Abstract
When two miscible fluids are brought into contact with each other, the concentration gradients induce stresses. These are referred to as Korteweg stresses and are analogous to interfacial tension between two immiscible fluids, thereby acting as an effective interfacial tension (EIT) in inhomogeneous miscible systems. EIT governs the formation of a viscous thread in flow-focusing of two miscible fluids. To further investigate its significance, we have studied thread formation of a colloidal dispersion focused by its own solvent. Experiments are combined with three-dimensional numerical models to systematically expand previous knowledge utilising different flow-focusing channel setups. In the reference setup, the sheath flows impinge the core flow orthogonally while in four other channel setups, the sheath flows impinge the core flow at an oblique angle that is both positive and negative with respect to the reference sheath direction. As an initial estimate of the EIT, we fit the experimentally determined thread shape in the reference setup to a master curve that depends on EIT through an effective capillary number. By numerically reproducing these experimental results, it is concluded that the estimated EIT is within 25% of the optimal EIT value that can be deduced by iteratively fitting the numerical results to the experimental measurements. Regardless of channel setups, further numerical calculations performed using the optimal EIT evaluated from the reference setup show good agreement with the experimental findings in terms of thread shapes, wetted region morphologies, and velocity flow fields. The one-to-one comparison of numerical and experimental findings unveil the crucial role of EIT on the thread detachment from the top and bottom walls of the channel, bringing useful insights to understand the physical phenomenons involved in miscible systems with a high-viscosity contrast.
Highlights
A boundary between two fluids is identifiable, irrespective of whether the fluids are immiscible or miscible
The numerical simulations performed with an immiscible fluid solver show good agreement with the experiments in terms of 3D thread shapes, wetted region morphologies, and velocity fields provided an ultralow interfacial tension is applied between the low viscosity sheath flows and the high viscosity core flow
These stresses mimic the effect of interfacial tension, and are often modeled as an effective interfacial tension (EIT), an approach chosen in the present work as well
Summary
A boundary between two fluids (here, the term fluid is used in a generic form, encompassing both molecular liquids and suspensions) is identifiable, irrespective of whether the fluids are immiscible or miscible. When two miscible fluids come into contact, a boundary between them can persist till an equilibrated homogeneous mixture have been formed due to diffusive mixing This boundary zone can act as a de facto interface with some of its properties resembling that of a distinct interface observed between immiscible fluids [1,2,3,4,5]. In 1901, Korteweg first proposed that when two nonpremixed miscible fluids are brought into contact, the composition inhomogeneties and gradients of the fluid property at the zone of contact gives rise to additional stresses (so-called Korteweg stresses) These stresses effectively mimic capillarylike stress effects [6] across the boundary zone that can be seen as a sharp de facto interface. Analogous to the interfacial tension γ in the immiscible fluids, an effective interfacial tension (EIT) for miscible fluids in nonequilibrium state, commonly denoted as e [7,8] can be written as e=K δ ,
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