Scaling of interface displacement in a microfluidic comparator

The authors quantify both experimentally and theoretically the scaling behavior between interface displacement and excess pressure drop in a microfluidic comparator. Unlike previous studies, the authors measure the interface displacement in the outlet channel of the comparator that yields a unique power-law scaling. For an outlet channel width to depth ratio r=3, the authors experimentally determine the scaling exponent to be 0.60±0.01, which is in excellent agreement with theory. In general, the authors find the scaling exponent to increase from 0.51 for square channels (r=1) to 0.93 for very wide channels (r>100). This geometry dependent scaling exponent offers greater sensitivity and flexibility in measurement of hydrodynamic resistance of soft objects.