I got to thinking about some of the various designs suggested here last night when I couldn't sleep, and a couple of important design considerations occurred to me. Provided I'm remembering my various engineering classes properly, using a funnel or flared tubing will not have a significant impact upon the reaction time for a drop checker. Theoretically, it could even slow the reaction down. Second, the diameter of the tubing is not the most important factor in determining the response time. Let me try and explain.
The rate at which a gas dissipates from or is absorbed into a liquid depends upon the following factors.
1. The concentration of the gas present in the liquid (in this case ppm of CO2)
2. The partial pressure of the gas in contact with the liquid
3. The surface area of the liquid(s) in contact with the gas
4. The Reynold's number of the fluids involved (remember that gas is a fluid)
(I'll save this one for last as it is complicated and will only have a small affect)
Item number 1 is what we are trying to measure. For a closed system such as a drop checker, #2 is dependent almost entirely upon #1. Neither of these is affected by the physical design of the drop checker. Item #3 is dependent upon two dimensions: the first is the ID of the top of the tubing (the part in contact with the gas); the second is the ID of the jar minus the OD of the tubing. A funnel at the bottom of the tubing does not impact either of these.
When the drop checker is placed into the tank, CO2 begins to diffuse out of the aquarium water and into the air trapped in the drop checker. The rate at which this occurs depends mostly upon the concentration of the CO2 in the tank and the surface area of the water in contact with the air, ie. the tubing ID. This reaction will continue until the system reaches steady state (equilibrium). The time to reach steady state will depend mostly upon the volume of air trapped in the drop checker. The more air in the system, the more CO2 it can hold at a given temperature/pressure.
At the same time, CO2 is being absorbed by the indicator fluid from the trapped gases. Once again the rate of this reaction is primarily dependent upon the surface area of the indicator fluid. As before, this will continue until the concentration of the CO2 in the indicator fluid matches that of the aquarium water, assuming that CO2 has the same permeability for both liquids. The total time for this reaction to reach steady sate will depend mostly upon the volume of the indicator solution.
In simpler terms, in order to get the quickest response time a drop checker should have the following characteristics:
1. Equal areas of indicator fluid and aquarium water in contact with the trapped air.
The smaller of the two areas will be the limiting factor for the rate of gas diffusion.
(This means a bottle with an ID roughly 1.4 times the diameter of the mouth).
2. A large surface area to volume ratio for the indicator fluid.
3. A large surface area to volume ratio for the gas with respect to both liquids.
Essentially you want a short, fat jar with the above diameter to mouth ratio.
Finally, the Reynold's number. For those of you that have never studied any type of fluid mechanics, Reynold's number is a dimensionless number (meaning it has no units such as meters, grams, seconds, etc.) that is used to indicate various properties of moving fluids. It depends upon density, viscosity, flow rate, turbulence, etc. For this application the important factor is the flow/turbulence in the water column of the tubing. The indicator fluid and the trapped gas are essentially motionless, so the only way to speed up the dissipation of CO2 is to get the water in the tubing moving.
Placing a funnel on the end of the tubing might help a tiny bit if it is oriented properly with respect to the water flow in the aquarium. On the other hand, if it is positioned improperly it could impede the flow of water below and therefore inside the tubing. The best way to help increase flow would be to place a "Tee" or "Y" shaped plumbing fixture at the bottom of the tubing, and then turn one end into the flow and the other end away from it. If you are using a "Tee", placing a funnel on the incoming end of the fixture would increase the flow rate through the fixture and thus help stir the water in the vertical section of the tubing. Overall, I'm guessing the water flow is a minor factor in the reaction time compared to the surface areas and volumes involved.
This is probably far more information than anyone wanted to know about a simple drop checker, but that's what happens when an engineer suffers from chronic insomnia. I hope this was in some way helpful (cutting a glass funnel sounds like a pain in the ass). Let me know if you have any questions or couldn't understand my techno-babble.