To the last poster: well you could use other kinds of
fluids, but I believe it's much easier with a gas because
the thermal conductivity of a gas is quite low compared
to most liquids, and because the gas can easily be made
to flow at high speeds / vorticities with low drag and
low friction. I believe those characteristics of gas vs.
liquids make the gas possibility much more practical
than the liquid one. It'd be interesting to study
the possibilities sciendifically, though.
To the original poster:
I'd think the air consumption rate would make a vortex
tube sourced with compressed air from a small portable
tank impractical. Even a large SCUBA tank at exceedingly
high pressure only holds 100 cubic feet of air relative to
atmospheric pressure. A small 175 PSI "5 gallon" tank
that you could refill at a service station holds even less
cubic feet. I don't know if you're talking about very
tiny dimensions (a few millimeters) here which might
consume only fractional parts of 1 CFM of air flow, but
for anything of a small but respectable size, you'll only
have minutes of cooling given the air supply.
IMHO I estimate that you'd be better off using a
straight SCUBA tank and expansion valve to create
freezing air straight from the expansion of the highly
compressed gases rather than trying to use a vortex tube
which would probably use more air for less cooling.
Even a 100-175PSI small tank of compressed cool or
ambient temperature air may perhaps be more
effectively used in cooling by simple expansion rather
than via a vortex tube, though I'm sure there are some
regimes of operation in which the vortex tube is
beneficial.
Another option that's inexpensive enough for use in
consumer electronics (portable DC powered beverage
coolers) is the peltier cooler which is a thermoelectric
device that can easily produce small areas of freezing
temperatures (given a stack of perhaps 2 junctions)
given something like a dozen watts of applied power,
though of course you'll have to efficiently dissipate
the waste heat from the other side of the device to the
ambient air to realize a cooling benefit from 'the cold side'
of the device.
Beyond these approaches, it's quite common to have
small sterling cycle coolers or other such refriigeration
devices that are even more efficient and
use electrically powered tiny motors/pumps for
specialized cooling of small areas, though usually they're
only either very expensive specialty items in limited
production or are produced in somewhat larger
numbers but only for specialty applications like their use
in thermal cameras so they're not so commonly available
as an "off the shelf" part. They're not so complex though
that they couldn't be produced cheaply in quantity given
sufficient funds to create the custom designed mechanism
in the first place.
The vortex tube is probably an OK idea though if you have
a larger capacity of compressed airflow available, though,
but, again, if the compressed air is at cool or ambient
temperatures to begin with, just expanding it from
a proper nozzle may produce all the cooling needed
without needing the vortex tube.