I am looking for sources which describe how to measure the contact angle between immiscible liquids in a tube. The literature seems to be extremely lacking so if anyone has any knowledge I would appreciate the help.
You might use an optical or an ultrasonic sensor. As you advance the sensor along the axis of the tube there will be a point where the conical surface of the contact annulus reflects directly back to the sensor. Block the direct axial reflection. Measure the sensor position with a micrometer or an LVDT.