The science of espresso, with a dash of geology

Almost every morning, I start the day with an experiment on flow in porous media. First, I generate some fine-grained sediment with a well-defined average grain size and proper sorting; then I use that sediment to fill a little basin of sort and try to mimic compaction. Finally, I use a machine to put water under pressure and force it to flow through this miniature sedimentary basin. Then I sit down to drink the fluid which is not simple water anymore, due to its interaction with the grains; and its taste and consistency tell me whether I got the grain size and the porosity right.

That's a geologist's view of making espresso. Unless you have a fully automated and ultra-expensive espresso machine, creating a high-quality caffeine concoction is not trivial, because the water must have the right temperature and has to spend the right amount of time in contact with the coffee grains that have the right size. The right temperature is 85–95 °C (185–203 °F), and, at least with our simple machine, the trick is to start the brewing at the right time. Better espresso machines do not use steam to generate pressure because that makes the water too hot; instead, they have a motor-driven pump that generates the ~9 bars of pressure. The correct grain size is easily achieved with a burr grinder (as opposed to a simple blender); a good espresso grind is a fine grind, because the water spends relatively little time in contact with the grains.

The duration of this contact is the most difficult bit to get right. To get a good shot with lots of crema, it cannot be less or more than 20 to 30 seconds. Not just grain size, but grain sorting as well play a role. If the coffee grinder produces a poorly sorted 'sediment' (and that's what a blender does), the coffee will not be porous and permeable enough. Another factor is how well the sediment is compacted; that is, how much pressure do you apply to the coffee during tamping. This affects permeability again. Finally, it matters how much coffee you put in the coffee holder; the thicker the layer that the water has to go through, the longer the trip becomes for the same amount of water.

After using the machine hundreds of times, I still manage from time to time to produce something undrinkable. The art and science of espresso making started to make more sense once I started to think of it in terms of Darcy's Law.

Henry Darcy was a French engineer who initially had made a name for himself by designing an enclosed and gravity-driven water-supply system for the town of Dijon. Later he had time and opportunity to do experiments of his own interest. In 1855 he measured the discharge of water under variable hydraulic heads through sand columns of different heights, and found that the discharge was directly proportional with the hydraulic head and inversely related to the height of the sand column:

Q = AK(H1-H2)/L,
where A is the cross sectional area of the sand column, L is the height of the sand column, K is the hydraulic conductivity (which is constant for the same granular material and same fluid), and H1-H2 is the hydraulic head. This is Darcy's drawing of his experimental setup:



The hydraulic conductivity depends on both the properties of the fluids and of the granular material; these properties are the viscosity and density of the fluid, and the permeability of the sediment:

K = kρg/μ,
where K = hydraulic conductivity, k = permeability, ρ = fluid density, and μ is the dynamic viscosity.

In coffee speak, the hydraulic head is given by the pressure generated by the machine, and is fixed; one cannot change the density and viscosity of water either. The most important variable is coffee permeability, which is influenced by size, sorting, and packing (compaction) of the coffee grains. Also, it helps if you get the value of L right, that is, you shouldn't try to save coffee.

Darcy's Law was established with some simple experiments, and it has since then been generalized and derived from the Navier-Stokes equations, but it has a huge range of applicability, from ground-water hydrology to soil physics and petroleum engineering.

Add to that list everyday espresso making.

ps. Fantastic resource on Darcy's work and his law here.

Earth, water, wind, and fire: 'Lava viewing' in Hawaii

Our Christmas gift to ourselves was a little trip to the Big Island of Hawaii, something we were thinking (dreaming) about for a long time. There are many great posts about the Hawaiian volcanoes on the geoblogosphere (see for example the ones here and here); I will try to add a few notes and pictures without being too repetitive (and will try to seem less ignorant in volcanic and hard-rock matters than I actually am).

Probably the most memorable experience we had was the lava viewing at Kalapana. This is where 'officially' you can get relatively close to the place where the lava from Pu`u `Ō`ō enters the ocean. The USGS has a nice website with updates on what's going on. I was so anxious to see this place that we had to go there on our first day in Hawaii, that is, on December 22. You have to drive all the way to the end of road 130; there are some big 'No trespassing' signs at one point, but everybody seems to ignore them, and there is an official parking lot at the end of the road, way beyond the 'no trespassing' signs. It is best to get there 30-60 minutes before sunset, and to stay until it's completely dark, to see the potential show both in daylight and in nighttime darkness. Unfortunately, on December 22 we didn't see much, apart from a beautiful sunset and a few small puffs of steam:

Sunset at the Kalapana viewing site on December 22, 2008

That was a bit of a disappointment, but I knew I had to give it another try. After talking to a ranger from Volcanoes National Park, we drove back to Kalapana five days later. This time, the show was definitely on. More than that, it was spectacular. A huge column of steam formed where the active lava tube spills the lava into the sea, and repeated explosions painted red the lower part of the column. From time to time, several tornado-like funnels formed and connected the steam cloud to the ocean.

Steam cloud with mini-tornadoes on December 27, 2008; lava-viewing boat on the left for scale

As the sun goes down, the explosions become more colorful and more obvious

S-shaped funnel between the steamy sky and cool hot ocean

This was such a uniquely beautiful scene. I wish we went there more than two times, because the whole spectacle changes as a function of the activity of lava flow, weather conditions, the direction and nature of lighting.

I have also learned that it is not easy to take good photographs of fast-moving and rapidly changing distant things in the dark. Here is the proof:

Zoom, baby, zoom*

For a few months now, I have been spending (wasting?) some time with a gadget called Gigapan, a robot that can take hundreds of shots of the same scene with a simple point-and-shoot camera. The pictures are taken in a well-defined rectangular grid pattern so that there is the right amount of overlap between all neighbors. Later the photos can be stitched into a gigantic photograph on a computer and shared with the world through the Gigapan.org website and, even better, through Google Earth. [If you are a tiny bit familiar with geoblogs, you must have seen some of the gigapans that Ron Schott has put together; he is one of the earliest and most enthusiastic adopters of the technology and has assembled an impressive set of panoramas on the gigapan site.]

I have to confess that I had to actually buy this thing and start playing with it to realize how different gigapixel panoramas are from the usual few-megapixel digital photographs. The idea is simple: a ten megapixel camera takes photos that contain ten million pixels; if you put together a 10x10 grid of such photographs into one image, you end up with a gigapixel panorama. Because some overlap is needed between the photographs, more than 100 pictures are necessary to exceed the gigapixel limit. But the point is that the more pixels there are in a photograph, the more information it contains and the more sense it makes to zoom in and see the details - details that are usually non-existent in a conventional digital picture. The other side of the coin is that it is only worth taking gigapans of scenes with plenty of small-scale and variable detail (although I am getting to the point that I see a potential gigapan everywhere).

I do not think that gigapixel images will replace conventional (that is, megapixel) photography. There is only a limited number of things that the human eye can see at one time; and often the value of a good photograph comes not from the pixels it captures, but from the ones it consciously ignores. Beauty and the message an image can hold are scale-dependent; and zooming in to see the irrelevant detail could be a distraction.

That being said, I am all for taking home as many pixels as possible from outcrops and landscapes in general. The gigapan system is simple and works surprisingly well, and it *is* exciting to explore big outcrop panels from the scale of entire depositional systems to the laminae of single ripples or even grains.

No photos or panoramas posted/embedded this time; but here is a link to my giga-experiments.

* title is courtesy of Kilgore661

Images from South Africa: Patterns

A few more photos from the same trip that I already posted photographic highlights from. To be more factual and fair, the title should be "Images from the Western Cape", because I have only seen a few places in South Africa, and all of those places are in the Western Cape province. Anyway, here are three photos of... well, not much, just some visually interesting patterns.

Halophytic (salt-loving) vegetation in the supratidal zone of the Langebaan Lagoon, West Coast National Park

Old tree trunk at Groot Constantia winery, Cape Town, the first winery in South Africa, created in 1685

A look at the pebble (beach near Cape of Good Hope)

Liesegang bands in sandstone

Liesegang bands are poorly understood chemical structures often seen in rocks, especially sandstones. They were discovered more than a hundred years ago by the German chemist Raphael E. Liesegang, when he accidentally dropped a drop of silver nitrate solution on a layer of gel containing potassium dichromate, and concentric rings of silver dichromate started to form.

In sedimentary rocks, Liesegang bands appear well after the sediment has become a rock (that is, it got compacted and cemented). Stratification and lamination within the sansdtone are typically cross-cut by the Liesegang bands; fractures usually have a more obvious effect on the distribution and orientation of these.

The rocks shown here are turbidites of the Permian Skoorstenberg Formation, in the Karoo desert of South Africa. This Liesegang banding developed in the neighborhood of a small thrust and consists of brown bands of iron oxide that entirely 'ignore' the original lamination of the sandstone (not visible in the photos), but clearly like to precipitate along some of the fractures in the rock.