Emergence of capillary waves in miscible coflowing fluids

We report the existence of capillary waves emerging at the interface between miscible liquids in viscosity-stratified microfluidic flows [1]. We find that wave propagation is dictated by interfacial stresses for fluids flowing at sufficiently high rates, where large concentration gradients characterize the liquid-liquid boundary. In contrast, dissipation dominates in an "inertial regime," where waves are more confined and a single wavenumber emerges.

The transition from the capillary to the inertial regime is generally smooth and occurs when the rate of the fastest fluid is decreased. This decrease allows diffusion to smear out interfaces, leading to vanishingly small interfacial stresses and concomitantly more confined waves. We found very good agreement between the effective tension values measured from capillary wave dispersion and a model [2] that goes beyond the known second-order gradient expansion of pressures and mixing free energy far from equilibrium [3, 4].

Our results indicate that interfacial tension in miscible molecular fluids decays much more rapidly than the temporal decay predicted by square gradient models, Γ_e​∼t^-1/2, as also suggested by previous results in static conditions [5]. Capillary waves observed in microfluidic flows of miscible liquids are a novel and unexpected phenomenon, which is proposed as a probe for tensions with unique properties, where steady wave patterns provide access to interfacial stresses over the millisecond scale after the first liquid-liquid contact.

[1] A. Carbonaro et al., Phys Rev. Lett., 134, 054001 (2025).

[2] D. Truzzolillo et al., Phys. Rev. X 6, 041057 (2016).

[3] D. Korteweg, Arch. Neerland. Sci. Exact. et Naturell. 6, 1 (1901).

[4] I. Rousar et al. Chemical Engineering Communications 129, 19 (1994).

[5] P. Cicuta et al. Applied Optics 40, 4140 (2001).