I have three 16 mm 40 kHz transmitters like these (transmitter only, no receiver): https://i.ebayimg.com/images/g/uF0AAOSwO7hZ8EeM/s-l225.jpg
That looks rather small. But, no specs...
know there are atomizers and mist makers out there, but wanted to create something from scratch.
I've got a mist maker that would probably be overkill for what you're doing, but just as a reference point the power supply is 100 Watts (24V @ 4.17A). I don't know how much power is actually going to the transducer.
But, you'll need some sort of driver. The maximum current from an Arduino I/O pin is 40mA. 5V @ 40mA is 0.2 Watts (200mW) and I'm pretty sure that's not going to stir-up anything.
I don't know what the impedance of that thing is (a piezo is essentially a capacitance when there's no mechanical load) so I don't know how much voltage (or current) it takes to get power into it.
[u]Here is a driver circuit[/u], but without knowing the voltage/current requirements it's just a starting-point.
I know how to generate a 40 kHz wave from a post on this forum: 40KHz pwm square wave - Project Guidance - Arduino Forum
The [u]tone()[/u] function should work.