Scaling crossover in a viscous regime of capillary replacement between two mutually immiscible liquids in an open channel

Capillarity-driven microfluidic devices have been receiving considerable attention in engineering and medical applications [1]. Most of previous capillarity-driven microfluidic devices involve spontaneous flow of a single liquid. In recent years, the spontaneous replacement between two mutually immiscible liquids has begun to be used for microfluidics, and its application is expected to droplet microfluidics [2]. However, the physical understanding of the replacement is still premature for microfluidic implementation. At the last APS March meeting, we reported a quantitative analysis of the dynamics of the capillary replacement of aqueous solution with oil in open channels, which were fabricated by a digital light processing 3D printer. This time, we report that the replacement distance first linearly scales with time, but later scales with the square root of time. By extending a previous theory, we explain that this scaling crossover is of viscous origin.

[1] A. Olanrewaju, M. Beaugrand, M. Yafia and D. Juncker, Capillary microfluidics in microchannels: from microfluidic networks to capillaric circuits, Lab Chip 18, 2323 (2018).

[2] E. Berthier, A. M. Dostie, U. N. Lee, J. Berthier, and A. B. Theberge, Open Microfluidic Capillary Systems, Anal. Chem. 91, 8739–8750 (2019).