Unruled Notebook

Entries from May 2007

The Boiling Song by the Kitchen Band

May 31, 2007 · 4 Comments

In this post, I am presenting to you all the rambunctious boiling song from the one and only kitchen band. There is also an accompanying small video clip of the live performance of the band that you can get to watch later in the essay. Although the song is a mix of hard rock and grunge instrumental with high-pitched multiple wailing guitar sounds and cacophonous tempo changing beats, I assure you, for recording this song no musical instrument has been used.

Warning: The sound is really cacophonous (what else you expect from a hard rock?). So, if you are reading my blog at your work place, take precautions like wearing a headphone to listen to the music. Again, I am not responsible for the well being of your ear. However, I urge you to listen to the music as closely as possible as it is only about a minute long and contains some interesting sounds.

Now for the song.

[Boiling Song MP3 ~ 1.1 MB - links to boxnet page for file play/download]

And now for some sleeve notes about the record

For those of us who are born elsewhere from anywhere, the Kitchen Band comprises of Gas Stove, Water Vessel, Heat Energy and Mother Nature.

We all have witnessed the phenomenon of boiling. For most of us, it begins in our kitchen or bathroom and proceeds until the dining room and perhaps stops there, forever. For the purpose of this essay we shall take it a bit further. Boiling comes in several shapes and sounds, grouped under the two broad categories, pool boiling and flow boiling. Unlike an Italian Screwdriver (which is not a screwdriver made in Italy), Pool Boiling, as the name suggests is associated with a boiling pool of liquid. It is usually associated with the boiling of a stationary mass of liquid heated with a stationary heater. An example is the familiar water boiling in the pan on a kitchen stove. Flow boiling is associated with a flow of the boiling fluid. An example is the flow inside the boiler tube (water wall panels) of a thermal power plant.

Pool boiling includes five regimes of reasonably distinct characterizations. Taking the familiar liquid water as the example liquid let us start heating it in a kitchen vessel kept over our standard gas stove to explore, if possible, these five regimes.

And in the process, we shall create the song.

As we know, water boils at 100 degree C. Not exactly true. A better way to say that is liquid water that is in contact with its vapour boils at 100 degree C. If it is not in contact with its vapour, but still in contact with a heating surface – a situation that is true for room temperature water heated in a pan on a kitchen stove – it continues to remain in liquid form and raises its temperature to more than a few degrees above 100 degree C, for conventional machined surfaces like our kitchen vessel. Then is bubbles up. This range of heating of water from its room temperature falls within a regime that is identified with natural convection of water. See how the red curve is depicted in the left bottom corner of Fig. 1 below.

Before proceeding further, an explanation of Fig. 1 is in order. The abscissa is the excess temperature between the wall temperature (in the kitchen vessel, it is the bottom wall that is kept over the stove) and the saturation temperature of the fluid (in our case, water). The ordinate is the heat flux that is released into the boiling fluid (in our case, water). The red curves are paths that characterize what happens to a fluid undergoing pool boiling in all of its five distinct stages.

Figure 1: Pool Boiling Regimes

Beyond this region, marked by a bubble inception point – where the first bubble can be noticed in our vessel of heated water – water boils and the nucleate boiling phase begins. This means, initially isolated bubbles are formed in the nucleation sites, which are nothing but gaps or imperfections in the heater surface – in our case, the bottom inner surface of the heated vessel on the stove. When the nucleation sites become aplenty, as the heating increases (see Fig. 1), the bubbles generated from these sites merge together to form vertical columns and slugs that could in principle reach the top free surface of water in the vessel.

By the way, no commercial kitchen stove is capable of supplying heat energy fast enough to the water to reach the slugs and columns regime itself so don’t expect to see this range in your kitchen experiment. Unless you conjure up a mini nuclear reactor as your kitchen stove. In which case, keep me informed of it, before you invite me over for dinner.

Proceeding to heat and boil the water beyond the slugs and columns regime in a laboratory set-up, there results a situation when a “peak heat flux” value is reached (marked q”max, see Fig. 1). Further increase of heating results in sudden increase of temperature difference (marked in abscissa) and many times commonly used heater material surface melts. The transition boiling region connects this peak heat flux limit with the film boiling regime, wherein the heater surface is completely blanketed by a film of vapour of the liquid (water, in our case) across which heat transfers into the liquid water residing unstably above the vapour layer.

For the brevity of this post I shall skip further explanation of many of these interesting phenomena and go back to the song of our kitchen band. Suffice to say that there are separate monographs of knowledge available for pool boiling alone (and more for flow boiling). If interested, take a look at the reference [1] given at the end.

By now you should have gotten a hang of the simple kitchen experiment that we have performed. In this experiment just after the bubble inception point as explained before, hot vapour bubbles form near the bottom of the vessel (close to the stove) and raise to the top surface of the vessel through the liquid water. The rest of the water column along the vertical path of the bubble is colder than the hot vapour bubble and so the bubble collapses suddenly by condensing when the top surface of these bubbles come in contact with the colder water above. This “cavitation” collapse of the vapour bubble results in the high pitched noise (ping) that falls within our audible range.

It is to be understood that the noise is a mixture of pings from several thousands of bubble collapse at the same instant. The process of bubble formation and collapse at a higher point is repeated at a high frequency resulting in us hearing the high pitched sound continuously. Further, the smaller the bubble size, the higher the pitch. Also, longer the vertical column of water, the longer the duration of singing one can hear, as the vertical residence distance (hence the “cooling” distance) for the bubbles are increased, before it reaches the top free surface of the water inside the vessel.

Again, it should be kept in mind that in a given instance, bubbles of very many sizes are always present in the boiling process and so the “singing” is always a mixture of sounds of several frequencies influenced further by the cross dispersion before it reaches our ears. See for instance, in Fig. 2, the bubble distribution across the surface of the water inside the kitchen vessel.

Figure 2: Boiling Bubbles

The original picture by me in our kitchen is doctored a bit (again by me) to visualize the bubbles better. Of course, more sophisticated techniques exist to capture these bubbles better and I claim no expertise in this.

As the heating results in further increase of temperature, the bubble sizes also grow bigger and the sound becomes muted. The bubbles no longer condense within the water column in the vessel but reach the surface of the water and escape. Water continues to boil with a dull gurgling sound. We don’t hear this in our recorded song as it takes a while in my experiment to reach this stage (about 4 minutes for the vessel I used) so I have cut those parts out. The actual “outro” after a pause that you hear in the end part of the audio is the very well isolated bubble situation when the system cooled down after the stove is switched off.

One more important thing before we conclude. The “staccato drumming” that you hear over the “singing” (the wailing guitars like sound) is more due to the pinging noise from the collapse of the bubbles that originally form on the inner surface of the hot side walls of the “ever silver” vessel that I used in this experiment. One could reduce this drumming noise with another type of vessel, but the initial singing largely depends on the nucleation sites at the bottom of the vessel. If you take it from me for now (see reference [1] otherwise), the required size of these nucleation sites range between 0.005 mm to 5 micro-m – a range completely in tune with the commercially manufactured surfaces (of vessels).

Anyway, all of the noise explained so far and the accompanied phenomena are well within the bubble inception and isolated bubble region of Fig. 1. We don’t reach the slugs and columns range of Fig. 1 in our kitchen.

There ends the sleeve notes for the boiling song from our kitchen band. Wouldn’t you want to go back now and enjoy listening to the nucleate boiling bubble cavitation grunge again?

Reference:
[1] A Heat Transfer Text Book, Third Edition, by John H. Lienhard IV and John H. Lienhard V

[Disclaimer1: The explanation given in this post is not very rigorous in many places and I am aware of it. Gross mistakes, if any, are encouraged to be pointed out and I shall stand corrected at the earliest.]

[Disclaimer2: The boiling song audio given in this essay is copylefted and is very much available for copy-lifting under a re-creative non-commons license. For hearing a live version of it with a variation of the theme, stay close to the hot water that you are making next time.]

Categories: Lecture Notes · Science Notes · Thermal Sciences
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Baggage

May 25, 2007 · 2 Comments

Are you two “no baggage”? asked us the airlines attendant in the terminal, when we were waiting in a long queue in front of the check in counter to receive our gate pass. In fact we didn’t have any check-in luggage and so we said yes to the query and she promptly redirected us to the counter in the opposite corner of the lounge marked “No Baggage”.

We were happy that there were only three such people waiting already in that counter and were sure we would be served “quickly” and could save some life time for us, which would be spent otherwise waiting in the longer queue.

So we left our place as 29 and 30 in the longer “Yes Baggage” queue and proceeded to stand as 4 and 5 in the shorter “No Baggage” queue.

And we waited. Some time later we did waited 2.0 and proceeded to waited 3.0 until we effectively watched the 24 and 25 in the original queue received their gate pass and move on.

Reason: The computer in the “No Baggage” counter is abnormally slow.

Later when we lodged ourselves in one more already swelling queue for security check expecting it to take forever to move, we were asked by another attendant to move on to another shorter queue. Not to believe in conspiraacy theories too soon, we took the bait. The shorter queue did move quickly and allowed us to reach our designated flight leaving gate too soon. Bemused, we waited, as there was about thirty minutes left for the departure time.

When it was about ten minutes to departure, the attendant near the gate matter of factly informed us that the flight departure gate has been changed and we (about thirty of us) aare supposed to go back to another gate which is two floors away.

Reason: The computer in the gate area counter is abnormally slow.

The escalator refused to be “reversed” from its original operation direction (moving downwards). Cursing to ourselves, we climbed the stairs to take us back to the second floor, from which we had come down comfortably using the escalator. When it doesn’t “escalate”, and does exactly the opposite I wonder whether it is correct to call it that.

Anyway, upon reaching the re-designated gate, we were informed by the security that he was not aware of any such gate change for that flight and so, although we could actually see the flight standing across the glass doors, we were denied entry. And so, we waited in the lounge.

Later, a new temporary check-in was setup near the gate that made us wonder why this couldn’t have been done in the previous gate itself, where the “computer was slow”.

Reason: The attendants in that situation were slower.

About thirty minutes past the scheduled departure time for the flight, we were allowed to board the flight. A “full flight” it was. And we waited in there for about an hour watching brats bray. It wasn’t our day. Finally, the time at which we should actually have landed in our destination, the flight departed.

Reason: computers in the airport air traffic control was slow

In the flight a six year old boy kept yelling and crying non-stop because he simply decided to be that way on that day on that location for that many hours. His parents were going through all of the possible rich spectrum of human emotions and their combinations ranging from stoic non-chalance to scintillating rage. To get ourselves distracted, we tried returning to our book and realized out of about 168 overhead reading lamps on that flight, only the one above us had an electrical snag (loose contact). The overhead lamp, like the parents of the yelling kid, kept offering light flickering continuously in all possible frequencies of the visible electromagnetic spectrum.

Conclusion: Respect the hidden normalization laws of life that, by striving to maximize the collective functional incompetence of man plus machine in a given situation, brutally marshall what one can take for granted in life.

Categories: Muse · Narration
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A rude introduction to carnatic music

May 20, 2007 · 7 Comments

What with a Gentle Introduction [1, 2, 3, 4] to Carnatic Music by the inimitable Ramesh Mahadevan, let me present my short, rude version of it. Rest assured, there are ruder versions of this…

Carnatic (pronounce kar-naa-tic) music is the South Indian classical music form, Hindustani being the North Indian equivalent. Carnatic music, one of the oldest (a few thousand years) and richest musical traditions, in its basic form, is monophonic as opposed to Western music that is primarily polyphonic.

Rooting firmly on manodharma (creative extemporization), Carnatic music has a definitive past, housing a staggering variety of raagas (scales – 72 major ones with potentially infinite sub-combinations); unique melodic sustenance of the individual notes called gamaka(m); precisely crafted and meticulously organized rhythmic structure called taalas; all offering a grand creative scope for the capable musician and a rich variety of contents to delve and bask into for the listener.

Along with the above, Carnatic music has lots of practitioners, more regurgitating with very few creating and experimenting; lots more of critics, more self proclaimed and open (on all sides) minded with few critiquing for progress; lots and lots of listeners, more idolizing than inquisitive; and a good amount of cavalier vocabulary like sampradhaaya (norm), guru-parampara (teacher-student lineage), raaga baava (feel(?) of a scale) etc. whose highly subjective meanings foster more often than not, an even higher degree of sterility.

More can be said on what is Carnatic music and why Carnatic music but my thoughts, until I write it more elaborately here, are more closely reflected by Krishna whose rhetorical question of how stupid a music critic can get?, I sympathize with.

Some of my recent carnatic music reviews written in Tamil language can be found here under music category

Categories: Carnatic Music
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Halogen Family – a science and fiction toon

May 16, 2007 · 4 Comments

Here is my feeble attempt at “science fiction”, literally. Literature and science buffs amongst my readers, roll those names in your tongue, to see if they sound right. and of course, check out if you can spot the science and the fiction (literature) in these instances… :)

[ ommachi is the screen name I used at toon-doo to create this strip ]

Categories: Cartoons
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Borromean Rings

May 15, 2007 · 16 Comments

My colleague Prof. Arul Lakshminarayanan recently wrote in Resonance about the Borromean triangles embossed on the stone pillars of Marundeeswarar temple, a place of worship few miles from my institute. [article pdf]. Following is my extended note on Borromean rings.

borromean_triangle Observe the accompanying picture of a stone inscription at the Marundheeswarar Temple [front picture]. At first glance, it looks like Sri-Chakra, the familiar Hindu symbol. It isn’t. The overlapping triangles do something more interesting. Observe how if each triangle is traced, it goes “under” or “above” the other two triangles, although it forms a coupling on the whole. Pull out one triangle from the inscription, the other two fall off. They can be taken out separately, as they lie one over the other.

The basic idea of a Borromean ring is that the three rings are inseparable when taken together, but if one of the ring is taken out, the other two fall apart. It is an idea where the sum is more than the parts. An idea where things that individually don’t stand up to make sense, when combined not in pairs but in three, makes something meaningful.

A possible example is the model of the atom, with its usual proton, electron and the neutron. A combination of all these three forms a stable atom, while individually these components are unstable.

Arul gives another example in his article

The adjective Borromean is in use in few-body quantum systems it describes the situation where a 2-body configuration is not stable, while a 3-body configuration may be. An example is provided by halo nuclei with some neutrons loosely bound to a core, such as in the case of 6He, which is stable against dissociation while 5He is not. Thus while the 3-body configuration involving (α, ,n,n) is stable (there exists a bound state), the 2-body ones (α,n) and (n,n) involving a Helium nucleus (α) and a neutron (n) or just two bare neutrons are unstable (there are no bound states).

The etymology of Borromean rings from wikipedia reads

The name “Borromean rings” comes from their use in the coat of arms of the aristocratic Borromeo family in Italy. The link itself is much older and has appeared in the form of the valknut on Norse image stones dating back to the 7th century.

A detailed web page dedicated to Borromean rings now include the pictures taken by Arul.

The late Australian sculptor John Robinson (4/5/1935 – 6/4/2007) used extensively such mathematical curiosities in his sculptures. Accompanying picture is one of his Borromean rings sculpture, using three rhombuses made of stainless steel offering nice light reflections. The sculpture called Genesis is located in the green lawns of the University of Wales. You can visit the website that discusses his works extensively.

Intrigued, I attempted to create the Borromean ring at home. Overlapping circles will not do, as proved rigorously in the “Borromean circles are impossible,” Amer. Math. Monthly, 98 (1991) 340-341, by B.Lindstrom and H.-O. Zetterstrem. So I started with ellipses. From household rubber bangles suitably squashed to form ellipses, here is my attempt to create Borromean rings in pictures.

Obviously, one of the three bangles has to be compromised of its topology. I hope the Mystery of the Three Missing Rubber Bangles will not be solved by my daughter too quickly.

The home-made borromean rings is also shown below in almost (forced) 2 dimension. Compare it with the 2-D rings and the 3-D orthogonal rings (formed with bangles) shown above. The second picture below shows how a “cut” is required to form the borromean ring at home.

Borromean rings are used as symbolisms for the Christian Trinity. Even in the Marundheeswarar Temple, as Arul observes, the inscription of the Borromean triangles is found near the sanctum of Tri-pura-sundari, the female deity, perhaps symbolizing Shakthi, the female omniscience as the unification of the Trinity of the Hindu Gods, Brahma, Vishnu and Shiva.

As Arul writes in his article, Marundheeswarar temple

[...] has been in existence from about the 6th century AD (it has been sung by Saivite saints of the 8th century) and it has at least 11th century inscriptions, I cannot comment on the era inwhich the pillars with the motifs discussed here were carved. Such motifs are also certainly not unique to this temple and the use of geometric patterns (yantras) is prevalent in both Hindusim and Buddhism. Further explorations may throw up more intriguing uses of mathematics to build bridges with the inner worlds that these temples seek to connect. The Borromean triangles or the Stevedore’s knot as logos of Tripurasundari may be part of a larger spectrum.

Recent ripples of this idea in scientific community include the molecular borromean reported in 2004 by the research group of J. Fraser Stoddart in the Science Vol 304, Issue 5675, 1308-1312 , 28 May 2004 [Abstract]. A recent 2007 paper in the J. of Chemical Education reports [Abstract] how to make these molecular borromean rings in the undergraduate laboratory.

I am now on the look out for more such intrigues in our temples. A nice reason to visit them I guess.

Categories: Maths · Science Notes
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