Hydrodynamic resistance of single confined moving drops in rectangular microchannels

We integrate a sensitive microfluidic comparator into a T-junction device and report measurements of the excess pressure drop due to a single moving droplet confined in a rectangular microchannel. We specifically focus on drops that are not coated with surfactants and study the effects of drop size, droplet viscosity and capillary number on their hydrodynamic resistance. In the capillary number range of ≈ 10^-3-10^-2, we find two distinct regimes for hydrodynamic resistance behavior based on drop size. In regime I associated with small drops (drop length/channel width ∼ <4), we find that the pressure drop is independent of the drop size and the capillary number, and depends weakly on the ratio of the viscosities of the two immiscible phases. In regime II, associated with large drops (drop length/channel width > ∼4), depending on the viscosity ratio of the two phases, the hydrodynamic resistance could increase, decrease or remain unchanged with drop size. We present a simple model that qualitatively captures these experimental trends. This model reveals that the pressure drop in regime I is dominated by the dissipation due to the end caps, and in regime II by both the end caps and the central body of the droplet. Such fundamental understanding will enable the design of large-scale energy-efficient fluidic circuits by minimizing the overall pressure drop in a network and may also provide insights into controlling droplet traffic to build functional passively-driven two-phase microfluidic technologies.