Why less ice result into more dilution

This is a post, which promotes curiousness and scrutinize information which seems to be a given.

We learned already a lot about ice. For example the size of ice doesn't matter [if surface ice is not a subject]. We even learned, that you need to shake a drink for at least 15 seconds, to ensure the right temperature - but you hardly can overshake a drink - as the dilution and temperature almost keeps exactly the same - even if you attempt to shake a drink for a minute.

However the reason, why you should always fill a glass full of ice stays a mystery.
You could argue, that a lot of ice chills the drink faster [and as soon as the drink is cold enough, ice tempt to melt on a very slow rate] - you certainly be right.

But this might need not be the full truth.

Today I felt fancy for cherry coke - but as I had only my normal bad @ss 2.5 liter regular coke bottle, I used Fabbri amarena syrup, to give it the typical cherry/almond ting. And as I am a incurable coke addict, I used the biggest proper container I could find [which was a plastic inversion blender cup].

I added a lot of ice [though it wasn't full. as the container roughly holds ¾ liter of liquid], added coke and the syrup.

And because I had my digital thermometer hanging on the fridge [magnets] and I was curious [well not really curious - cause I know, that the drink will chill down to around 0ºC] I used the thermoprobe to stir. Obviously the temperature dropped quite fast to 0. But the funny thing was, that in the bottom, where no ice was, the temperature dropped only to 4 - later to 2ºC. Even with little stirring it didn't changed much.

What happened?

I can answer it with a simple question: what is heavier cold or warm water?

Sorry - it was a catch question. Yes "colder" water is heavier [or physically correct "denser"] than "warmer" water - but water has the densest point at 4ºC - colder water than 4ªC water is lighter again!

And that means in turn that convection stops. What the hell is convection? Well this is the movement of a medium [can be liquid or gaseous] due to temperature difference. E.g. you heat a soup in a pot - the plate [bottom] is heating the liquid, which raises to the top - there it chills down and it drops [due to the difference in density] again to the bottom - where it is heated again - so a circulation is happening.

Again - if "acquateous" liquid is around 4ºC [and there is no heat source at the bottom] this circulation won't happen.
If it comes to drinks, we are often around this very interesting physical point!

And that means, don't add only "few ice cubes" to stir or to build a drink, as a lot of recipes are suggesting. Always add the glass full of ice [as much ice, that it fills top to bottom].

Then the ice can "chill" [physically correct spoken, it draws heat energy] from the bottom as well as from the top and the drink will be throughout 0ºC - at this point ice will no further melt [only on a small rate to compensate the heat transfer from the warmer surrounding].

Please comment, if you have any question or comment!