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IM 2.02 The No-Slip Boundary Condition

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Have you ever noticed that ceiling fans can gather dust, even though their blades spin rapidly? You might think the dust would just blow off. Or, have you ever thought about the wake created by a boat as it speeds through a lake? These situations illustrate a law in physics known as the no-slip boundary condition (NSBC). This law states that the velocity of a liquid flowing past a surface is exactly zero at the surface itself. In other words, particles of fluid will adhere to the walls (or boundary) of a solid. That’s why the wake forms behind a boat. The water molecules that come in contact with the boat are moving at the same speed as the boat, and the water molecules are strongly attracted to each other; this has the effect of towing some of the water along with the boat. 

If the fluid velocity at the particle surface is zero, then the only way that flavour molecules can escape the particle is by diffusing through this boundary layer. Because diffusion is such a slow process, the rate of extraction from the surface is very slow. Further away from the particle surface, if the fluid is moving, the flavour molecules can be carried away by the movement of the liquid, a process called advection.

Surprisingly, the NSBC is still sometimes a factor even when there seems to be a huge amount of agitation going on in a slurry — for example, when a kettle stream flows extremely quickly from a pouring kettle and blasts its way into a coffee bed. This sort of high-speed flow can be ‘laminar’, wherein molecules move in straight lines (see left graphic, below). In laminar flow, the boundary layer can be relatively large, which means molecules have to diffuse a longer distance to escape the grind surface. Turbulent flows form eddies, or back-currents (right graphic, below), which can penetrate the boundary layer and carry away flavour molecules, increasing the rate of extraction. For the same reason, whirlpools, which we discussed in Lesson 1.05, are not effective at stirring a coffee slurry; they don’t produce the eddies required to overcome the NSBC.

Laminar flow (left). Turbulent flow (right).

Professor Steven Abbott explains, ‘The only way for these [large and harder-to-dissolve] molecules to escape is to get turbulent flow coming as close as possible to the no-slip boundary.’ 

In this short video, a drop of ink is deposited onto the wall of a glass container, with water moving around in a whirlpool (i.e., an environment without turbulence). The ink remains on the wall until someone uses a paddle to create enough turbulence to wash the ink away. 

Because of the NSBC effect, all immersion brew methods require some kind of agitation. Without agitation, immersion brews simply take too long to prepare, and they generally underextract. Without turbulent flow caused by agitating the slurry, the water molecules responsible for extraction of coffee flavours are unable to overcome the no-slip boundary condition, and flavour molecules are able to escape into water only via diffusion. For some flavour molecules that are larger and less soluble, such as the bitter-tasting pseudotannins in coffee, this is a slow process. 

 

Solubility and Flavour

The highly soluble compounds in coffee, such as caffeine, sugars, and organic acids, are extracted very soon after water is poured onto coffee grinds — reaching over 90% in the first few seconds of espresso extractions, according to Severini et al (2015). Differences in the solubility of substances found in roasted coffee explains why an underextracted coffee can be dominated by flavours associated with a sweet and highly acidic profile (Mestdagh, Glabasnia, and Giuliano 2016). 

Less-soluble compounds are extracted only after some time has elapsed (or after a certain volume of water has flowed through the coffee bed in the case of drip coffee or espresso). Among these less-soluble compounds, several bitter- or astringent-tasting substances, such as phenylindanes, are associated with overextraction. Because they extract almost continuously throughout the brewing process, they are thought to make more of a contribution to the flavour profile of very long extractions (Mestdagh, Glabasnia, and Giuliano 2016). More-soluble compounds, such as caffeine or citric acid, are almost fully extracted earlier in the brewing process. 

‘Overextraction favors the extraction of less soluble bitter and astringent compounds. As a consequence, the ratio between early extracted acids or sugars and bitter lactones and indanes will change over time, which imbalances the sensory profile. It will move from a sweet acidic one toward a more bitter-harsh, astringent one.’ (Mestdagh, Glabasnia, and Giuliano 2016)

 

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