Programming methods for detecting liquid drops with phototransistor
Assumption: This is a DIY hobby project, rather than production quality.

Here is how I would approach this problem:


Fit an IR LED on one side of the tube
Fit a TSOP17xx on the other side, aligned precisely with the IR LED, with the tube fully occluding the LED beam path. e.g. TSOP1738.
Implement a mechanism for moving the TSOP part closer or further away as needed
Feed the IR LED with a fixed frequency pulse, (= 38 KHz if using a TSOP1738) by using one of the Timer outputs of the Arduino, say Timer1 for precision.
Use the output of the TSOP17xx to drive one of the interrupt enabled input pins of the Arduino, e.g. Pin 2, for INTR 0
Attach an ISR to the interrupt, e.g.
attachInterrupt( 0, TSOPChangeIsr, FALLING);
In the ISR, save the current micros() value into a circular queue
In loop code, read off the queue to display / send to serial the timestamp in microseconds for each time the ISR is activated


Working:


Each time a liquid drop passes through the tube, this will occlude the 38 KHz infrared beam from the LED, thus causing the TSOP1738 to see a "low" for that duration.  
You may have to fine-tune the distance of the TSOP1738 to get the sensitivity to a reliable middle value such that both small and big drops cause a trigger, but there are neither false positives, nor missed drops.
For greater reliability in capturing drops, the IR beam may be made incident on the tube at an angle, as also the TSOP sensor. Thus, the liquid will occlude the beam for longer while passing through the tube.


If there is further clarification needed, please comment accordingly: I will try to address any queries.



Updates based on some experiments:


If you obtain one of the 5 volt "toy" red lasers sold quite cheaply on eBay, it can be modulated at the same 38 KHz by using the Arduino Timer1 waveform pin (I used pin 9) to drive a basic N-MOSFET (2n7000 in my experiment) with drain connected via the laser to a 5 Volt supply. Ground is connected to Arduino GND pin.
This allows the laser to be directed through the glass tube at a very acute angle, thus providing much greater occlusion period per water droplet, hence higher precision on sensing. With just the LED, smaller droplets were sometimes being missed.
Though the TSOP part was not expected to be triggered by visible wavelengths, the red laser evidently generates sufficient excitation for detection to occur just as reliably as though it were an IR beam.
The laser is of course much brighter when reaching the TSOP1738, compared to an LED beam. To adjust sensitivity of the TSOP sensor, instead of changing its distance, it is easiest to simply change its angle away from the perpendicular of the laser beam. With a simple gear assembly the sensitivity can be finely tuned by such rotation.
Reflection as a sense mechanism isn't working as well as occlusion, since the tube surfaces, and even dust particles, seem to trigger the TSOP sensor.
Fun fact: The water droplets cause the laser beam to produce interesting and very visible fan patterns on nearby walls at each occlusion.