MARGINAL GAINS - IT'S ALL IN THE MIX

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…….. I’ll wait here.

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, and it forms a nice trilogy alongside these two posts. 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, because what the fuck am I drinking?”

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. It’s a bit of a mouthful, and I’ll sum it up later with one of my patented analogies (baseball anyone?).

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. To be frank research into fluid flow and dissolution in granular packed beds has been going on for decades now, by people far cleverer than us and with far bigger resources, these are incredibly complex problems that may not be solvable numerically in 3 dimensions. So what we are aiming to do is work with an ideal system and use that as an overview of what we think may be causing the dramatic differences in flavour we experienced.

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. It’s a fundamental measure of mass transfer and is used widely in the pharmaceutical industry, amongst others. But 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. Its is an exponential function of temperature. So as temperature rises, diffusivity rises exponentially. This is one reason why extraction is faster at higher temperatures. It’s important to note at this point that each of the 1000’s of dissolvable compounds in coffee will have it’s own value of D with relation to water. 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. This helps explain why the majority of the extraction we see happens early in the brew, when the Cs-Cb is at its highest. Cs-Cb will also be higher at the top of the puck than at the bottom as the water reaching the bottom of the puck already contains dissolved solids. It also limits our total extraction as if there is no concentration gradient, there is no dissolution, or in our case extraction.

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. But that's not all, by varying the temperature we can alter both the rate of dissolution and the diffusivity of our solutes. In this way we can influence not only how much we extract, but what we extract. Hold on to that thought, we’ll come back to it later. 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. This will not be equal throughout the whole puck, and is one of the key things we will manage later.

We’ll refer back to the Noyes-Whitney equation, but but for now let’s consider our coffee puck. In strict terms this a packed granular bed, but I’m going to keep calling it a 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 (from line pressure to atmospheric), and so the velocity of flow. In terms of what we are considering now, this is the key point.

“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. You see this when the flow rate changes during the course of brewing the shot. Darcy’s law isn’t going to apply if we change grind size. The space between particles is gonna be different, so effective cross-sectional area of the flow path is different.” Whilst I agree with Greg, our aim is to simplify the system, so we’ll stick to the ideal situation."

Lower flow velocity may also alter any potential fines migration, boundary layer depth (although this looks incredibly complicated for any more than one particle!) 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. Imagine the heat energy being passed along from hot to cold by a lot of jostling molecules….when you touch something hot and it burns you, that's conduction.

Advection - this is heat transfer due to bulk fluid flow and actually describes convective heat loss as it is commonly known. Its why if you leave something hot, a cup of coffee for example, in a breeze it will cool quicker. The breeze facilitates the flow of heat away from the drink.

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. What we do know, apart from the fact that heat diffusion works in a similar way to the diffusion of coffee solutes if left to steep in water, is that 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. I.e. heat transfer within the mass is so much quicker than diffusion out of the mass that it is almost instantaneous, therefore each mass is considered to be at the same temperature at any point. (This is what i was talking about when referring to ideal situations.) 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” so the bigger the temperature difference, the faster the exchange of heat. This model will be of use until the puck has become saturated, at this point the dry coffee is full of water, so the rate of heat transfer approaches that of the brewing water.

Still with me? Good. So why is all this important? If we think about our puck, the coffee at the top gets exposed to all of the heat, I mean all of it. Heat transfer occurs pretty quickly too as the higher the temperature gradient, the faster the rate of transfer. 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!

Gah!!!! Here we are trying to aim for an even extraction, and it’s never been possible!! Extraction under these conditions will always be uneven, your espresso will always be a melange of flavours and extraction levels. This is all very interesting, but it doesn't offer any explanation for what we found yet.

Okay, back to Heat Transfer. 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. If we can do this, it follows that less heat energy will be transferred. 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. The movement of heat into the puck is by forced convection. 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. The reason for that is that as energy is given up to the coffee via diffusion of heat near the top of the cake (conduction), it becomes unavailable to heat the coffee particles further down in the cake. Thus there is less available energy at the bottom compared to the top. “

Take a break and grab a coffee if you made it this far, its been a long haul but thanks for sticking with us.

Okay, time to pull all this back together let’s re-look at our shot;

“What he was drinking was 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.“

(Yeah, I quoted myself, so what I was feeling it.)

Let’s ignore brew ratio for the moment, and assume it’s of little interest. But what else is happening?

• 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 (and extraction) as per the Noyes-Whitney equation by increasing area. Why 10 secs? that was the extra brew time needed to balance the flavours again. Don't believe me? check this data out. Also note how the Extraction % has no relation to taste or balance.
  

• 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. It’s worth noting that this may be offset by the longer dwell time from grinding finer.

• 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 within a known range (40-50c). This is higher than most other grinders and causes a reduction in the temperature gradient, meaning less heat energy is needed to raise the coffee to near brew water temp. In theory this should free up more heat energy from the upper sections of the puck and allow a higher rate of extraction in the lower sections. In the 19g shot mentioned earlier, this effect would raise the temp at the bottom of the puck by as much as 1c for every 7c of increased dry coffee 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. This leads reduced channelling and with a potential for more even thermal distribution, a more uniform extraction.
  

“ A note from Greg Scace - One thing that needs to be discussed is that we have a model that we know to be correct. Noyes Whitney is just as valid for coffee as for any other system of solute and solvent. Of interest are things that deviate from the model. For example, local channelling has the result that local flow rate increases, thus increasing the local available energy, increasing the concentration gradient, and changing the boundary layer thickness. Local overextraction occurs and underextraction occurs elsewhere. We assume more or less uniform flow through a uniformly behaving bed (across the bed, but not top to bottom). If our extraction times for a given shot mass are consistent, then the assumptions of uniformity across the cake are probably pretty good. If not, then we have deviations from our assumption that things are uniform. Noyes Whitney still applies, but it applies differently than we think it does. Gentle pre-infusion cycles and other strategies to prevent channelling seem like a really good idea to me. To me, this seems like the simplest benefit of a low-pressure brewing strategy. Higher pressure may work well with systems that perturb dry coffee the least. Examples of such systems would be groups with spring-loaded preinfusion chambers.”

There’s a of of things going on there, lots of pluses and minuses that would appear to balance out. Conveniently they are all interconnected by a control of temperature and heat flow. Through this we can influence the diffusivity of a myriad of compounds, altering sweetness, balance and acidity. We can also create a more uniform extraction from top to bottom of the puck, creating a more consistent extraction throughout our dose, still a melange, but a different one and that’s what we think is happening here.

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.

Although this is a lot of rehashing of previous knowledge, we've come at it with a new perspective and new information. We've also learned during the process. I hope and encourage you to explore this and prove us wrong or right.

If you've stayed with me this far, then this is the part where you get you the take home message.

If the above proves anything it’s that we need to be more flexible in our approach to espresso brewing, (that and the science of flow through the puck is stupidly complex). 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. How many different variables do you tweak and change when brewing a filter coffee? Moving the time, grind, temp, flow speed in relation to each other like the sliders on a mixing desk in order to maximise your flavour? The sound engineer's job is to produce the best balance from the available frequencies, 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.