With a widened ed beam power will drop off and I believe it's not linear as in 2x the size 1/2 the power. The only laser that could do something like that would be a c02 laser as you need more than a few watts to do what you're attempting. Trouble is regular glass blocks the Co2 WL 10,600nm. You'd have to aim it right over the open container. Also you need to know variables such as the liquids boiling point and such and such.
Not really possible to have it "instant" with those kinds of restrictions. If you can forgo the "instant" part then it might be possible, but I'd need a time frame in which the material will be heated.
also keep in mind different WLs interact differently with different materials, so do you need it heated evenly or can it just be heated in one spot?
it would need to reach its max temp within a couple of seconds so it does not have to be instant but pretty quick. This fluid will actually start to evaporate at 400+ and that is what the sensor picks up. As the fluid degrades it evaporates at a higher temp.
The fluid has the viscosity of glycerin, is room temperature and when the machine is running the fluid actually warms up to 80+ degrees.
I would say it would be best to uniformly heat a surface area of an 8mm diameter circle. a rather small area. the more surface area the better. there is a sensor tube of corts situated above.
exploded view
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laser lense ceramic fluid small chamber cap sensor + tube/cord
So it's just thermodynamics. Since I cannot actually see the setup you have it will just be easier if you do the calculations.
If you want it heated evenly it's going to be harder to do. You're going to want a visible WL and have it resonate inside the liquid, allowing it to heat evenly. This will of course up the time it takes to heat, and the complexity of the device. Due to the heat capacity of said liquid you're probably going to need a pretty high powered laser.