Much recent research on microfluidics has focused on two-phase flows. This often involves generating and then conveying a single file flow of drops in microfluidic channels. Here we ask the question: what is the effective viscosity of such a two phase flow? I.e. what is the relationship between flow rate and pressure drop? Such knowledge would be useful, e.g. in designing on-chip microfluidic pumps.

While the flow rate- pressure drop relationship for single-phase microfluidic flow of a Newtonian liquid is quite straightforward (since Re is small), it can be complicated for the case of two-phase droplet type flows. We characterized the flow-pressure relationship for the single-file flow of water drops in oil in microfluidic channels of rectangular cross sections. The pressure for such droplet flows was always larger – sometimes over 50% larger – than that for corresponding single-phase flows of the continuous phase. This is in spite of the fact that the water drops had a substantially lower viscosity than the continuous phase oil. The excess pressure was found to correlate reasonably well with the size of the drops relative to the size of the channels. This correlation for the excess pressure, as well as a correlation presented here for the size of drops in microchannels, should provide convenient guidelines in designing microfluidic devices for two-phase flows.