UPDATE 20/5/16 – This post has been updated following feedback from Greg Scace. His original piece of work for a talk at Toby’s Estate in Australia and contains the theories and observations that helped shape our hypothesis.

“There’s not a problem that I can’t fix, ’cause I can do it in the mix” – Michael Cleveland, Last Night a DJ Saved My life, 1981

This a companion piece to Michael Camerons “This Low Pressure Rehash”. Whilst it’s not essential to have read that before continuing, it’d probably help.

Michael does a great job of taking us on his journey from brewing traditionally to exploring all of the parameters he could in search of flavour. What’s all that go to do with me? Well, it turns out that he came across a previous Marginal Gains post from a year ago, where we had experienced what he did: that dropping our pump pressure seemed to improve the quality of our espresso’s. So we got talking, new theories cropped up and we sought counsel from other sources (notably Greg Scace and Chris Hendon) in an attempt to explain what we were observing. A task that has fallen to me.

So, what were we observing? Simply that by rethinking how we view the interactions of the brewing variables for espresso, regardless of the traditional norms, we had vastly improved the final product.

Or as Michael described it: “I was staring down at my cup, trying to comprehend what I was drinking. Sweet, dense, lip-smacking acidity, voluptuous, concentrated, complete ctrl-alt-delete, reset my brain.”

What he was drinking was espresso brewed at his usual brew ratio, brewed at 92.5c, for +10 secs brew time, at 6bar, with a consistent tamp pressure and using a Mythos.

But in the meantime follow me now as we take a journey into extraction and puck dynamics.

I’m going to cover each of those variables in Michael’s shot, but to attempt to explain and build a hypothesis, we’re going to have to simplify things. Let’s start with the Noyes-Whitney equation;

Rate of Dissolution = A x D/d x (Cs-Cb)

The Noyes-Whitney tells us how fast things dissolve by linking various factors to the speed of dissolution. In our case this will tell us how fast the soluble coffee dissolves into the water. Let’s go through each of those factors individually.

The Rate of Dissolution, is the speed at which a solvent dissolves a solute, in our case it’s how fast the water acts on the soluble compounds in the coffee. This gives us an extraction speed.

A is the surface area of the interface of solvent and solute. Its affected by both grind size and particle irregularity. This is why by grinding finer, we speed up extraction.

D is the diffusivity coefficient. It is a constant between two species and expresses how likely it is two substances will diffuse into each other, i.e. the higher D is the faster diffusion, our extraction, happens. It is an exponential function of temperature. So as temperature rises, diffusivity rises exponentially. In this way by manipulating temperature, we vary the likelihood for dissolving different compounds, and so alter the taste.

d is what’s known as the boundary layer. This surrounds the coffee particle and is the region between Cs (the concentration at the surface of the coffee) and Cb (the concentration in the brewing water) and can be influenced by flow velocity.

Cs-Cb is the concentration gradient. In our case this is the difference in concentration of solutes between the coffee and the brewing water. A larger difference means a larger rate of dissolution.

What can we take from this? Firstly we can see why surface area and temperature are so important to extraction. Raising both increase the rate of dissolution. One last point before we move on, diffusivity and the concentration gradient are linked. If we are able to diffuse a compound more easily, the rate at which the concentration gradient reduces will increase.

We’ll refer back to the Noyes-Whitney equation, but for now let’s consider our coffee puck. Michael already described the importance of a consistent tamp pressure, to ensure a consistent force is applied at the interfaces between coffee particles. When combined with a consistent distribution of particles this creates a consistent and uniform puck density. This should be your goal, to make your density gradient within the puck as close to zero as is possible. Why? Because this is going to influence fluid flow.

In an ideal situation we can use Darcy’s law to relate the velocity of the fluid flow to both the pressure drop through the puck, and the overall puck depth. So as we drop the system pressure, we also drop the pressure gradient across the puck, and so the velocity of flow.

“Note from Greg Scace – Darcy’s law will work if we hold all things constant with respect to the aggregate of effective cross sectional area of the flow path. But we don’t really because that cross sectional area changes as dissolvable solids are removed from the ground coffee. Darcy’s law isn’t going to apply if we change grind size.”

Lower flow velocity may also alter any potential fines migration, boundary layer depth and it certainly decreases instances of channelling, but it’s the interaction with heat transfer that we are interested in.

Heat Transfer in coffee brewing goes, as in all things, from reservoirs of hot to cold. We are primarily concerned with Convective Heat Transfer, which is made up of:

Conduction – this is the transfer of heat across the surface interface between two substances by random interactions between particles, it’s also known as heat diffusion.

Advection – this is heat transfer due to bulk fluid flow and actually describes convective heat loss as it is commonly known.

Conduction is a function of both the temperature gradient across the surface between the two substances and the area of that surface, so as grind finer, we increase the capacity for thermal conduction. Dry coffee is a fantastically bad conductor of heat, this helps us if we consider the two masses, water and coffee, to be discrete individual thermal masses. This model, called Lumped Capacitance, leads in to Newton’s Law of Cooling which states that the rate of cooling is directly proportional to the temperature gradient. This model will be of use until the puck has become saturated, at this point the rate of heat transfer approaches that of the brewing water.

So why is all this important? If we think about our puck, the coffee at the top gets exposed to all of the heat. This means that the next layer of coffee will see less heat, which in turn makes the heat transfer and dissolution that little bit slower, on and on until we reach the bottom of the puck. Calculations by Greg Scace show that for a 19g dose to a 35g shot weight, this effect can lead to a 7c drop in water temp from top to bottom.

What this means is that Diffusivity is greater at the top of the puck than at the bottom and so is extraction rate!

Extraction under these conditions will always be uneven, your espresso will always be a melange of flavours and extraction levels.

If we are initially dealing with a lumped capacitance model, then it may be reasonable to posit that the driving force of the heat transfer is advection not conduction, given that the flow of water through the puck speeds heat transfer by dragging it away from the surface. Darcy’s Law can be used to show that advection is directly proportional to both the temperature gradient and the flow velocity, so if we reduce either, we reduce the heat transfer by advection. Basically if we change the temp difference or flow velocity, we change the rate of heat loss.

“A note from Greg Scace – Heat transfer is by a combination of both convection and conduction. What we should keep in mind is that energy moves into the coffee from top to bottom, and there is more energy available at the top, compared to the bottom.”

Okay, time to pull all this back together let’s re-look at our shot; “espresso brewed at his usual brew ratio, brewed at 92.5c, for +10 secs brew time (over his 9bar recipe), at 6bar, with a consistent tamp pressure and using a mythos.”

• To brew at 6bar, you have to change your grind from a usual 9bar set-up, probably a little coarser as you need less resistance.
• But, to increase the time sufficiently you’ll need to grind a whole lot finer to keep the same brew ratio. This further reduces our flow rate at the start of the shot and increases the dwell time in the puck. It will also increase the rate of dissolution as per the Noyes-Whitney equation by increasing area.
• Flow rate will increase as we take out solutes, but will still be reduced due to a lower pump pressure.
• By slowing the flow rate, and so velocity, we have potentially reduced the rate of convective heat transfer. This would result in more heat energy being available to other portions of the puck, raising diffusivity and so the rate of extraction as well as greatly influencing the flavour compounds that are extracted.
• By brewing @ 92.5c we have reduced the diffusivity slightly, reducing the rate of extraction.
• The Mythos creates dry coffee grounds at a raised temperature (40-50c). This causes a reduction in the temperature gradient, meaning less heat energy is needed to raise the coffee to near brew water temp. For me the Mythos is key to what is happening here.
• The consistent tamp pressure and lower pump pressure allows for a more uniform flow when combined with accurate distribution to create a uniform density, leading to reduced channelling and a more uniform extraction.

There’s a lot of things going on there, lots of pluses and minuses that would appear to balance out. Through this we can influence the diffusivity of a myriad of compounds, altering sweetness, balance and acidity.

Hypothesis: Brewing at both reduced pressure and reduced water temperature combined with a consistent tamp pressure and elevated dry grinds temperature over an extended time frame, results in a more uniform extraction within the puck.

If the above proves anything it’s that we need to be more flexible in our approach to espresso brewing. Consider that espresso brewing is really just a pour over under pressure, a brew method where we control the water flow through the coffee rather than controlling the steep time. Our job is to move those sliders to balance the extraction of flavours. Only rather than adjusting the tone, we manipulate the temperature, flow velocity and contact time to alter the flavour compounds we extract.

When it comes to maximising your extraction, its all in the mix.

Originally published on FCP Coffee.