2024 AIChE Annual Meeting

(465h) Multiphase Fluidic Oscillator in a Heart-Spade Micro-Mixer

Authors

Lyes Kahouadji - Presenter, Imperial College London
Seungwon Shin, Hongik University
Jalel Chergui, LISN CNRS
Damir Juric, LISN CNRS
Omar Matar, Imperial College London
Two-phase flow in complex microchannel geometries is of central importance to various applications in natural, chemical, medical, and pharmaceutical processes. For instance, it plays a critical role in inkjet printing, DNA chips, lab-on-a-chip technology, and micro-propulsion (1; 2; 3). Moreover, the phenomenon of ”Fluidic Oscillators” has become a fascinating research topic due to their particular utility in applications where reliability and simplicity are essential, such as in fluid mixing and control systems. Fluidic oscillators produce oscillatory flow patterns despite being designed symmetrically, with boundary conditions also applied symmetrically. Most of the previous studies involving Fluidic oscillators are basically operated with only a single phase (4). In this study, we present a three-dimensional two-phase flow dynamics inside a Heart-Spade Micro-Mixer (see Fig.1) able to behave as a Multiphase Fluidic Oscillator under specific conditions, using a parallel, hybrid front-tracking/level-set solver.
Kahouadji et al (5) were able to easily construct solid objects using a module that defines them via a static distance function, thereby bypassing the need for time-consuming construction, meshing, and remeshing. This construction method combines primitive objects such as cylinders, spheres, planes, cones, and tori using simple geometrical operations. This novel and intelligent approach to construction is well-suited for popular device designs such as flow-focusing designs, T-junctions, or cross-junctions. However, for much more complex configurations, such as the one illustrated in Fig. 1, more sophisticated geometrical shapes are required. Therefore, the method illustrated in (5) has been generalized to complex three-dimensional distance functions, negative for the solid parts and positive for the fluid parts, and the geometrical contour mainly consist of the zero-iso-contour of this distance function.

The mathematical model for the two-phase flow inside the microfluidic ‘heart/spade’ micro-mixer, illustrated in Fig. 1, consists of solving the full set of the Navier-Stokes equations in a three-dimensional domain x = (x, y, z) ∈ [0, 19.125] × [0, 6.12] × [0, 0.37] mm3 using the projection method where temporal discretisation follows the second-order Gear scheme. The computational domain is discretised with a uniform fixed 3-D finite-
difference mesh (1600 × 512 × 32) following the procedure of standard staggered MAC cell arrangement. All three components of the velocity field are defined on the corresponding cell faces while the pressure field, considered here as a scalar variable, is located at the cell centres, and all spatial derivatives are approximated by second-order central differences. Finally, the treatment of the interface relies on our high-fidelity hybrid front-tracking/level-set method, which uses a Lagrangian triangle interface mesh. Figure 1 depicts various flow regimes. For instance, a fast dripping regime occurs at (Qc, Qd) = (4, 0.5) mL/min, described as regular and quasi-symmetric, where the capillary pinching phenomenon occurs behind the C-shaped barrier. At (Qc, Qd) = (5, 1.5) mL/min, an irregular and non-symmetrical capillary pinching effect manifests itself far downstream after passing the C-shaped barrier. At (Qc, Qd) = (1, 2) mL/min, a Multiphase Fluidic Oscillator finally occurs. This oscillatory behaviour results from a slight delay in symmetrical interfacial breakup events occurring behind the C-shaped barrier, ultimately leading to simultaneous oscillation and pinching. This is the first observation of such oscillatory behaviour in a multiphase and microscale flow. A more laminar and
parallel regime is observed for (Qc, Qd) = (3, 1) mL/min, and the Multiphase Fluidic Oscillator regime can be described as a transition towards regimes that exhibit complex dynamics.
The vortical structures highlighted in Figure 1 (right panel) depict interesting closed recirculating zones that typically trap satellite droplets. Due to differences in flow rates between the continuous and dispersed phases, we can also observe vortical structures reminiscent of Kelvin-Helmholtz instabilities. As droplets form in the initial cell of the channel with some undergoing coalesce before entering the converging section of the cell.
An in-depth discussion of the flow dynamics associated with the Heart-Spade micro-mixer will be provided during the presentation.
Acknowledgements
This work is supported by the Engineering and Physical Sciences Research Council, United Kingdom, through the EPSRC PREMIERE (EP/T000414/1) Programme Grant.O.K.M. acknowledges the Royal Academy of Engineering for a Research Chair in Multiphase Fluid Dynamics. We also acknowledge the HPC facilities provided by the Research Computing Service (RCS) of Imperial College London. D.J. and J.C. acknowledge support through computing time at the Institut du Developpement et des Ressources en Informatique Scientifique (IDRIS) of the Centre National de la Recherche Scientifique (CNRS), coordinated by GENCI (Grand Equipement National de Calcul Intensif) Grant 2022 A0122B06721.
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