## Biscuit Dunking

**Arunn Narasimhan**

Some of us, butter-toothed blokes, dunk our biscuits in tea or coffee before chewing on them. Dunked biscuits are tasty, but have their fender-bender moments. The dunking should be done within a critical time, else the soaked biscuit, before reaching our mouth, would bend in slow-mo back into the coffee with a splatch or worse, spatter on the inside of our thigh like hot crow-poo.

Nevertheless, dunking biscuits is popular across the World -- be it in UK, where about five hundred burn themselves annually with a badly timed lift-up of the soaked biscuit, or in Indonesia, where the famous Tim Tam Slam is performed annually, wherein you slurp the tea or coffee through the specially made porous biscuits, before eating them in one piece.

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During a recent 'academic meeting', while dunking a Good-day biscuit in hot coffee, I was wondering about the 'critical time' for safe-dipping. So I timed my Good-day dip much to the dismay of those around me, snicking (snacking) a few more biscuits from the passing tray. The time for safe-dip was just about 5 seconds; dip longer, it is bound to buckle when you attempt eating.

Is this safe-dip time universal? Is it valid for all other biscuits -- Marie with 9 or 18 holes; Krack-jack with 9 holes; Tiger biscuit with no holes; Bangalore Iyengar Rusk with random number of holes in differing sizes. What about dog biscuit?

After an internet search, accompanied calculation and few more experiments later I am convinced that 5 seconds is a safe bet for the safe-dip time. Rusk takes a few more seconds, while Tiger could be subdued in less than 5 seconds, but in general, that time-limit is fine.

I am not the first guy to do this experiment nor am I the first one to explain the physics behind dunking. The biscuit dunking physics has won an IgNobel in 1999. Physicist Len Fisher of the University of Bristol won it for "calculating the optimal way to dunk a biscuit." The physics of biscuit dunking was explained by Len Fisher using the Washburn equation for capillary flows throguh porous medium, driven primarily by surface tension force. The final simplified form of the Washburn equation is,

For a flow through a long horizontal pore (like a capillary or narrow pipe), in the absence of gravitational forces, the above equation states the length L upto which a fluid will flow inside the pore is proportional to the square-root of time t of flow; the proportionality is determined by the strength of the surface tension force σ as it dominates the brake offered to the flow by the viscosity η of the fluid.

Fisher used the above equation for biscuit dunking assuming the porous biscuit is one long pore. The predictions were excellent. In his Nature commentary, he recounts when he explained it, the media lapped it and several reporters spoke to him to get the equation right in their articles. Fisher attributes this craze over his application of Washburn equation to the public's (and media's) clamour for understandable science; here is a relevant quote from Fisher's Nature note:

Scientists are seen by many as the inheritors of the ancient priestly power of the keys, the owners and controllers of seemingly forbidden knowledge. Equations are one key to that knowledge. The excitement of journalists in gaining control of a key was surely a major factor in their sympathetic promotion of the story. By making the Washburn equation accessible, I was able to ensure that journalists unfamiliar with science could use the key to unlock Pandora'sbox.

The final form of the Washburn equation was simple and the effects when applied to biscuit dunking were there to be verified by anyone. But the media did their share of oversight by identifying the equation as 'Fisher equation'. Len Fisher muses in his note, "Washburn will be turning in his grave to learn that the media have renamed his work the "Fisher equation"."

For our share, let us do a calculation for the Good-day biscuit. Good-day biscuit length L ~ 4 cm (0.04 m) and it has a pore size less than a millimeter (~ 0.00001 m) -- most biscuits/cookies are of these L and D; one exception is Rusk. If this biscuit is dipped entirely in coffee at 50°C, the thermophysical properties would be viscosity η = 0.547 × 10^{-3} Nsm^{-2} and surface tension σ = 0.0679 N/m (these values can be obtained from from Engineering Toolbox here and here).

The only unknown in the Washburn equation then is time t, which works out to be about 5.1 seconds. If we increase the D by an order of magnitude and set L ~ 5 cm to resemble a Rusk, the time for dunking would be around 8 seconds.

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Explaining the outcome of the Washburn equation for biscuit dunking, Len Fisher suggested one shouldn't dip the biscuit vertically in coffee, as it would soak quicker. Instead, it should be dipped slanting or horizontally (as shown in the picture) so that only the bottom gets wet and the top remains dry, leading to a fine balance of dunked biscuit that is tasty yet dry and rigid enough not to buckle.

When I explained the results to my wife and asked what she thinks about my understanding, pat comes the reply, "So are your 'academic meetings' this listless?". Well, they aren't tasteless.

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[Here is the Tamil version, richer in style and stuff.]

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References- Washburn, E. W. (1921), The Dynamics of Capillary Flow, Phys. Rev. 17, 374–375 [http://link.aps.org/doi/10.1103/PhysRev.17.273 | DOI: 10.1103/PhysRev.17.273].
- Dunk Biscuit http://en.wikipedia.org/wiki/Dunk_(biscuit)
- Len Fisher (1999), “Physics takes the biscuit,” NATURE, v 397, 11 FEBRUARY. http://www.nature.com/nature/journal/v397/n6719/full/397469a0.html
- Tim Tam Slam http://en.wikipedia.org/wiki/Tim_Tam_Slam#Tim_Tam_Slam