for most of the pure liquids we encounter in daily life such as distilled water and alcohol, but can get very large for more complex or heterogeneous stuff like honey or olive oil.

Dynamic viscosity is sometimes also called absolute viscosity, and it represents how much a liquid resists to deformations. The more viscous a liquid is, the harder it will be to pass it through small pores. L is the total length of the percolation medium, which in our case usually corresponds to the depth of a coffee bed. ρ is just the mass density of the liquid (for example in kg/m³), g is how fast objects accelerate when falling freely at the surface of the Earth (approx. 9.8 m/s²) and h is the total height of the column of liquid that is percolating (also counting the liquid above the surface of the solid medium). Δp refers to the difference in pressure below versus above the percolation medium (in physics and maths, we use this weird upward triangle to represent a variation or a change). In the context of espresso, this would be the atmospheric pressure (below the puck) minus the pressure a machine applies on top of the coffee bed. There’s a minus sign here because of how we defined the pressure differential, such that a downward pressure results in a positive flow of liquid.

Those of you who have worked with Darcy’s law may not have encountered it in the form above: it is often shown in a simpler form where the ρgh term is ignored, because it is often applied in a context where the pressure applied on the fluid is much more important than the fluid’s weight (as is the case with espresso). But for pour over coffee, we are in a context of gravity-driven flow, and therefore this more general form of Darcy’s law is useful.

Now that we defined all the terms in Darcy’s law, let’s explain it with words in the context of coffee. Basically, it says that any of these changes will make water flow come out from under the at a faster rate:

• A more permeable coffee bed;
• A wider coffee bed;
• A shallower coffee bed;
• Water that is less viscous;
• Water that is denser;
• Brewing from the surface of a denser planet;
• Applying pressure on top of the coffee bed.

These changes are combined and independent of each other, and they are also linear, which means that doubling any of the things mentioned above will double the flow, for example. The geometry of the brewer won’t change all of these relations, and will only add a constant of proportionality (i.e., a number) in front of the right-hand side of the equation.

As you can imagine, the faster water flows through the coffee bed, the shorter your brew time will be. Therefore, we can look at all of these terms in Darcy’s law as potential variables that will affect brew time. You can already start seeing that there are quite a few of them, but it’s even worse than that; some of the terms above hide more than one variables that are combined together. The most dramatic one is permeability; in the context of pour over, it is affected by the following variables:

• The grind size (coarser coffee is more permeable, finer coffee is more resistive);
• The permeability of the coffee filter (affected by its pores and thickness);
• The ridges on the inside of the brewer’s wall and filter creping (they allow air to flow upward outside the filter and increase permeability);
• The saturation of the coffee bed (a coffee bed saturated with water increases its permeability, which is probably the most important reason why we bloom).

If you though this was starting to look like a rabbit hole, brace yourselves, because grind size also hides several other variables:

• The grind size that you set your grinder to (which will differ even between two units of the same grinder model);
• The grinder rotation rate (a faster rotation will generally produce finer grounds);
• The grinder design;
• The grinder burr size, geometry, material and alignment;
• The bean temperature when you grind them (here’s a paper about that and another interesting discussion, but I want to discuss this more in the future). 
• The bean terroir, varietal, processing, roast development, and aging − all of these variables affect the bean hardness and density, which will make it shatter less or more during grinding. I will talk more about this in a future post, but if a coffee shatters more, it will generate more fines and result in a less permeable coffee bed. The exact defects and variations in green coffee bean ripeness, humidity will also likely have an effect on roast and shattering.

The width and depth of the coffee bed can be expressed as being dependent on more intuitive and practical variables:

• The dripper geometry;
• The dose of coffee (in grams);
• The mass density of coffee (less dense coffee will result in a deeper bed for the same dose).

Ah, finally… we listed all the variables.

Nope ! We are far from being done. You might think that the viscosity and density of water are known, fixed quantities, but they are not: they depend on its temperature ! The effect of changing water density is very small in the context of coffee brewing, as this data illustrates:

At sea level atmospheric pressure, the difference of room temperature vs boiling water density is just about 4%. The change in viscosity, however, is not small. I talked about this a little bit in an earlier Instagram post, where I built this graph of water viscosity (in red) from literature data (specifically, IAPWS 2008 and Engineers Edge Machinery’s Handbook):

The difference between room and boiling water viscosity is therefore about 70% ! In the figure above, I also marked some typical slurry temperatures I obtained with a glass or plastic V60, and how the flow is affected if everything else is kept constant (in blue).

As you can see, warmer water is significantly less viscous, and it will therefore flow faster through the coffee bed. And please do not go thinking I am talking about kettle temperature here ! I don’t only say this because kettle thermometer readings are not reliable (which they are not in my experience), but also because kettle temperature is only one of the variables that will affect the temperature of water as it percolates through the coffee (i.e., in the slurry); these additional variables will also significantly affect the slurry temperature:

• The dripper material (i.e. both its thermal mass and conductivity);
• The room temperature;
• Any air flow in the room;
• The temperature of your ground coffee;
• The moment during the brew (temperature will typically fluctuate);
• How many pours your recipe has (more pours tend to result in cooler slurries).

The viscosity of water is also affected by its hardness and total alkalinity (I talk about these concepts in detail here), but the effect is very small unless you have very unusual water. Let’s quantify that a bit more. According to this scientific publication, the viscosity of water does depend on its bicarbonate content:

To put this into a bit more context, the addition of Na2CO3 at a concentration of 1 mol/L would result in a total alkalinity of 2000 meq/L, or in units we are more familiar with, about 100,000 ppm as CaCO3. That much bicarbonate is needed to almost double the viscosity of water. Given that brew water recipes for coffee are almost mostly below 80 ppm as CaCO3, we can safely ignore the effect of total alkalinity on viscosity.

The viscosity of water is similarly affected by its general hardness, here’s an example of how it increases as Calcium Chloride is added to water:

Yet again, we are talking about a 10% concentration (by mass) for a doubling in water viscosity, which is insanely larger than typical water hardness we use for coffee: even achieving the “Hard AF” Barista Hustle hardness with calcium chloride would necessitate less than 0.03% concentration by mass. We can thus also safely ignore the effect of water’s total hardness on its viscosity, and only care about its temperature.

There is another thing that affects viscosity in the slurry; the concentration of coffee compounds being extracted from the coffee particles. In espresso brewing, the high concentration of the beverage can cause it to become 2 to 3 times as viscous as the input water (e.g., see Clarke & Vitzthum 2001). For filter coffee, we can expect the effect to be much smaller, about a 30% increase if we assume it is a linear function of concentration. This is still not negligible, and means that the viscosity of water near the bottom of the coffee bed will flow a bit slower because if this higher concentration, therefore making the global flow slightly slower than one would expect based on pure water. However, for a fixed brew method, dripper geometry, and coffee type, the profile of concentration versus depth and time should be the same every time the coffee is brewed, so this effect can be categorized under the umbrella of these three more direct variables.

We have still not unwrapped most of the variables between the big parentheses of Darcy’s law, and those are the ones that make pour over timing much nastier than espresso timing. In the case of espresso, the Δp term is much larger than the ρgh term, and this means that repeating the exact same pressure profile every time will ensure that the shot time only depends on the variables we already studied above.

As we won’t be brewing coffee on the surface of Mars (that would suck), there is only one other variable we haven’t considered, and it’s not a fun one: the height of water in your V60, or h, is what makes pour over timing much harder. This is true mostly because it depends on one input variable that we control and measure only rarely: the rate at which we pour water from the kettle. Someone that pours a lot of water very fast in a single pour will build a very tall column of water in the V60, and it will flow much faster, and finish brewing much before, a barista who pours slower or in several smaller pours. Similarly, the bloom length will obviously affect the total brew time because it’s a period where no water is being poured from the kettle. The geometry of the dripper also has an effect on the height of the water column, but that’s much easier to control or keep constant.

There are also circumstances during pour over brewing where Darcy’s law fails, although typically only momentarily. Darcy’s law is valid only for a fixed porous medium, and there are a few things that can change the structure of the coffee bed, which is our porous medium:

• The preparation of the coffee bed (distribution, bloom, swirling after bloom, and tamping in the context of espresso);
• The amount of agitation: water poured faster or from higher up will lift the upper parts of the coffee bed and temporarily make it shallower, increasing flow (using devices like the Gabi B or Melodrip will eliminate most or all agitation);
• Channeling: the appearance of a large channel can increase the coffee bed’s permeability;
• Erosion, also called fines migration: finer coffee particles being displaced to the bottom by water can decrease the permeability of the coffee bed. This can also cause the filter to clog, which will decrease the permeability even more.

Another possibly important factor that may affect brew time is how much coffee particles swell during the bloom phase. As coffee swells, it slightly closes the gaps between particles, effectively making the coffee bed less porous. I’m not sure what properties of coffee affect how much they swell, but it’s possible that beans of varying hardness or particle porosity may swell differently.

There’s also one final thing that can easily be forgotten: the exact way in which we choose to define the start and end of a brew is also a factor. For pour over coffee, an obvious choice of when the timer starts is when kettle water hits the dry grounds, but the moment where the brew ends is a bit less obvious. I personally choose to stop the timer when the level of brew water just passed the surface of the coffee bed and I can see ambient light first reflecting on the surface of the wet coffee; I mostly choose this moment because it’s easily repeatable.

I think we have now finally detailed all of the most important variables that affect brew time ! But hey, maybe I forgot about others. If you think about more, I’d love to hear about it, but please don’t send me suggestions about light speed travel and kiloGauss magnetic fields lol.

It would be useful to regroup all of the important variables that we discussed above, in terms of what we can control directly when brewing (i.e., not viscosity), so here’s an extensive list:

• Grinder setting, rotation rate, model, zero point, burrs and alignment;
• Coffee terroir, varietal, processing and other bean characteristics (defects, drying, ripeness etc.), exact roasting process and development and bean aging;
• Dripper model (geometry, material, inner wall ridges);
• Exact brew recipe (bloom length and efficiency, number of pours, pressure or suction devices, coffee dose, pressure profile in the context of espresso);
• Brew temperature;
• Kettle flow speed and height, or anything else that affects agitation;
• Room, bean and grinder temperature;
• Exact filter model (e.g., Hario tabbed and tabless are different);
• Air currents in the room;
• Coffee bed distribution and preparation (and tamping if applicable);
• Channeling and erosion;
• How the brew start and finish are defined.

Now, if you want to have a consistent brew time, you need to measure and control and fix all of the things above, which is no easy feat. If you want to use brew time to communicate grind size, not only the two persons talking need to have the same grinder, zero point, and burr alignment, they must also be drinking the same coffee, have the same exact dripper, filters, water temperature, recipe down to the pour rate, etc. You can see why I think brew time is not that useful for communication ! If you are insane like I strive to be and measure most of the things above, then and then only changes in brew time will inform you that something is going on.

I’d like to thank Kevin Moroney for useful comments.